Research Article Modeling of RFID-Enabled Real-Time ...

Research ArticleModeling of RFID-Enabled Real-Time Manufacturing ExecutionSystem in Mixed-Model Assembly Lines

Zhixin Yang1 Wei Xu2 Pak-Kin Wong1 and Xianbo Wang1

1 Department of Electromechanical Engineering Faculty of Science and Technology University of Macau Macau2 School of Management Henan University of Science and Technology Luoyang 471000 China

Correspondence should be addressed to Zhixin Yang zxyangumacmo

Received 7 May 2014 Revised 9 July 2014 Accepted 14 July 2014

Academic Editor Qingsong Xu

Copyright copy 2015 Zhixin Yang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To quickly respond to the diverse product demands mixed-model assembly lines are well adopted in discrete manufacturingindustries Besides the complexity in material distribution mixed-model assembly involves a variety of components differentprocess plans and fast production changes which greatly increase the difficulty for agile production management Aimingat breaking through the bottlenecks in existing production management a novel RFID-enabled manufacturing executionsystem (MES) which is featured with real-time and wireless information interaction capability is proposed to identify variousmanufacturing objects including WIPs tools and operators etc and to trace their movements throughout the productionprocesses However being subject to the constraints in terms of safety stock machine assignment setup and schedulingrequirements the optimization of RFID-enabledMESmodel for production planning and scheduling issues is a NP-hard problemA new heuristical generalized Lagrangian decomposition approach has been proposed for model optimization which decomposesthe model into three subproblems computation of optimal configuration of RFID senor networks optimization of productionplanning subjected to machine setup cost and safety stock constraints and optimization of scheduling for minimized overtimeRFID signal processing methods that could solve unreliable redundant and missing tag events are also described in detail Themodel validity is discussed through algorithm analysis and verified through numerical simulationThe proposed design scheme hasimportant reference value for the applications of RFID in multiple manufacturing fields and also lays a vital research foundationto leverage digital and networked manufacturing system towards intelligence

1 Introduction

In recent years with the development of information tech-nology and advanced manufacturing technology modernmanufacturing industries have changed greatly to matchfierce global competition The development trends includeincreased personalization diversified product demandsgradually shortening product life cycle and increasing deliv-ery requirements from customers which make shop-floormanagement be crucial in the whole manufacturing systemTo quickly respond to the diverse product demands in termsofmultiple product types and different delivery timesmixed-model assembly lines as a flexible production mode arewell adopted in discrete manufacturing industries Com-pared with single mass production mixed-model assemblyproduction needs to handle complex material distribution

Mixed-model assembly involves a variety of parts com-plex processes and fast production changes which greatlyincrease the difficulty for agile production management Theworkstations used process sequences and operating timevary according to different products that are fed into themixed-model assembly linesThe productionmanagement ofshop-floor with mixed-model assembly lines faces challengesto reach agility when information among manufacturingobjects could not be acquired and processed to generate inter-active means in real-time Although many enterprises haveadopted ERP or MRP for leveraging production manage-ment however in dynamic shop-floor environment mate-rials can hardly be distributed accurately and sequentiallydue to the lack of real-time production status trackingMeanwhile unpredictable and fast changingmarket demandsrequire manufacturing enterprises to have quick response

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 575402 15 pageshttpdxdoiorg1011552015575402

2 Mathematical Problems in Engineering

ability which however is usually insufficient in the currentlyavailable production line modeling and simulation softwarepackages The performance of manufacturing process agilityis a major determinant of whether or not enterprises couldprocess manufacturing events quickly respond to dynamicdemands of market customers robustly build dynamicalliances efficiently with partners for increasing innovativecapabilities and eventually win in global competitionThere-fore aiming at breaking through the development bottle-necks in existing production management a novel manu-facturing execution system (MES) which is featured withreal-time and active information interaction technologies isurgently required to be deployed in mixed-model assemblyshop-floor through innovative production organization andmanagement model

Meanwhile RFID (Radio Frequency Identification) tech-nology has been increasingly realized as a promising infor-mation interaction tool and has been widely used in manu-facturing industries to conduct real-time monitoring of largeamount of site data Owing to the intrinsic properties of RFIDtechnology including large information storage capacity abil-ity to simultaneously identify multiple tags in one momentand noncontact recognition it enables a fundamental changein the ways to control industry process especially in fieldsof manufacturing and logistics supply chain Potential benefitand influence of RFID technology onmanufacturing industryinclude increasing the visibility and accuracy of informationreal-time production control improving the flexibility ofproduction planning and scheduling tracking productionrelated objects (such as Work-In-Process (WIP) worksta-tions and workers) tracking the utilization rate of reusableassets (such as containers tools and removable equipment)effective maintenance management inventory control ofraw materials and finished products cost reduction andimproving customer satisfaction level [1 2] Therefore RFIDis an attractive technology for fitting real-time requirementsin terms of data acquisition and process control in modernmanufacturing system However existing researches on theapplication of RFID technologymainly focus on how to buildcorresponding RFID application systems individually In theopen literature the theoretical model regarding the optimalconfiguration and framework integration of RFID sensornetworks in various applications are still lacking a unifiedand detailed study Many systematic researches are based onthe assumption that the acquisition system underlying RFIDcould meet specific application environment by generatingsignal in ideal status while in fact RFID system may outputunreliable data Few researchers addressed how to optimizeRFID system performance to reduce the influence of noisefactors and guarantee system stability in specific applicationenvironment This paper adopts RFID equipment the highcaliber wireless communication tool for real-time infor-mation acquisition and processing in complex productionsystem towards real-time MES The relevant model config-uration data purifying and optimization issues are thereforeworth being studied in this paper

The remainder of this paper is organized as follows Inthe following section relevant works related to this studywill be reviewed The system architecture model analysis

for optimization of system configuration and productionplanning and scheduling are described in Section 3 In addi-tion the reliability of RFID data processing and generalizedLagrangian decomposing approach are presented in Sections4 and 5 respectively The algorithm analysis and modelvalidity are examined in Section 6 Finally a summary ofmodeling methodology together with a discussion on thedirections for future research is made

2 Literature Review

To study a real-time MES model for complex productmanufacturing system the study involves research efforts intwo subareas wireless technique for information acquisitionand optimization of production planning and schedulingCorrespondingly this section reviews the applications ofRFID for real-time information acquisition and facility mon-itoring in manufacturing execution system and also givesa brief summary on production planning and schedulingoptimization studies of manufacturing system

21 RFID-Enabled Real-Time MES Researches on the appli-cation of RFID in manufacturing process control mainlyaddressed the following three aspects determination of spe-cific application fields and functions of RFID technology pro-cess control of RFID system and RFID system integrationCurrentlymany scholars begin to focus onRFID applicationsin manufacturing workshops to strengthen production pro-cess management by effectively improving the transparencyof manufacturing workshop [3ndash5]

The automatic control problem in production processcould be solved using RFID technology [6] A RFID basedintelligent product was proposed to make products haveautomatic information interaction accurate information andreal-time acquisition ability and thus support workshopproduction decisions and automatic control Based on thecharacteristic comparison of RFID and barcode technologyRFID was selected to manufacture control system basedon programmable logic controller The control system wascombined with multi-agent technology as information inter-action media between RFID equipment and other agents[7] A manufacturing system framework based on RFID wastherefore built Huangrsquos group [8ndash10] proposed the concept ofrealizing JIT through wireless manufacturing (WM) technol-ogy whereWMcollected real-timemanufacturing workshopsite information by fully relying on wireless devices such asRFID Auto ID sensor or wireless information network Theapplication of RFID in remote monitoring in enterprise pro-ductionmanagement was reported [11] which could improvethe efficiency of production process by readapting IT systemand reduce human errors via applying RFID technology Anew device based on RFID technology has been reportedto strengthen information exchange among workshops andinformation system optimization throughout the whole fac-tory [5] Another effort on system design using RFID couldassist grinding apparatus production when combined withERP system [12] It was also reported to apply such combinedsystem for logistics control of integrated circuit assembly

Mathematical Problems in Engineering 3

industry in order to improve production efficiency [13] Withrespect to production control problem of flexible assemblyline a production control mathematic model based on RFIDreal-time data collection was built [14] which could be usedfor designing an intelligent production control decision sup-port system Chen and Tu [15] put forward a manufacturingcontrol and collaboration system based on multi-agent andapplied RFID to real-timemanufacturing workshop tomoni-tor and control dynamic production process for improvementof visual tracking ability of product customization of a largenumber of customers Risk management system based onRFID technology in manufacturing industry was analyzedwhich could not only identify potential risks in productionbut also propose relevant solutions to control risks [16 17]Huang et al [18] appliedWM concept to workshop real-timemanagement of work in process workshop adaptive assemblyplanning and control and fixed worker mobile assemblymanagement of working points More recently Huang etal [19] employed RFID technology and wireless networkcommunication technology (such as Bluetooth and Zigbee)in manufacturing workshop and proposed an advancedwireless manufacturingmodel via building andmanipulatingsmart workshop objects

22 Production Planning and Scheduling Production plan-ning and scheduling integrated optimization problem canbe solved by three categories of strategies (1) layered serialsolution (2) layered iteration solution and (3) full space solu-tion Production planning and scheduling belong to differentdecision layers in manufacturing system respectively Whilethey are closely related the decisions made on productionplanning layer are treated as optimized constraining condi-tions for the optimization computing in schedule layer andvice versa Researchworks on solving strategies of productionplanning and scheduling integrated optimization model aresummarized in Table 1

3 Model Analysis

31 Model Framework In modern industries such as auto-motive and mobile phone makers mixed-model assemblylines are typical configuration where a set of workpieces willbe assigned on different workstations and be transportedalong correspondingly different assembly lines This paperassumes that the workshop has 119872 sets of machines withdifferent stamping processing capacity119872 = 1 119872119898 ismachine index and119898 isin 119872 Each machine is installed with aRFID information collection sensor that is the RFID readersfor relatively fixed manufacturing resources (such as man-ufacturing equipment) and RFID tags for relatively movingmanufacturing resources (such as manufacturing workerscontainers for loading materials and key components andparts) are deployed in the system When those moving tagsthat aremounted onmanufacturing objects fall into the activeidentification range of their nearby readers tags informationcan be automatically acquired in real-timeThroughmappingmechanism the attached manufacturing resources couldthen be identified for dynamic control It is planned to

produce 119873 types of workpieces in a period consisting of 119879production cycles where 119879 = 1 119879 119873 = 1 119873In addition 119894 119895 are workpiece indexes where 119894 119895 = 1 119873V 119908 are product process index where V 119908 = 1 119899

119894 Each

workpiece 119894 contains 119899119894processes 119899

119894= 1 119899

119894 (119894 V)

is the Vth working process of workpiece 119894 we also assumethat multiple machines can complete each processing plansimultaneously In cycle 119905 (119905 isin 119879) the demand of workpiece119894 is known to be 119889

119894119905 Reasonable production planning and

scheduling are required to be conducted so as to ensure allof the production tasks in each cycle can be completed andprocessing time can be extended within appropriate ranger

The RFID configuration in sensing network for infor-mation collection in mixed-model assembly manufacturingis complex The optimization of such configuration mainlyaims at minimizing RFID total costs while meeting theobjective of detecting 119870 collection capacity and collectionaccuracy through 119872 RFID equipment corresponding tomanufacturing resources configuration In addition the keyof production planning is to formulate production capacity119883119894119905of various workpieces so as to minimize the total cost

of production cost inventory cost and shortage penalty costProduction scheduling is to assign machines for each typeof products and to determine product process sequence ofeach piece of equipment The start and completion time ofeach workpiece in one machine could be computed whichmay require workers to work overtime in some machinesFor minimizing the total cost that includes machine setupcost and overhead the interacting production planning andscheduling processes will be optimized in an integratedmanner that covers all relevant cost while ensuring feasiblescheduling

It is well known that setup process often involves dieand mold changes changes of tools or workpieces and thecorresponding calibration and so forth which usually takecertain significant time during a planning cycle For theexample of stamping process the stamping part with differentsetup requirements may be produced insufficiently and thusbe unable tomeet the demands from the downstreamweldingworkshop Meanwhile as product demands are dynamicallychanged for fitting urgent orders or emergency weldingworkshop will increase the demand for stamped parts Tocopewith such case certain level of inventory controlmethodwill be explored typically how to set the safety stockGenerally safety stock is a rigid requirement and is treated asa constraint However this requirement cannot be met underlimited production capacity Therefore safety stock can betreated as an objective for fulfilling instead of a constraintIf the safety stock level cannot be satisfied penalty cost willbe incurred accordingly

32 Notations and Assumption 119868119894119905(119868119894119905ge 0) is used to denote

the inventory of product 119894 at the end of production cycle119905 If it is greater than the specified safety stock value 119877119868

119894119905

that is 119868119894119905ge 119877119868119894119905 then the exceeded parts are called excess

safety stock which is denoted as 119878119868+119894119905

(ie if 119868119894119905ge 119877119868

119894119905

119878119868+119894119905= max119868

119894119905minus 119877119868119894119905 0) If the inventory is smaller than

119877119868119894119905 119868119894119905le 119877119868119894119905 then the insufficient part is called shortfall


Table 1 Brief summary of solving strategies for production planning and scheduling optimization

Literature works Research domain and approach

[20 21] Decomposing according to the structure of integrated modeliterative standard mathematical programming approach

[22ndash24] Decomposing according to the structure of integrated modelLaplace relaxation decomposition approach

[25ndash28] Solve production planning problem under total capacity constraintensure the feasibility of scheduling layer

[29] Single-stage continuous multiproducts workshopsimultaneous optimization of production planning and scheduling

[30] Pharmaceutical industry layered iterative solutionmultiscale planning and scheduling model

[31] Production planning and scheduling integrated optimization problemstandard mathematical programming approach

[32] Operating workshop linear programming solutionproduction planning and scheduling integrated optimization

[33] Single-stage production system linear programming solutionbatch determination and scheduling sequence optimization model

safety stock which is denoted as 119878119868minus119894119905

(ie if 119868119894119905le 119877119868

119894119905

119878119868minus119894119905= max119877119868

119894119905minus 119868119894119905 0) Therefore the inventory status of

one product 119894 is composed of specified safety stock119877119868119894119905 safety

stock excess 119878119868+119894119905 and safety stock shortfall 119878119868minus

119894119905which could

be denoted as 119868119894119905= 119877119868119894119905+ 119878119868+119894119905minus 119878119868minus119894119905 The unit penalty costs

for safety stock shortfall and excess of product 119894 in productioncycle 119905 are represented using variables119862ℎminus

119894119905119862ℎ+119894119905 respectively

and meet the condition of 119862ℎminus119894119905gt 119862ℎ+

119894119905 The summary of

notations is used in this paper (see Notation)

33 Optimal Configuration of RFID Equipment To leveragewireless application in mixed-model assembly manufactur-ing environment identifying physical objects and tracingtheir movement throughout the production processes will beone of the fundamental supporting factors Targeted objectsare stuck or embedded with RFID tags which are visible andtraceable by those nearby physical readers that are deployedat some key control points The identified physical objectsbecome intelligent via dynamic information feedback andsharing capability provided by RFID facilities Each uniqueRFID tag is mounted with one individual object When onetag falls into the identification range of the active readersthese active readers will execute simple link layer protocolto retrieve the object identification information embeddedin the identified tag However due to the characteristicsof frequency identification wireless communication and theinfluence of complex application environment in mixed-model assembly manufacturing workshop it suffers fromreceiving repeated readings of tags missing reading of tagsand redundant objects data whenmultiple tags are associatedwith it Consequently the raw RFID data flow is unreliablein terms of data redundancy and incompleteness which inturn results in difficulties for rational downstream applica-tions and also limits its application feasibility Therefore themixed-model assemblymanufacturing environment requiresproper configuration of RFID equipment prior to data col-lection and analysis which is essential for effective system

monitoring The schematic diagram of RFID based real-timemanufacturing information in physical workshop operationsystem is shown in Figure 1

The nature of production monitoring techniques is toinfer whether the manufacturing objects under tracking arein a specific ldquostaterdquo ldquoeventrdquo or matching certain ldquorulesrdquoaccording to basic object information such as time spaceand interrelationship A real-time MES monitoring systemrequires synthesising all the relevant information relatedto those selected objects for monitoring and will ignorethe other objects and system noise To sum up there arelots of objects that can be monitored in any productionenvironment while it is neither practical nor necessary toimplement full monitoring for all of them For example theobjects under tracking could be selective and only thosehigh-value parts or staffs materials and equipment locatedin key regions are included When designing the modelconfiguration of production monitoring schemes ldquocost per-formancerdquo of monitoring tasks will be adopted as the primaryindicator for determination of whether the targeting objectsdata collectionmethods and relevant processing technologiesshall be applied or not

RFID devices are used to track manufacturing objects bymeans of reading and writing radio signals without physicalor optical contact with the objects to be identified The tech-nology mainly consists of two types of sensor mechanismsPassive sensors are not equipped with internal battery whichabsorb and convert energy from RFID reader Comparablyactive sensors send signals by internal power which canmeasure multiple types of sensors such as temperaturepressure and motion sensors Which sensor is optimal forthe real-time manufacturing process It mainly depends onthe workshop physical operating environment Active sensoris suitable for trackingmoving objects in a wide area whereasit is a viable choice for passive sensor to identify informationin nearby field In this paper RFID active and passive tags areassumed to be attached to single component or whole batch


RFID complex eventRFID readerprocessingdetecting basic event

RFID readerA

RFID readerB

Items identified by RFID tags

Processing time

Package with Physical packagingRFID tags

middot middot middot

Figure 1 Schematic diagram of RFID based real-time MES in physical workshop environment

package With respect to RFID equipment configurationregarding sensor network for manufacturing informationacquisition in MES the following mathematical model canbe used for computing the optimal configuration

Min1198851=

119872

sum119894=1

cost (ActiveSensor 119894)

+

119873

sum119895=1

cost (PassiveSensor 119895)

(1205941 120594

119870) isin (120594Sensor 1 120594Sensor 119872+119873)

(1205931 120593


radic(119883Sensor Ψ minus 119883119894)2+ (119884Sensor Ψ minus 119884119894)

2+ (119885Sensor Ψ minus 119885119894)

2

le Θ119894

SensorΨ=

ActiveSensor 119894 (Ψ = 119894) 119894 isin [1119872]

PassiveSensor 119895 (Ψ = 119895) 119895 isin [1119873]

Ψ isin [1119872 + 119873]

(1)

where the objective function is for 119870 number of RFID dataacquisitions to be detected to minimize total costs whilemeeting the objective of detecting119870 acquisition quantity andaccuracy through119872+119873 sensing equipment (ActiveSensor 119894and PassiveSensor 119895) and accessory equipment correspond-ing tomanufacturing resource configurationThe constraintsare to ensure that the selected sensing equipment could meet119870 number of RFID acquisitions (120594

1 120594

119870) and acquisition

accuracy (1205931 120593

119870) respectively as well as to ensure the

reliability of sensor equipment configuration that is the

distances between the installation location of the selectedsensing equipment (119883Sensor Ψ 119884Sensor Ψ 119885Sensor Ψ) and work-ing position of effective Reader

119894(119883119894 119884119894 119885119894) are within the

farthest sensor identification range

34 Optimization of Production Planning Production plan-ning is for enterprises to make a series of decisions regardingproduction rate inventory and shortage quantity and soforth for various products under the constraint of productioncapacity The optimization of production planning aims atminimizing total expenses of the above decisions where theproduction objectives and inventory level in each produc-tion cycle form control parameters Generally productionplanning and scheduling are formulated in sequence thatis generating production planning first and then specifyingscheduling based on such planning result The main draw-back of formulating production planning and schedulingby hierarchical approach is that information in detailedscheduling layer is not taken into account when formulatingproduction planning The resulted scheduling thus tends tobe infeasible that is to say decisions made according tothe planning layer may cause infeasible scheduling There-fore machine setup time which is used for adjusting themachine configuration according to mixed-model assemblyworkshops processes will be estimated for production batchoptimization In this paper machine setup is set as variable120572119898119905

119894V the production planning model could be determinedusing the formula where the minimum overall productionexpense is adopted as the objective function

Min1198852=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119905119878119868+

119894119905+ 119862ℎminus

119894119905119878119868minus

119894119905+ 119862119901119894119905119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

(2)


The main expense in this model is composed of penaltycost of safety stock excess penalty cost of safety stockshortfall production expenses shortage cost and productionpreparation cost The constraint conditions are given by

INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+

119873times119879 119910119894119905isin 0 1 forall119894 119905 (10)

where constraints (3) and (4) express materials balance equa-tions Formula (5) is production capacity constraint where120572119898119905119894V is a constant 1205961015840 represents coefficient of production

capacity and 1205961015840 = 1 if it is not allowed to work overtimeotherwise 1205961015840 gt 1 Constraints (6) and (7) give formulasto calculate safety stock excess and safety stock shortfallrespectively Constraint (8) represents upper limit and lowerlimit of production batch Constraints (9) and (10) restrict theupper limits of safety stock shortfall and workpiece shortagequantity

35 Optimization of Production Scheduling Production plan-ning and scheduling which are the twomost important tasksin manufacturing production and operation managementare closely related to each other and significantly influenceprofits gaining resource utilization efficiency and punctualproduct delivery Solutions of production planning (produc-tion objectives) are the input conditions for scheduling prob-lemsMeanwhile production capacity constraints involved inproduction planning problems are often related to schedulingsolutions

The main task of production scheduling is to makemachines assignment decision and to specify the sequenceof production processes in each production cycle formulatedin production planning It could thus determine the startand completion time of each product in every working pro-cedure on corresponding machines Currently the key thatseriously hinders classical scheduling theoretical researchesfrommakingmajor progress and breakthroughs is NP natureof scheduling problem The actual scheduling problems arealways very complex without certain rules to follow andexact solutions are difficult to be obtained within limitedtime Applying the classical scheduling theory based analyticoptimization to actual scheduling problems that belong toNP-hard problems will inevitably encounter such obstacles

The scheduling problem we are handling is with deliveryconstraint which assigns machines based on the minimumprocessing time for each process andmachine load condition

according to processing schedule from top to bottom Sincesuch NP-hard scheduling problem cannot find an overallexact solution directly we propose to partially fix the solvedbatch planning result as a basis and use it to solve schedulingproblem Such method could finally get a near optimalsolution through limited iterations When the value of pro-duction batch119883

119894119905is known variables119883

119894119905 119910119894119905in the following

constraints are knownThen production schedulingmodel isas follows

Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)

Formula (11) takes minimum setup cost in terms of dieand mold change calibration cost and overtime cost asobjective functionsThe corresponding constraint conditionsare given by

120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119894V 119898 isin 119872 (119894 V) V isin 119899119894 forall119894 119905 (19)

sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)

where constraint (12) expresses that working procedure canonly be processed on the allowed machines Formulas (13)and (14) are processing sequence constraints of the sameworkpiece respectively Constraints (15) and (16) mean pro-duction adjustment and processing work which can onlycomplete at most one working procedure at the same time onany one machine in the same period respectively Constraint(17) shows that each process can only be processed on onemachine when producing products Constraints (18) and (19)emphasize that each working procedure has one immediatepredecessor activity and one immediate successor activityConstraints (20)ndash(23) denote that virtual working procedurecan only be processed firstly and lastly on each machineConstraint (24) gives an approach to calculate completiontime of eachmachine Formula (25) indicates that completiontime of eachmachine cannot exceed the available time whichensures feasibility of scheduling and constraint (26) remarksthe overtime limit

4 Reliability of RFID Data Processing

The ability to track real-time manufacturing informationof workshop physical operating environment is the key forachieving agile production management RFID technology isa promising technology to acquire real-time manufacturingfeedback information However data acquisition using RFIDtechnology in complex manufacturing environment mayencounter redundant or missing readings and signal fluctua-tion due to obstacles and noise Consequently a large amountof unreliable data flowwill be output to the downstreamMESapplications Therefore how to process RFID events so as toprovide reliable and meaningful real application informationfor downstream applications is the key technical issue thatwill be solved for successful application of RFID

This paper proposes a hierarchical data processing modelto improve RFID system application reliability in multitagand multireader mixed-model manufacturing system appli-cation environment It could clean and compensate unreliabledata and solve RFID abnormal reading phenomena fromthe perspective of system application so as to improve sys-tem identification rate and reliability level Data processingmodel uses a hierarchical structure which is composed ofRFID equipment network layer basic event processing layercomplex event processing layer and application layer asshown in Figure 2 RFID equipment network generates basicevents using a set of multiple types of readers that receivesignal from neighbouring tags Redundant RFID basic eventscaused by repeated reading could be filtered out and formsimplified logical reading events Complex event processinglayer receives logical reading events uploaded by basic eventprocessing layer It could analyze and classify logical readingevents based on default application integrity constraint rulesthen be able to detect abnormal reading and perform clean-up operations on received unreliable data Such data processmodule will ensure the system integrity provide meaningful

application data and output reliable interrelated informationamong tags and their associated objects such as interdistanceand moving directions for agile production managementapplications in the application layer

41 RFID Basic Event Processing Plenty of data recordingsignals fired by tags will be sent out by the distributed logicalcontrol point reader network as input for the basic event pro-cessing layer The distributed deployment in logical controlpoints and its structure consists of distributed physical readeradapter RFID basic event queue tag event filter logicalreading event filter object event queue and logical mappingengine as shown in Figure 3 The logical mapping enginestores the mapping relations between one identified tag andits corresponding physical object

Reader adapter first collects raw data generated by corre-sponding physical readers and forms RFID basic events foruploading into tag event filter which cleans redundant taginformation collected by multiple readers according to theunique tag logical matching mechanism

In multitag and multireader application schemes morethan one tag event in RFID basic event queue may be pointedto one physical object In other words RFID basic eventsmay contain repeated records for single physical objectLogical reading event filter will filter out duplicated objectevents according to logical mapping engine via following theprinciple of not allowing repeated physical object event ineach logical control point Finally each object and its solelyassociated tag event are stored in the object event queue andwill be uploaded into the correlated logical control point forfurther processing in the complex event processing module

42 RFID Complex Event Processing Although basic eventlayer could clean repeated and redundant data in logicalcontrol points and eliminate duplicated tag reading bymultiple readers it does not deal with unreliability causedby redundant and missing reading of tags Complex eventprocessing layer will be followed to improve the reliability ofRFID system application through detecting and correctingredundant data according to RFID application integrityconstraint rules Integrity constraints are based on differentperspectives such as weight location and motion pathsof tag and of course their associative identified physicalobjects The constraints could also be based on mutual rela-tions among different objects such as inclusion and exclusionrelationshipsThe structure of complex event processing layeris shown in Figure 4 whichmainly consists ofmanufacturingobject information base integrity constraint rules base eventclassification engine normal event processor redundantreading processor and missing reading processor Integrityconstraint rules are the fundamental rules and are set as thedefault constraint in initial condition

In manufacturing system some identified physicalobjects tend to move along predetermined routes todestinations such asWIP in production lines and warehouseproducts When the detected actual route is different fromthe pre-specified one it can report that physical objecthas encountered unreliable reading phenomena at some


Figure 2 Data processing model structure of RFID manufacturing information system reliability

logical control points So redundant and missed read-writephenomena are extracted using management informationbase that records motion routes of physical objects Theassociated relationship between objects and schema is alsoutilized

5 Generalized LagrangianDecomposition Approach

The model described above contains RFID optimal config-uration production planning and scheduling optimizationwhich belongs to a typical NP-hard problem Although noexact solution could be found within the limited time thispaper proposes to solve the problemusing a novel Lagrangiandecomposition approach By introducing three groups of newconstraints and setting 120594(119911) = 1 if 119911 gt 0 and 120594(119911) = 0otherwise the overall objective function can be shown asfollows

Min119885 = Min1198851+Min119885

2+Min119885

3 (28)

The new constraints for integrated optimization modelinclude the following

119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)


Logical reading event filter

Object event queue

Logical mapping engine

RFID basic event queue

Tag event filter

RFID basic event

Tag


Tag event filter

Readerl Readeri Readern

Reader adapterl

Reader adapterk

middot middot middotmiddot middot middot


middot middot middot middot middot middotLogical control pointl

Logical control pointk Logical control point

N+

RFID basic event

Figure 3 Structure of RFID basic event processing layer

Agile production management application

Application interface

Event processor

Event classification engine

Logic control point

Redundant read-write processor

Missing read processor

Logic control point

Logic control point

Logic reading event Logic reading event

Management information

base

Integrity constraints


Figure 4 Structure of RFID complex event processing layer


where 119876119894119905 120573119898119905119894V as specified in constraints (29) and (30)

are artificial variables that connect production planning andscheduling Constraint (31) determines whether product 119894 isproduced in cycle 119905 and ensures that production preparationis carried out only when certain kinds of products are deter-mined to be processed In order to use Lagrangian algorithmwhich carries out computing the variables in productionplanning and scheduling will be transferred and coordinatedin each time of Lagrangian iteration cycle The variables119876119894119905 119910119894119905

in scheduling problem are set to be the corre-sponding output values119883

119894119905 119910119894119905 computed in the production

planning process Similarly variable 120572119898119905119894V of machine setup

in scheduling problem is assigned as 120573119898119894

used in planningproblem In order to decompose and coordinate planningand scheduling constraints (32) and (34) are followed inLagrangian treatment of planning subproblem where 120573119898119905

119894V isa constant

Formulas (33) (35) and (36) will be used in schedul-ing subproblem of Lagrangian approach (119876

119894119905and 119910

119894119905are

treated as constants) Constraint (33) shows that process-ing machines are assigned only when there is productiondemand that is 119910

119894119905= 1 We introduce Lagrangian multi-

pliers 120583 = 120583119894119905 V = V119898119905

119894V 119894 isin 119873 V isin 119899119894 119898 isin 119872 119905 isin 119879

and 120579 = (120583 V) Lagrangian multipliers 120583119894119905 V119898119905119894V correspond to

the artificial variables 119876119894119905and 120573119898

119894 which will be considered

as shadow prices 120583119894119905can be interpreted as profits obtained

by selling unit production capacity and resources and V119898119905119894V is

profits gained by enterprises leasing equipmentLagrangian multipliers 120583 = 120583

119894119905 V = V119898119905

119894V areused in the objective function to relax the constraints thecorresponding relaxation model is then given by

119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)

Note that this model in fact cannot be decomposedinto mutually independent subproblems of planning andscheduling and thus this problem cannot be solved by

being decomposed into a series of subproblems by standardLagrangian decomposition approach However approximatesolution of this problem can be obtained by a generalizedLagrangian decomposition approach That is to say thisproblem is decomposed into two subproblems involvingproduction plan problem assigned by fixed machines andproduction scheduling problem with fixed volume andthen is solved by alternating iterations This generalizedLagrangian decomposition approach can be seen as a com-bination of standard Lagrangian approach with Gauss-Seideliterative principle In previous literature the establishedaggregate production planning model is decomposed intolabor model and production planning model when studyingproduction batch planning problem of labor-constrainedproduction system However these two subproblems are notindependent and production planning model involves twovariables namely production batch and labor force amongwhich quantity variable of labor is related to variables inlabor subproblem Besides when solving inventory routingproblem by Lagrangian this problem is decomposed intoinventory problem and routing problem Vehicle distribu-tion route is fixed when solving inventory problem whileinventory variable is seen as a constant when optimizingdistribution vehicle routes Therefore these are essentiallygeneralized Lagrangian decomposition approach

We can set 119909 = (119878119868+ 119878119868minus 119883 119871 119910) and 120587 = (120572 120575 119861 119862) asdecision variables of batch production plan and schedulingsubproblem respectively and denote 119885

2(119909 | 120579 120573) as

relaxation production planning problem with fixed machineassignment 120573 as 120573 and 119885

3(120587 | 120579 119876) as relaxation scheduling

subproblem with fixed production batch 119876 as 119876 Machineassignment variable 120573119898119905

119894V can be fixed as constant 120573119898119905

119894V Ineach time of iteration of Lagrangian algorithm take the valueof constant 120573

119898119905

119894V in production planning as constant 120575119898119905

119894V119895119908that is fix the sequencing results of scheduling subproblemin last iteration and substitute 120573

119898119905

119894V and 120575119898119905

119894V119895119908 into originalconstraint formula Thus we can get Lagrangian model ofproduction planning subproblem specifically as follows

1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)

Formula (41) is production capacity constraint with fixedmachine assignment variable and the remaining formulas areproduction batch constraints after fixing machine process-ing sequence aiming at completing formulated productionplanning in prescribed production cycle that is ensuring thatthe obtained planning is feasible It is worth pointing outthat for overtime variable 119874

119898of each cycle in Lagrangian

production planningmodel 119905 is substituted by the maximumavailable overtime and this change does not affect solutionto the objective function because in the optimal solution thebatch planning ensures obtaining feasible scheduling whilespecific overtime is determined by Lagrangian schedulingsubproblem Here we denote variable 119876

119894119905in the above con-

straints as constant 119876119894119905and reach constraints of Lagrangian

scheduling subproblem During the running of Lagrangianalgorithm for each time of iteration119876

119894119905takes batch value119883

119894119905

obtained in last iteration in production planning Lagrangianscheduling model is specifically given by

1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)

With a given batch planning Lagrangian relaxationscheduling problem (LRSP) is a scheduling problem withdelivery constraint and is solved by hierarchical approachin this paper Firstly an improved localization approach isdesigned to determine machine assignment problem andassigns machines for operating process with machine loadconditions The main idea is to form a processing schedulefirstly by lining up processes of all workpieces (the same

workpieces are not separated when lining up and workpiecesare lined up according to workpiece number) and thenassign machines based on the minimum processing timeof each process and machine load conditions accordingto processing schedule from top to bottom However theassignment results rely on workpiece arrangement locationsReferences [34 35] improve this method that is select-ing two workpieces randomly and exchanging locations ofboth workpieces in the schedule This paper makes furtherimprovement that is machines are not required to beassigned for processes in strict accordance with sequencespecified in schedule An unassigned process could be ran-domly selected each time (select from processes that havenot been assigned with machines and have the minimumnumber of processes) and be assigned with a machine for itaccording to theminimumprocessing time andmachine loadconditions

6 Algorithms and Numerical Simulations

61 RFID Data Processing Algorithm in MES

Definition 1 At time 120591 all tags within the identificationrange of physical readers are detected and data interaction isconducted onceThat is to say physical readers detect the tagsthat generate just one RFID basic event 119890 at time 120591 Generallydata generated by RFID basic event can be expressed by triple119901119890 = (119901119903 119890119901119888 120591) where 119901119903 is a physical reader identifier 119890119901119888is a tag identifier 120591 is the time of event and 119901119890 denotes anexample of RFID basic event

The above definition is used for Algorithm 1In consideration of physical object route constraint

119877(119871119875 119860) where logical control points are corresponding to119897119901 isin 119871119875 possible routes of physical object among logicalcontrol points are corresponding to 119886 isin 119860 Physical objectmoves along the prespecified routes ⟨119897119901

1 119897119901

119898⟩ which are

called default object routes To judge sequence relationshipof logical control points on object routes the followingdefinition is given

Definition 2 For any two logical control points 119897119901119894and 119897119901

119895

if 119897119901119894is in front of 119897119901

119895 then physical object passes 119897119901

119894first and

then 119897119901119895 and 119897119901

119894lt 119897119901119895 If logical reading event 119897119890

119896= (119897119901119896 119900119896 120591)

is currently received redundant reading and reading leakphenomena of physical objects can be determined by thefollowing method

Search for physical object that will pass in default routesin logical control point 119897119901pre If 119897119901pre = 119897119901119896 physical objectis identified in normal status if 119897119901pre lt 119897119901119896 it is redundantreading phenomenon otherwise if 119897119901pre gt 119897119901119896 physical objecthas reading leak phenomenon at all logical control points119897119901leak will be positioned in between 119897119901

119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901

119896 119897119901pre 119897119901119895⟩ The relationship 119897119901

119896lt

119897119901leak lt 119897119901pre or 119897119901119896 = 119897119901leak will be held

According to the above definition RFID complex eventprocessing algorithm can be obtained as in Algorithm 2


Step 1 Receive RFID basic reading events 1199011198901= (119901119903

1 1198901199011198881 120591) generated by physical readers

Step 2 Query RFID basic event queue based on 1198901199011198881 and skip to Step 7 if there are RFID

basic events with the same tag numbersStep 3 Insert 119890119901119888

1into the RFID basic event queue

Step 4 Search physical object numbers in mapping relation table between objects and tagsbased on 119890119901119888

1 if none is found skip to Step 7

Step 5 Search logical reading events with the same object numbers in logical reading eventqueue according to physical object numbers If it is positive skip to Step 7

Step 6 Assemble 1199011198901into logical reading events according to physical object numbers and

insert 119897119890119896= (119897119901119896 119900119896 120591) into logical reading event queue

Step 7 Abandon RFID basic event skip to Step 1

Algorithm 1 RFID basic event processing algorithm

Step 1 Receive logical reading event 119897119890119896= (119897119901119896 119900119896 120591) uploaded by logical control points where 119896 is from 1 to 119870

Step 2 Get logical control point 119897119901pre that should be actually passed at present from route constraints ruleIf 119897119901119896= 119897119901pre skip to Step 4 if 119897119901

119896lt 119897119901pre skip to Step 5

Step 3 Find logical control point of reading leak 119897119901leak from route constraints rule based on 119900119896and 119897119901

119896

The system executes compensation reading from object 119896 and adds reading leak records(119900119896 119897119901leak ldquocompensationrdquo 120591) to the object information base

Step 4 Add normal identification records to object information baseStep 5 Abandon logical reading event 119897119901

119896 and skip to Step 1

Algorithm 2 RFID complex event processing algorithm

62 Production Planning and Scheduling Optimization Algo-rithm For generalized Lagrangian relaxation algorithm usedin this paper planning and scheduling subproblems willbe solved respectively in each time of Lagrangian iter-ation Among each iteration planning subproblem usesthe sequencing results of scheduling in last iteration andvice versa That is solving planning subproblem with fixedsequence (by accurate optimizationmethod solved by branchand bound method) and solving scheduling by fixing thesolved batch Thus this algorithm is essentially an alternat-ing iteration method Lasserre proposed to solve workshopproduction planning and scheduling integrated optimizationproblem by alternating iteration method that is alternatingldquosolving planning problem with a fixed sequencerdquo and ldquosolv-ing scheduling problem with fixed planningrdquo [32 36] It wasproved that this algorithm can converge to a local optimalsolution through limited iterations under the condition thatplanning and scheduling subproblems are solved by accurateoptimization method Solution to scheduling by fixed plan-ning of this algorithm is actually to seek good schedulingwithgiven planning so that planning objectives can be furtherimproved in the next iteration It will be pointed out thatldquoaccurate optimization method applied to both planningand scheduling subproblemsrdquo is an ideal condition as itis unpractical to solve scheduling subproblem by accuratemethod (Algorithm 3)

Comparing to Lasserrersquos method this paper proposes tosolve planning subproblem and scheduling subproblem inpairs in each time of iteration These two subproblems arecoordinated and optimized through Lagrangian multipliers

In addition generalized Lagrangian relaxation algorithmused in this paper is essentially a heuristic algorithm and theend condition of it is set as the number of iterations reachesthe prescribed number

63 Numerical Simulations Joint decision model is a non-convex and nonconcave nonlinear programming model witha fraction Traditional nonlinear programming approach canbe adopted such asGINO gradient search and semi-Newtonmethod However these approaches tend to suffer from localminima As the number of suppliers manufacturers andproduct categories increases multiple components manufac-turing lineswill produce diverse products simultaneously andfeed them to correspondingmixed-model assembly linesThecalculation and optimization solution becomes very complexand difficult It is hard if not impossible for traditionalnonlinear programming algorithms to solve the optimalsolution

This paper takes the automobile stamping workshop withfive sets of equipment (119898

1 119898

5) as the case study example

the interval of production plan covers three productioncycles The normal production capacity of each cycle is 8-hour working time (ie 28800 s) and the largest overtime is4800 s Six kinds of workpieces can be stamped The otherrelevant parameters are set as follows 119889

1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210

119894 = 1 6 119905 = 1 3 Stamping processing capacity of eachmachine is assumed to be 119898

1= 1198982= 650 119898

3= 1198984= 850

1198985= 1000 respectively In addition the equipment with low


Step 1 (initialize) Set coefficient 1205820 = 0 in formula (39) and select a group of 1205730

randomlySet Lagrangian multiplier upgrade step size Δ120582 and maximum number of iterationsiteration number 120578 = 1 and 119881 = +infin

Step 2 (update penalty coefficient) Calculate new penalty coefficient 120582120578 = 120582120578minus1 + Δ120582 and determine the value of 120579120578Step 3 (solve production planning subproblem) Obtain solution 120579120578 of 119885

2(119909 | 120579120578 120573

120578minus1

)where the solution of batch119883 is denoted as119883120578 and set 119876120578 = 119883120578

Step 4 (solve scheduling subproblem) Obtain the solution 120587120578 of 1198853(120587 | 120579120578 119876

120578

) wheresolution of assignment variable 119886 is denoted as 119886120578 and set 120573

120578

= 119886120578 120575120578

= 120575120578Step 5 (target values of problems) Set target values 119885120578 = 119885

2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578

Step 6 (determine whether the end condition is met) If 120578 is less than iterationsoutput target value 119881 and solution 119880 the algorithm ends otherwise set 120578 = 120578 + 1 and skip to Step 2

Algorithm 3 Production planning and scheduling optimization algorithm

Table 2

Working procedure 1198691

1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1

stamping capacity cannot process those working procedureswith high stamping requirement (see Table 2)

The production batch can be obtained from the aboveproduction plan model 119883 = (119883

1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The

shortage quantity of production in three cycles is initializedas 1198711= 1198712= 1198713= 0 The objective function of the

production planning is achieved as 668300 If we assignthe WIP to pass along the computed machining sequencethe completion time of each production cycle is beyond themaximally allowed processing time It means that there is nomatch between production plan and production schedulingHowever if we adopt the model proposed in this paper toresolve the global optimum solution the total completiontimes of the three production cycles are 33247 33247 and32567 respectively Each of them is less than its correspond-ingly maximally allowed production capacity Therefore thecomputed production plan is feasible which indicates theeffectiveness of the proposed optimization model

7 Conclusion

Mixed-model assembly lines have been widely used in vari-ous industries including automotive assembly mobile phonemaking and computer production This paper introducesRFID technology to manufacturing workshop to convertmanufacturing objects to be ldquosmart manufacturing objectsrdquowhich are enabled for dynamic interactions among them inreal-time Considering the theoretical model regarding theoptimal configuration and framework integration of RFID

sensor networks for general applications has not yet beenwell addressed this paper proposes a novel generalizedRFID-enabled MES model that integrates three submodelsincluding RFID network configuration the production plan-ning and scheduling optimization This combined modelovercomes the local minima defects of subobjective functionperspective where linear summation approach is deployed forsolving only one part of the overall problemThe individuallyformed subproblems that include RFID optimal allocationproduction planning and scheduling could be solved byalternating iterations The closely connected scheduling andproduction planning are well taken care of by setting theprecomputed parameters as constraints For production plan-ning to ensure its feasibility the machine assignment anddetailed scheduling parameters are treated as constraintswhen formulating production planning optimization modelTo maintain the intercoordination production planningsubproblem and scheduling subproblem are solved in pairsin each time of iteration through Lagrangian multipliersThe optimization of such integrated model is complicatedand belongs to NP-hard problem which however could besolved using the proposed generalized Lagrangian decompo-sition approach that combines standard Lagrangian approachwith Gauss-Seidel iterative principle The algorithm analysisand numerical simulation have verified the feasibility andeffectiveness of the proposed method for modeling andoptimization

In addition reliable identification and tracking of man-ufacturing objects is the key to realize agile productionmanagement Due to the influence of characteristics ofwireless communication and complex application environ-ment in manufacturing workshop raw data acquired fromRFID devices is often duplicated missing or with noise Bydefining the RFID data flow as event the real-time RFID dataprocessing technology is proposed via construction of RFIDeventmodel which contains basic events and complex eventsThe proposed RFID configuration model could improvethe accuracy of the MES monitoring information in realshop-floor environment The proposed model structure andits optimization solution are quite generally applicable for


converting the traditional MES into real-time interactivewireless manufacturing scenario

Notation

119870 Quantity of RFID devices for dataacquisition

INV119894 Initial inventory of product 119894 in the first

production cycle119869(119898) A set of working procedures that can be

processed on machine119898 excludingvirtual ones

119869119894(119898) A set of working procedures that can be

processed on machine119898includingprocesses of virtual product1198690(119894 = 1) and 119869

119899+1(119894 = 2)

119872(119894 V) A set of machines that can process (119894 V)119862ℎ+119894119905 Unit penalty cost for safety stock excess of

product 119894 in production cycle 119905119862ℎminus

119894119905 Unit penalty cost for safety stock shortfall

of product 119894 in production cycle 119905119862119901119894119905 Unit production expenses of product 119894 in

production cycle 119905119862119887119894119905 Unit shortage cost of product 119894 in

production cycle 119905119862119906119894119905 Production preparation cost of product 119894

in production cycle 119905119862119904119898

119894V Production adjustment costs (ie diechange costs) of process (119894 V) on machine119898

119862119905119898119905

Unit overtime cost in production cycle 119905119889119894119905 Demands of product 119894 in cycle 119905

119872119897119894 Upper limit of production lot of product 119894

119898119897119894 Minimum lot size of product 119894

120596 The scaling factor of overtime upper limit119882119905 Available production capacity in

production cycle 119905 here it is assumed thateach machine has the same productioncapacity

119883119894119905 Output of product 119894 in production cycle 119905

119871119894119905 Shortage quantity of product 119894 in

production cycle 119905119910119894119905 The value is 1 if product is being produced

in production cycle 119905 otherwise it is 0119861119905

119894V Start time of process (119894 V) in productioncycle 119905

119862119905

119894V Completion time of process (119894 V) inproduction cycle 119905

119865119898119905

The completion time of the last processedworkpiece on machine119898 in cycle 119905

120572119898119905

119894V The value is 1 if process (119894 V) is assigned tobe processed on machine119898 in cycle 119905otherwise it is 0

120575119898119905

119894V119895119908 The value is 1 if process (119894 V) is in front ofprocess (119895 119908) on machine119898 in cycle 119905otherwise it is 0

119874119898119905

Overtime on machine119898 in productioncycle 119905

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the funding support bytheUniversity ofMacau Grant nosMYRG153(Y1-L2)-FST11-YZX and MYRG079(Y1-L2)-FST13-YZX The authors wouldalso like to thank the reviewers for their helpful and detailedcomments

References

[1] E W T Ngai K K L Moon F J Riggins and C Y YildquoRFID research An academic literature review (1995ndash2005) andfuture research directionsrdquo International Journal of ProductionEconomics vol 112 no 2 pp 510ndash520 2008

[2] A Sarac N Absi and S Dauzre-Prs ldquoA literature review onthe impact of RFID technologies on supply chainmanagementrdquoInternational Journal of Production Economics vol 128 no 1 pp77ndash95 2010

[3] D McFarlane and Y Sheffi ldquoThe impact of automatic identifi-cation on supply chain operationsrdquoThe International Journal ofLogistics Management vol 14 no 1 pp 1ndash17 2003

[4] F Thiesse and E Fleisch ldquoOn the value of location informationto lot scheduling in complexmanufacturing processesrdquo Interna-tional Journal of Production Economics vol 112 no 2 pp 532ndash547 2008

[5] R G Qiu ldquoRFID-enabled automation in support of factoryintegrationrdquo Robotics and Computer-Integrated Manufacturingvol 23 no 6 pp 677ndash683 2007

[6] D McFarlane S Sarma J L Chirn C Y Wong and K AshtonldquoAuto ID systems and intelligent manufacturing controlrdquo Engi-neering Applications of Artificial Intelligence vol 16 no 4 pp365ndash376 2003

[7] P Vrba F Macurek and V Marık ldquoUsing radio frequencyidentification in agent-based control systems for industrialapplicationsrdquo Engineering Applications of Artificial Intelligencevol 21 no 3 pp 331ndash342 2008

[8] G Q Huang Y F Zhang and P Y Jiang ldquoRFID-basedwireless manufacturing for walking-worker assembly islandswith fixed-position layoutsrdquo Robotics and Computer-IntegratedManufacturing vol 23 no 4 pp 469ndash477 2007

[9] G Q Huang Y F Zhang and P Y Jiang ldquoRFID-based wirelessmanufacturing for real-time management of job shop WIPinventoriesrdquo International Journal of Advanced ManufacturingTechnology vol 36 no 7-8 pp 752ndash764 2008

[10] G Q Huang Y F Zhang X Chen and S T Newman ldquoRFID-enabled real-timewirelessmanufacturing for adaptive assemblyplanning and controlrdquo Journal of Intelligent Manufacturing vol19 no 6 pp 701ndash713 2008

[11] S Zhou W Ling and Z Peng ldquoAn RFID-based remote moni-toring system for enterprise internal production managementrdquoInternational Journal of Advanced Manufacturing Technologyvol 33 no 7-8 pp 837ndash844 2007

[12] A J C Trappey T H Lu and L D Fu ldquoDevelopment of anintelligent agent system for collaborative mold production withRFID technologyrdquo Robotics and Computer-Integrated Manufac-turing vol 25 no 1 pp 42ndash56 2009


[13] C Liu L S Chen and RM Romanowski ldquoAn electronic mate-rial flow control system for improving production efficiency inintegrated-circuit assembly industryrdquo International Journal ofAdvanced Manufacturing Technology vol 42 no 3-4 pp 348ndash362 2009

[14] Z X Guo W K Wong S Y S Leung and J T FanldquoIntelligent production control decision support system forflexible assembly linesrdquo Expert Systems with Applications vol36 no 3 pp 4268ndash4277 2009

[15] R-S Chen and M A Tu ldquoDevelopment of an agent-based sys-tem for manufacturing control and coordination with ontologyandRFID technologyrdquoExpert Systemswith Applications vol 36no 4 pp 7581ndash7593 2009

[16] K T C Poon K L Choy and H C W Lau ldquoA RFID-basedlocation tracking scheme for inbound operations in warehouseenvironmentrdquo in Proceedings of the Portland International Con-ference on Management of Engineering amp Technology (PICMETrsquo08) pp 872ndash877 July 2008

[17] K T C Poon K L Choy and H C W Lau ldquoA real-timemanufacturing risk management system an integrated RFIDapproachrdquo in Proceedings of the Portland International Centerfor Management of Engineering and Technology (PICMET 07)pp 2872ndash2879 IEEE August 2007

[18] G Huang P Wright and S T Newman ldquoWireless manufactur-ing a literature review recent developments and case studiesrdquoInternational Journal of Computer Integrated Manufacturingvol 22 no 7 pp 579ndash594 2009

[19] G Q Huang T Qu Y Zhang and H D Yang ldquoRFID-enabledproduct-service system for automotive part and accessorymanufacturing alliancesrdquo International Journal of ProductionResearch vol 50 no 14 pp 3821ndash3840 2012

[20] J F Benders ldquoPartitioning procedures for solving mixed-variables programming problemsrdquo Numerische Mathematikvol 4 no 1 pp 238ndash252 1962

[21] AMGeoffrion ldquoGeneralized Benders decompositionrdquo Journalof Optimization Theory and Applications vol 10 no 4 pp 237ndash260 1972

[22] H Everett III ldquoGeneralized Lagrange multiplier method forsolving problems of optimum allocation of resourcesrdquo Opera-tions Research vol 11 no 3 pp 399ndash417 1963

[23] M L Fisher ldquoThe Lagrangian relaxation method for solvinginteger programming problemsrdquo Management Science vol 27no 1 pp 1ndash18 1981

[24] M Guignard and S Kim ldquoLagrangean decomposition a modelyielding stronger Lagrangean boundsrdquoMathematical Program-ming vol 39 no 2 pp 215ndash228 1987

[25] A D Dimitriadis N Shah and C C Pantelides ldquoRTN-basedrolling horizon algorithms for medium term scheduling ofmultipurpose plantsrdquoComputers andChemical Engineering vol21 no 1 pp S1061ndashS1066 1997

[26] H-S Yan Q-F Xia M-R Zhu X-L Liu and Z-M GuoldquoIntegrated production planning and scheduling on automobileassembly linesrdquo IIE Transactions vol 35 no 8 pp 711ndash7252003

[27] G Sand and S Engell ldquoModeling and solving real-time schedul-ing problems by stochastic integer programmingrdquo Computersand Chemical Engineering vol 28 no 6-7 pp 1087ndash1103 2004

[28] J D Kelly and D Zyngier ldquoHierarchical decomposition heuris-tic for scheduling coordinated reasoning for decentralizedand distributed decision-making problemsrdquo Computers andChemical Engineering vol 32 no 11 pp 2684ndash2705 2008

[29] M Erdirik-Dogan and I E Grossmann ldquoSimultaneous plan-ning and scheduling of single-stage multi-product continuousplants with parallel linesrdquoComputers and Chemical Engineeringvol 32 no 11 pp 2664ndash2683 2008

[30] H StefanssonN Shah andP Jensson ldquoMultiscale planning andscheduling in the secondary pharmaceutical industryrdquo AIChEJournal vol 52 no 12 pp 4133ndash4149 2006

[31] J Kallrath ldquoPlanning and scheduling in the process industryrdquoOR Spectrum vol 24 no 3 pp 219ndash250 2002

[32] J-B Lasserre ldquoAn integrated model for job-shop planning andschedulingrdquo Management Science vol 38 no 8 pp 1201ndash12111992

[33] K Haase and A Kimms ldquoLot sizing and scheduling withsequence-dependent setup costs and times and efficientrescheduling opportunitiesrdquo International Journal of ProductionEconomics vol 66 no 2 pp 159ndash169 2000

[34] I Kacem S Hammadi and P Borne ldquoApproach by localizationand multiobjective evolutionary optimization for flexible job-shop scheduling problemsrdquo IEEE Transactions on Systems Manand Cybernetics C Applications and Reviews vol 32 no 1 pp1ndash13 2002

[35] I Kacem S Hammadi and P Borne ldquoPareto-optimalityapproach for flexible job-shop scheduling problems hybridiza-tion of evolutionary algorithms and fuzzy logicrdquo Mathematicsand Computers in Simulation vol 60 no 3ndash5 pp 245ndash2762002

[36] J Lasserre An Integrated Approach in Production Planningand Scheduling vol 411 of Lecture Notes in Economics andMathematical Systems Springer Berlin Germany 1994

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


ability which however is usually insufficient in the currentlyavailable production line modeling and simulation softwarepackages The performance of manufacturing process agilityis a major determinant of whether or not enterprises couldprocess manufacturing events quickly respond to dynamicdemands of market customers robustly build dynamicalliances efficiently with partners for increasing innovativecapabilities and eventually win in global competitionThere-fore aiming at breaking through the development bottle-necks in existing production management a novel manu-facturing execution system (MES) which is featured withreal-time and active information interaction technologies isurgently required to be deployed in mixed-model assemblyshop-floor through innovative production organization andmanagement model

Meanwhile RFID (Radio Frequency Identification) tech-nology has been increasingly realized as a promising infor-mation interaction tool and has been widely used in manu-facturing industries to conduct real-time monitoring of largeamount of site data Owing to the intrinsic properties of RFIDtechnology including large information storage capacity abil-ity to simultaneously identify multiple tags in one momentand noncontact recognition it enables a fundamental changein the ways to control industry process especially in fieldsof manufacturing and logistics supply chain Potential benefitand influence of RFID technology onmanufacturing industryinclude increasing the visibility and accuracy of informationreal-time production control improving the flexibility ofproduction planning and scheduling tracking productionrelated objects (such as Work-In-Process (WIP) worksta-tions and workers) tracking the utilization rate of reusableassets (such as containers tools and removable equipment)effective maintenance management inventory control ofraw materials and finished products cost reduction andimproving customer satisfaction level [1 2] Therefore RFIDis an attractive technology for fitting real-time requirementsin terms of data acquisition and process control in modernmanufacturing system However existing researches on theapplication of RFID technologymainly focus on how to buildcorresponding RFID application systems individually In theopen literature the theoretical model regarding the optimalconfiguration and framework integration of RFID sensornetworks in various applications are still lacking a unifiedand detailed study Many systematic researches are based onthe assumption that the acquisition system underlying RFIDcould meet specific application environment by generatingsignal in ideal status while in fact RFID system may outputunreliable data Few researchers addressed how to optimizeRFID system performance to reduce the influence of noisefactors and guarantee system stability in specific applicationenvironment This paper adopts RFID equipment the highcaliber wireless communication tool for real-time infor-mation acquisition and processing in complex productionsystem towards real-time MES The relevant model config-uration data purifying and optimization issues are thereforeworth being studied in this paper

The remainder of this paper is organized as follows Inthe following section relevant works related to this studywill be reviewed The system architecture model analysis

for optimization of system configuration and productionplanning and scheduling are described in Section 3 In addi-tion the reliability of RFID data processing and generalizedLagrangian decomposing approach are presented in Sections4 and 5 respectively The algorithm analysis and modelvalidity are examined in Section 6 Finally a summary ofmodeling methodology together with a discussion on thedirections for future research is made

2 Literature Review

To study a real-time MES model for complex productmanufacturing system the study involves research efforts intwo subareas wireless technique for information acquisitionand optimization of production planning and schedulingCorrespondingly this section reviews the applications ofRFID for real-time information acquisition and facility mon-itoring in manufacturing execution system and also givesa brief summary on production planning and schedulingoptimization studies of manufacturing system

21 RFID-Enabled Real-Time MES Researches on the appli-cation of RFID in manufacturing process control mainlyaddressed the following three aspects determination of spe-cific application fields and functions of RFID technology pro-cess control of RFID system and RFID system integrationCurrentlymany scholars begin to focus onRFID applicationsin manufacturing workshops to strengthen production pro-cess management by effectively improving the transparencyof manufacturing workshop [3ndash5]

The automatic control problem in production processcould be solved using RFID technology [6] A RFID basedintelligent product was proposed to make products haveautomatic information interaction accurate information andreal-time acquisition ability and thus support workshopproduction decisions and automatic control Based on thecharacteristic comparison of RFID and barcode technologyRFID was selected to manufacture control system basedon programmable logic controller The control system wascombined with multi-agent technology as information inter-action media between RFID equipment and other agents[7] A manufacturing system framework based on RFID wastherefore built Huangrsquos group [8ndash10] proposed the concept ofrealizing JIT through wireless manufacturing (WM) technol-ogy whereWMcollected real-timemanufacturing workshopsite information by fully relying on wireless devices such asRFID Auto ID sensor or wireless information network Theapplication of RFID in remote monitoring in enterprise pro-ductionmanagement was reported [11] which could improvethe efficiency of production process by readapting IT systemand reduce human errors via applying RFID technology Anew device based on RFID technology has been reportedto strengthen information exchange among workshops andinformation system optimization throughout the whole fac-tory [5] Another effort on system design using RFID couldassist grinding apparatus production when combined withERP system [12] It was also reported to apply such combinedsystem for logistics control of integrated circuit assembly




3 Model Analysis



119894 Each


119894= 1 119899

119894 (119894 V)









119894119905



(ie if 119868119894119905ge 119877119868

119894119905

119878119868+119894119905= max119868















(ie if 119868119894119905le 119877119868

119894119905

119878119868minus119894119905= max119877119868







119894119905119862ℎ+119894119905 respectively










RFID readerA

RFID readerB


Processing time





Min1198851=

119872

sum119894=1


+

119873

sum119895=1


(1205941 120594


(1205931 120593



2+ (119885Sensor Ψ minus 119885119894)

2

le Θ119894

SensorΨ=



Ψ isin [1119872 + 119873]

(1)


1 120594


accuracy (1205931 120593




119894(119883119894 119884119894 119885119894) are within the




Min1198852=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119905119878119868+

119894119905+ 119862ℎminus

119894119905119878119868minus

119894119905+ 119862119901119894119905119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

(2)



INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+









119894119905 119910119894119905in the following


Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)


120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905


sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












3 Model Analysis



119894 Each


119894= 1 119899

119894 (119894 V)









119894119905



(ie if 119868119894119905ge 119877119868

119894119905

119878119868+119894119905= max119868















(ie if 119868119894119905le 119877119868

119894119905

119878119868minus119894119905= max119877119868







119894119905119862ℎ+119894119905 respectively










RFID readerA

RFID readerB


Processing time





Min1198851=

119872

sum119894=1


+

119873

sum119895=1


(1205941 120594


(1205931 120593



2+ (119885Sensor Ψ minus 119885119894)

2

le Θ119894

SensorΨ=



Ψ isin [1119872 + 119873]

(1)


1 120594


accuracy (1205931 120593




119894(119883119894 119884119894 119885119894) are within the




Min1198852=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119905119878119868+

119894119905+ 119862ℎminus

119894119905119878119868minus

119894119905+ 119862119901119894119905119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

(2)



INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+









119894119905 119910119894119905in the following


Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)


120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905


sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















(ie if 119868119894119905le 119877119868

119894119905

119878119868minus119894119905= max119877119868







119894119905119862ℎ+119894119905 respectively










RFID readerA

RFID readerB


Processing time





Min1198851=

119872

sum119894=1


+

119873

sum119895=1


(1205941 120594


(1205931 120593



2+ (119885Sensor Ψ minus 119885119894)

2

le Θ119894

SensorΨ=



Ψ isin [1119872 + 119873]

(1)


1 120594


accuracy (1205931 120593




119894(119883119894 119884119894 119885119894) are within the




Min1198852=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119905119878119868+

119894119905+ 119862ℎminus

119894119905119878119868minus

119894119905+ 119862119901119894119905119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

(2)



INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+









119894119905 119910119894119905in the following


Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)


120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905


sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











RFID readerA

RFID readerB


Processing time





Min1198851=

119872

sum119894=1


+

119873

sum119895=1


(1205941 120594


(1205931 120593



2+ (119885Sensor Ψ minus 119885119894)

2

le Θ119894

SensorΨ=



Ψ isin [1119872 + 119873]

(1)


1 120594


accuracy (1205931 120593




119894(119883119894 119884119894 119885119894) are within the




Min1198852=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119905119878119868+

119894119905+ 119862ℎminus

119894119905119878119868minus

119894119905+ 119862119901119894119905119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

(2)



INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+









119894119905 119910119894119905in the following


Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)


120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905


sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











INV119894+ 1198711198941+ 1198831198941= 1198681198941+ 1198891198941 forall119894 (3)

119868119894119905minus1

+ 119871119894119905+ 119883119894119905= 119868119894119905+ 119889119894119905 119905 = 2 119879 forall119894 (4)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894 119905) 120572119898119905

119894V le 1205961015840119882119905 forall119898 119905 (5)

119878119868+

119894119905= max 119868

119894119905minus 119877119868119894119905 0 forall119894 119905 (6)

119878119868minus

119894119905= max 119877119868

119894119905minus 119868119894119905 0 forall119894 119905 (7)

119898119897119894119910119894119905le 119883119894119905le 119872119897119894119910119894119905 forall119894 119905 (8)

119871119894119905le 119889119894119905 forall119894 119905 (9)

119878119868+

119894119905 119878119868minus

119894119905 119868119894119905 119871119894119905 119883119894119905isin 119911+









119894119905 119910119894119905in the following


Min1198853=

119872

sum119898=1

119879

sum119905=1

119873

sum119894=1

119899119894

sumV=1119862119904119898

119894V120572119898119905

119894V +

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905 (11)


120572119898119905

119894V le 119891119898

119894V V isin 119899119894 forall119894 119898 119905 (12)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(13)

119862119905

119894V le 119861119905

119894V+1 V isin 119899119894 forall119894 119905 (14)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(15)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119909119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(16)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (17)

sum(119894V)isin1198691(119898)

120575119898119905

119894V119895119908 = 120572119898119905

119895119908 119898 isin 119872(119895 119908) 119908 isin 119899

119895 forall119895 119905 (18)

sum(119895119908)isin1198692(119898)

120575119898119905

119894V119895119908 = 120572119898119905


sum(119894V)isin119869(119898)

120575119898119905

0119908119894V le 1 119908 = 119898 forall119898 119905 (20)

sum(119894V)isin1198692(119898)

120575119898119905

119894V0119908 = 0 119908 = 119898 forall119898 119905 (21)

sum(119894V)isin119869(119898)

120575119898119905

119894V119899+1119908 le 1 119908 = 119898 forall119898 119905 (22)

sum(119894V)isin1198691(119898)

120575119898119905

119899+1119908119894V = 0 119908 = 119898 forall119898 119905 (23)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119897)119866 119908 = 119898 forall119898 119905

(24)

119865119898119905le 119882119905+ 0119898119905 forall119898 119905 V (25)

0 le 0119898119905le 120596119882

119905 forall119898 119905 (26)


119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119861119905

119894V 119862119905

119894V 0119898119905 ge 0 120572119898119905

119894V 120575119898119905

119894V119895119908 isin 0 1

0 le 120596 le 1 V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(27)
















Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Min119885 = Min1198851+Min119885

2+Min119885

3 (28)


119883119894119905= 119876119894119905 forall119894 119905 (29)

120572119898119905

119894V = 120573119898119905

119894V forall119894 119905 (30)

119910119894119905= 120594 (119876

119894119905) forall119894 119905 (31)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894 119905) 120573119898119905

119894V le 119882119905 + 119874119898119905 forall119898 119905 (32)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V V isin 119899119894 forall119894 119905

(33)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V V isin 119899119894 forall119894 119905

(34)

119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119876119894119905) 120572119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(35)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119876119895119905) 120572119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(36)

sum119898isin119872(119894V)

120572119898119905

119894V = 119910119894119905 V isin 119899119894 forall119894 119905 (37)



Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Object event queue



Tag event filter

RFID basic event

Tag


Tag event filter


Reader adapterl

Reader adapterk





N+

RFID basic event




Event processor


Logic control point



Logic control point

Logic control point



base














119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















119894119905and 119910

119894119905are



pliers 120583 = 120583119894119905 V = V119898119905








119894119905 V = V119898119905


119885LR = 119885 +119873

sum119894=1

119879

sum119905=1

120583119894119905(119883119894119905minus 119876119894119905)

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V (120572119898119905

119894V minus 120573119898119905

119894V )

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905+ (119862119901

119894119905+ 120583119894119905)119883119894119905

+ 119862119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V

+

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + V119898119905119894V ) 120572119898119905

119894V

+

119872

sum119898=1

119879

sum119905=1

119862119905119898119905119874119898119905

(38)

120583119894119905= 120582119862119901

119894 V119898119905119894V = 120582119862119904

119898

119894V 0 le 120582 le 1 (39)




2(119909 | 120579 120573) as






119898119905



119898119905

119894V and 120575119898119905


1198852(119909 | 120579 120573)

=

119879

sum119905=1

119873

sum119894=1

(119862ℎ+

119894119878119868+

119894119905+ 119862ℎminus

119894119878119868minus

119894119905

+ (119862119901119894 119905 + 120583

119894119905)119883119894119905+ 119866119887119894119905119871119894119905+ 119862119906119894119905119910119894119905)

minus

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1

V119898119905119894V 120573119898119905

119894V

(40)

sum(119894V)isin119869(119898)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V le (1 + 120596)119882119905 forall119898 119905 (41)

119862119905

119894V ge 119861119905

119894V + 119898 sum119898isin119872(119894V)

(119904119898

119894V119910119894119905 + 119901119898

119894V119909119894119905) 120573119898

119894V forall119898 119905 (42)


119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119861119905

119894V + (119904119898

119894V119910119894119905 + 119901119898

119894V119883119894119905) 120573119898119905

119894V minus (1 minus 120575119898119905

119894V119895119908)119866 le 119861119905

119895119908

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(43)

119861119905

119895119908+ (119904119898

119895119908119910119895119905+ 119901119898

119895119908119883119895119905) 120573119898119905

119895119908minus (1 minus 120575

119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(44)

119865119898119905= max(119894119899119894)isin119869(119898)

119862119905

119894119899119894minus (1 minus 120575

119898119905

119894119899119894 119899+1119908)119866

119908 = 119898 119898 isin 119872 119905 isin 119879

(45)








119894119905


1198853(120587 | 120579 119876)

=

119872

sum119898=1

119879

sum119905=1

119862119905119898119905

119879

sum119905=1

119872

sum119898=1

119873

sum119894=1

119899119894

sumV=1(119862119904119898

119894V + 120592119898119905

119894V ) 120572119898119905

119894V

minus

119873

sum119894=1

119879

sum119905=1

120583119894119905119876119894119905

(46)

119910119894119905= 119909 (119876

119894119905) forall 119894 119905 (47)

119862119905

119894V ge 119861119905

119894V + sum119898isin119872(119894V)

(119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898

119894V V isin 119899119894 forall119894 119905

(48)

119861119905

119894V + (119904119898

119894V119910119894V + 119901119898

119894V119876119894V) 120572119898119905

119894V minus (1 minus 120575119898119905

119895119908119894V)119866 le 119861119905

119894V

V isin 119899119894 119908 isin 119899

119895 forall119894 119895 119898 119905

(49)








1 119897119901

119898⟩ which are



119895

if 119897119901119894is in front of 119897119901


119894first and

then 119897119901119895 and 119897119901


119896= (119897119901119896 119900119896 120591)



119896and 119897119901pr119890 in default

routes ⟨1198971199011 119897119901


119896lt




















119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























119896










1 119898



1198941= 650 119889

1198942= 1198891198943=

800 119877119868119894119905= 200 119862119901

119894119905= 119862ℎ+119894119905= 40 119862ℎminus

1198941= 160 119862ℎminus

1198942= 135

119862ℎminus1198943= 110119862119887minus

1198941= 560119862119887minus

1198942= 375119862119887minus

1198943= 180119862119906minus

1198941= 210


1= 1198982= 650 119898

3= 1198984= 850






2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













2(119909 | 120579120578 120573

120578minus1



120578


120578

= 119886120578 120575120578


2(119909 | 120579120578 120573

120578minus1

) + 1198853(120587 | 120579120578 119876

120578

) 119904119900119897119879 = (119909119879 120587119879)and when 120578 = 1 set 119880 = 119904119900119897120578



Table 2


1198692

1198693

1198694

1198695

1198696

1198981

2 5 5 3 4 11198982

2 5 3 1 2 31198983

1 5 2 4 4 31198984

5 2 2 4 31198985

1



1 1198832 1198833) = (850 850

850 850 850 850) also 119878119868+119894= 119878119868minus119894= 0 (119894 = 1 2 3) The



7 Conclusion






Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Notation







119899+1(119894 = 2)









119862119905119898119905











119862119905


119865119898119905


120572119898119905


120575119898119905


119874119898119905




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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