Research ArticleDefining Scheduling Problems for Key Resources inEnergy-Efficient Port Service Systems

Daofang Chang Ting Fang Junliang He and Danping Lin

Institute of Logistics Science and Engineering Shanghai Maritime University 1550 Haigang Avenue Shanghai 201306 China

Correspondence should be addressed to Ting Fang fangting china126com

Received 7 August 2016 Accepted 31 August 2016

Academic Editor Si Zhang

Copyright copy 2016 Daofang Chang et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper addresses the problem of key resource scheduling of container terminals for energy-efficient operation A combinationof key resource scheduling and energy-efficient operation in container terminals is firstly described An energy-efficient evaluationmodel of the key resource scheduling is then proposed The objective set decision variable set and constraint set of key resourcescheduling of a container terminal for energy-efficient operation are established in this paper At the same time their mappingrelationship is carefully analyzed and the system structure of the key resource scheduling for energy-efficient operation of acontainer terminal is finally proposed

1 Introduction

The key resources in a container terminal usually includea berth quay cranes a storage yard and yard cranes asshown in Figure 1 Their scheduling must be proposed inadvance for coordination with container shipping lines thattransport containers on regularly scheduled service routes[1] These key resources work together to load and unloadcontainers Although this adds some value it is also themain contributor to energy consumption and environmentalpollution To obtain low energy consumption high efficiencyand better benefits portworkers have designed some effectivescheduling schemes for berths quay cranes storage yardsand yard cranes These activities improve the operationprocess of the container terminal and ensure that each link ofthe operation is environmentally friendly which fundamen-tally changes the opportunities and modes for current portsto seek throughput growth development Energy-efficientoperation of the container terminal is not a negative featureof production operation in traditional terminals but rathercomplements its development Energy-efficient operation hasencouraged the production operation process of containerterminals to become more environmentally friendly

ldquoEnergy efficiencyrdquo is also regularly called ldquoefficientenergy userdquo at an international level and together with

a renewable energy policy these are considered to be thetwo pillars of future sustainable energy policies [2] In thefield of academic research into energy efficiency physicistLovins proposed the concept of a soft energy path which isclosely related to energy efficiency [3] Researchers in theUS Department of Energy have studied an ldquoenergy-efficientdistribution systemrdquo (REEDS) and found 90 billion kilowattsof energy saving In the energy efficiency related internationalindustry the minimum energy efficiency standards andregulations of the European Union have come into forcein Zurich Switzerland This is a milestone for the EU inpromotion of energy efficiency of low-voltage motors [4]

Container terminals act as an important hub for globaleconomic and trade activities and are facing increasingenvironmental pressure [5] At a container terminal designlevel ZPMC have used the experience of HHLA containerterminals based on AGVs [6] and PSA container terminalsbased on high capacity storage [7] to propose a new con-tainer terminal based on a frame bridge This is the firstinternational energy-efficient port scheme that is based onmechanical and electrical integration technology

Within the industry model programming problems havebeen studied by many scholars Wang proposed a novelhybrid-link-based model that nests existing origin-link-based and destination-link-based models as special cases [8]

Hindawi Publishing CorporationScientific ProgrammingVolume 2016 Article ID 7053962 8 pageshttpdxdoiorg10115520167053962

2 Scientific Programming

Freight stationGasstation

Block 2

Quay crane Ship

Block 1

Block 3

Block 5

Block 4

Block 6

Yard crane

Controlroom

Serviceshop

Door

Figure 1 Key resources of a container terminal

AdditionallyWang proposed a global optimization approachthat is suitable for bilevel programming models with finitediscrete upper-level decision variables A conic quadraticmixed-integer linear programming approach was also devel-oped to solve relaxed models of bilevel formulation of speedlimit designs [9] Qu et al highlighted that the inaccuracy ofsingle-regime models is not caused solely by their functionalforms but also by the sample selection biasThey also applieda weighted least squares method (WLSM) that addressesthe sample selection bias problem [10] Qu et al discoveredthat the follow-up time is indeed significantly affected bythe traffic volume the number of vehicles that are waitingbehind the vehicle type and the driversrsquo gender An inverseGaussian regression model was also further developed inorder to establish a relationship between the follow-up timeand its contributing factors [11]

The scheduling problems of key resources in containerterminals have gradually become a hot topic in academiaand industry [12] There has been a lot of research intoscheduling space and equipment resources and operationalperformance optimization in container terminals For inte-grated scheduling of berths and quay cranes Imai et aldeveloped a dynamic method for berth scheduling basedon discrete berths which reduces the working time of ship5 [13] Kim and Moon proposed a scheduling method forberths based on the shortest delay time of the ship leaving aport using a simulated annealing algorithm [14] AdditionallyPark and Kim adopted a gradient algorithm to study berthscheduling methods [15] Guan et al designed a heuristicalgorithm for berth scheduling processing to ensure thatships spend the shortest time possible at the terminal [16]Chang et al developed a method to combine the heuristicalgorithm and simulation to solve the scheduling problemfor a combination of berths and quay cranes [17] Legato andMazza studied the problem of vessel arrival berthing andleaving using a queuing theory method [18] The main goalof all of these studies was to reduce the time that the ship

spends berthed while also decreasing the cost of berthingFor yard scheduling many researchers have undertakenthorough research into the overall yard distribution of importand export containers Zhang et al designed a storage modelto balance the number of containers loaded and unloadedin each block to achieve the shortest horizontal transportdistance across the yard [19] Chen et al proposed a hybridmethod that combines the Tabu search algorithm with anoptimization algorithm to solve the yard scheduling problem[20] Therefore yard scheduling has currently been theresearch priority for export containers Some problems stillexist for yard scheduling such as the scale of the models andlow solution efficiencies For yard crane scheduling manyresearchers have aimed to achieve high efficiency in the yardLinn et al established a scheduling model for yard cranesbased on integer programming [21] Additionally there aremany other similar methods in this area

Although current researchers have made certain progressin key resource scheduling of container terminals an energy-efficient and integrated scheduling method has not beeneffectively proposed Therefore there is no complete integra-tion of key resources scheduling systems nor any efficiencystudy including the objective set the decision-making vari-able set and the constraint set which defines the mappingrelationship between them In this paper an integrated keyresource scheduling systemwill be designed and themappingrelationship of the objective set the decision-making variableset and the constraint set will be defined

In Section 2 an energy-efficient evaluation model ofthe key resource scheduling will be proposed In Section 3the objective set decision variable set and constraint setof key resource scheduling of a container terminal forenergy-efficient operation are established and their mappingrelationship is carefully analyzedThe system structure of thekey resource scheduling for energy-efficient operation in thecontainer terminal will finally be proposed Conclusions willbe given in Section 4

2 An Energy-Efficient Evaluation Model

Energy-efficient scheduling of various types of core resourcesis the key to energy-efficient operation of a container termi-nal A container terminal includes four types of key resourcesa berth quay cranes a storage yard and yard cranesObviously the berth and storage yard are spatial resourcesand the quay cranes and yard cranes are equipment resourcesIn contrast with general resource scheduling problems theefficient scheduling of resources needs to consider not onlythe efficiency of the allocations but also the evaluation indexof the energy consumption

In this paper efficient operation of the container terminalrequires efficient scheduling of the four key resources theberth the quay cranes the storage yard and the yard cranesThe scheduling of each of these four types of key resourcesdepends on each other The scheduling results of one type ofresourcemay provide the initial conditions for the schedulingof another type of resource At the same time the results ofscheduling the second resource type may have an impact onscheduling of other resources

Scientific Programming 3

21 Parameter Setting In this section the parameters aredefined as follows

CT the time delay of the ship leaving the portBT the berthing time of the shipDT the planned departure time of the shipST the loading and unloading time of the quay craneD the offset of the berthing position (m)P the actual berthing position119875lowast the planned berthing locationTE119904 energy consumption of ships at the port120576 energy consumption of ships per unit of time at theportn total number of quay cranes allocated to the shipqn119894 loading and unloading quantity for the 119894th quaycrane120578 the handling efficiency of the quay crane119892 efficiency coefficient whenmultiple quay cranes areworkingst119894 starting working time of the 119894th quay craneTE119902 energy consumption of the quay crane120588 energy consumption of the quay crane per unit oftimeTd horizontal transport distanceb blocks allocated to the shipbn119894 the number of containers allocated to the 119894thblock119889119894 horizontal transport distance between the berthand the 119894th blockBP economic balance between the blocksbn119894 the handling quantity allocated to the 119894th blockBayd the distance between two baysba119894 the number of bays allocated to the 119894th block119875119894119895 the position of the jth bay in the 119894th blockBs the continuity of bays in the block119892119894119895119896 the serial number of the jth bay and kth roll inthe 119894th blockLpb the parallelism of the sending containersbnlp119894 the sum of the allocated blocks in the 119894th portlp the number of the port dischargeTE119905 energy consumption of horizontal transport120582 energy consumption of the truck per unit distanceDT the delay time of the task grouptn the number of the task groupST119894119895 starting working time of yard crane jNT119894119895 the allocated handling quantity of yard crane 119895in task group i

Et119901119894 the planned completion time of task group i

120590 the loading and unloading efficiency of the yardcrane

ny the total number of yard cranes

TM the total time of yard cranes to move from oneblock to another

1199051198941198941015840 time for a yard crane to move from task group 119894 totask group 1198941015840TE119910 the moving energy consumption of the yardcranes

Ls119894119895119896 the current position of yard crane 119895 for task 119896 intask group i

Lt119894119895119896 target position of yard crane 119895 for task 119896 in taskgroup 119894vt119895 quantity of task group i

120596 energy consumption of yard crane per unit dis-tance

TE119910 the energy consumption of the yard crane

120583 the handling energy consumption of the yard craneper unit time

22 Efficiency Evaluation for Berth Scheduling Primarily thescheduling of a berth requires decisions to be made on theberthing location and the berthing time of ships There aremany factors that can impact the results including the shipspecifications the ship arrival time the loading and unload-ing quantity required for each ship the currently mooredships and the length of each shoreline ship on the berthIn this efficiency evaluation model the objectives used formaking a decision are to ensure that a ship is at port for theshortest possible time while maintaining the lowest possibleenergy consumption for the ship at port and the shortesthorizontal transport distance The calculation models forenergy consumption and efficiency evaluation for berthscheduling can be illustrated as follows

(1) Efficiency Calculation Equation for Berth Scheduling Thetime delay of a ship leaving a port is calculated using (1) andthe offset of the berthing

CT = ST + (BT minus DT) (1)

119863 = 119875 minus 119875lowast (2)

(2) Energy Consumption Calculation Equation for BerthScheduling The energy consumption of a ship at a port isdetermined by its turnaround timeThe turnaround time of aship is determined by the shiprsquos berthing time and departuretime which is within the category of berth scheduling Theenergy consumption of a ship at port is calculated using

TE119904 = CT sdot 120576 (3)

4 Scientific Programming

23 Efficiency Evaluation for Quay Crane Scheduling Thescheduling of quay cranes depends mainly on the time wheneach quay crane starts service and the distribution of eachquay craneThere aremany factors that need to be consideredincluding the number of quay cranes the current positionof each quay crane the current state of each quay cranethe shipping carts the efficiency of each quay crane and theenergy consumption of each quay crane per unit of time Inthis paper the objectives that are used for decision-makingare based on obtaining the shortest service time of ships andthe minimum energy consumption of quay cranes duringloading and unloading operations

(1) Efficiency Calculation Equation for Quay Crane Schedul-ing The service time of a ship ends once loading andunloading operations have been completed at the quay sideThe acceptable service time of the ship is calculated as follows

ST = Max119894=12119899

( st119894 + qn119894(120578 (119899)119892)) minus BT (4)

(2) Energy Consumption Calculation Equation for QuayCrane Scheduling Equation (5) gives the energy consumptioncalculation equation for quay crane scheduling as follows

TE119902 = 119899sum119894=1

qn119894 sdot ( 120578(119899)119892) sdot 120588 (5)

24 Efficiency Evaluation for Yard Scheduling Generally thescheduling of a yard includes scheduling blocks and baysThere are some additional factors that have an impact on thescheduling of a yard such as the loading and unloading ofthe ship the division of blocks the location of blocks theposition of the berthing ship and the availability of the blocksin the container terminal The objectives used for decision-making aremainly based on achieving the shortest horizontaltransportation distance the highest economic balance ofthe blocks the shortest moving distance of the yard cranesand the minimum energy consumption for the horizontaltransportation

(1) Efficiency Calculation Equation for Yard Scheduling Equa-tion (6) can be used to obtain the horizontal transportationdistance as follows

Td = 119887sum119894=1

bn119894 sdot 119889119894 (6)

For yard scheduling there are two factors that influencethe moving distance of a yard crane the concentration ofbays in a block and the continuity of the block in the bayTherefore calculation of the moving distance of a yard cranecan be broken down into two steps The first step is the

calculation of the distance between distributed bays and thesecond step is calculation of the continuity assigned to thebay in the container terminal In (7) the economic balancebetween blocks is calculated The economic balance betweenblocks is based on the difference in production value betweenthe allocated blocks with the largest and smallest productionvalues As shown in (8) the distance between bays is includedin the calculations The continuity that is assigned to a bay inthe container terminal is expressed by (9)

BP = Max119894=12119887

(bn119894) minus Min119894=12119887

(bn119894) (7)

Bayd = 119887sum119894=1

ba119894sum119895=2

(119875119894119895 minus 119875119894(119895minus1)) (8)

Bs = 119887sum119894=1

ba119894sum119895=1

119897119894119895sum119896=1

10038161003816100381610038161003816119891119894119895119896 minus 110038161003816100381610038161003816

119891119894119895119896 =

119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816 if 119892119894119895119896 = 119892(119894119895119896minus1)1 otherwise

(9)

The continuity of the sending containers can be evaluatedbased on the continuity assigned to the bay The parallelismbetween the sending containers is mainly determined basedon whether the distribution of blocks in the same port isscattered or not as shown in

Lpb = lpsum119894=1

bnlp119894 (10)

(2) Energy Consumption Calculation Equation for YardScheduling The energy consumption of horizontal trans-portation is shown in

TE119905 = Td sdot 120582 (11)

25 Efficiency Evaluation for Yard Crane Scheduling Thescheduling of yard cranes requires decision-making on thetask group needing service the start time of that service andthe number of containers to be loaded and unloaded for thatservice There are many factors impacting this schedulingincluding the block and bay of the task group the handlingefficiency of the yard crane the current position of the yardcrane and the number of yard cranes The objectives fordecision-making are mainly based on achieving the mini-mumdelay in completing a task group theminimumnumberof transitions of yard cranes and the minimum energy con-sumption of yard cranes during both moving and handling

(1) Efficiency Calculation Equation for Yard Crane SchedulingThe time delay in finishing a task group is described by (12)and the transition time of yard cranes is described by (13)

DT = tnsum119894=1

( Max119895=12ny

(ST119894119895 +NT119894119895 sdot 120590) minus Et119901119894 ) (12)

Scientific Programming 5

TM = tnsum119894=1

tnsum1198941015840=1119894 =1198941015840

nysum119895=1

1199041198951198941198941015840sdot 1199051198941198941015840

1199041198951198941198941015840=

1 If the task group 119894 is finished by yard crane 119895 then the task group 1198941015840 will be done right now0 otherwise

(13)

(2) Energy Consumption Calculation Equation for Yard CraneScheduling Equation (14) represents the moving energyconsumption of a yard crane and (15) describes the handlingenergy consumption of a yard crane as follows

TE119910 = tnsum119894=1

nysum119895=1

vt119895sum119896=1

10038161003816100381610038161003816Ls119894119895119896 minus Lt11989411989511989610038161003816100381610038161003816 sdot 120596 (14)

TEyc = nysum119894=1

tnsum119895=1

NT119894119895 sdot 120590 sdot 120583 (15)

3 Framework of the Scheduling Model

In practice the scheduling of core resources in a containerterminal consists of a series of decision-making processesDecision-making is required for scheduling of the berth quaycranes storage yard and yard cranes Since the berthingposition of ships is required to make decisions on whento implement the scheduling of quay cranes the loadingand unloading time of ships must be considered for quaycrane scheduling which is decided by the berth schedulingTherefore integration is required between the schedulingproblems for quay cranes and berths In this paper theyare considered to be a unified problem for the purposes ofdecision-making and optimization The decision objectivesfor the core resource allocation in traditional container ter-minals are mainly based on time (T such as the turnaroundtime of a ship and the delay time of a task group) and distance(D such as the offset distance of the berthing position thehorizontal transport distance and the moving distance of theyard crane) In this paper not only is the efficiency objectivetaken into consideration but also the energy consumption (119864)is taken into consideration

31 Parameter Setting Theparameters are defined as follows

BQ the decision-making variable set for integratedscheduling of the berth and quay cranesBL the decision-making variable set for yard schedul-ingYC the decision-making variable set for yard craneschedulingTC the time constraint setSC the space constraint setEC the equipment constraint set

32 Modeling of the Objective Set The optimized objectiveset for efficient scheduling of key resources in a container

terminal consists of time (119879) distance (119863) and energyconsumption (119864) The mapping relationship between theobjective set and the decision-making problem is shownin Figure 2 These three decision-making objectives can befurther embodied based on the specific scheduling problemof key resources In addition each objective includes anumber of independent components Taking the energyconsumption objective119864 as an example119864 includes the energyconsumption of ships at port 1198641 the energy consumption ofthe loading and unloading operations of quay crane 1198642 theenergy consumption of horizontal transport 1198643 the energyconsumption of moving the yard crane 1198644 and the energyconsumption of the loading and unloading operations of theyard crane 1198645 Therefore each objective can be representedby a vector composed of various factors For example 119864 canbe expressed as a vector of n subobjects as shown in (16) Ina similar way the other objectives can be expressed as shownin (17) and (18)

= (1198641 1198642 119864119899) (16)

= (1198791 1198792 119879119899) (17)

= (1198631 1198632 119863119899) (18)

33 Modeling of the Decision Variable Set The schedulingof key resources in a container terminal consists of multi-ple optimization decision-making problems including theintegrated scheduling of the berth and quay cranes yardscheduling and yard crane schedulingThedecision variablesof each decision-making problem are shown in Figure 3

The decision-making problems of the application canbe regarded as being composed of many decision-makingsubquestions For this purpose each decision problem isregarded as a vector The decision-making variable vector forintegrated scheduling of the berth and quay cranes can beindicated by BQ = bq1 bq2 bq119898 Equation (19) showsthe decision-making variable set 119863 for the scheduling of keyresources within the overall container terminal

119863 = [[[[

BQ = (bq1 bq2 bq119898)BL = (bl1 bl2 bl119899)YC = (yc1 yc2 yc119896)

]]]] (19)

34 Modeling of the Constraint Set In the energy-efficientscheduling decision-making model of key resources in acontainer terminal the constraint set is quite complicatedThe optimization decision-making model of the constraintset usually includes time constraints space constraints andequipment constraints For example the berthing time of a

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

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International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

2 Scientific Programming

Freight stationGasstation

Block 2

Quay crane Ship

Block 1

Block 3

Block 5

Block 4

Block 6

Yard crane

Controlroom

Serviceshop

Door

Figure 1 Key resources of a container terminal

AdditionallyWang proposed a global optimization approachthat is suitable for bilevel programming models with finitediscrete upper-level decision variables A conic quadraticmixed-integer linear programming approach was also devel-oped to solve relaxed models of bilevel formulation of speedlimit designs [9] Qu et al highlighted that the inaccuracy ofsingle-regime models is not caused solely by their functionalforms but also by the sample selection biasThey also applieda weighted least squares method (WLSM) that addressesthe sample selection bias problem [10] Qu et al discoveredthat the follow-up time is indeed significantly affected bythe traffic volume the number of vehicles that are waitingbehind the vehicle type and the driversrsquo gender An inverseGaussian regression model was also further developed inorder to establish a relationship between the follow-up timeand its contributing factors [11]

The scheduling problems of key resources in containerterminals have gradually become a hot topic in academiaand industry [12] There has been a lot of research intoscheduling space and equipment resources and operationalperformance optimization in container terminals For inte-grated scheduling of berths and quay cranes Imai et aldeveloped a dynamic method for berth scheduling basedon discrete berths which reduces the working time of ship5 [13] Kim and Moon proposed a scheduling method forberths based on the shortest delay time of the ship leaving aport using a simulated annealing algorithm [14] AdditionallyPark and Kim adopted a gradient algorithm to study berthscheduling methods [15] Guan et al designed a heuristicalgorithm for berth scheduling processing to ensure thatships spend the shortest time possible at the terminal [16]Chang et al developed a method to combine the heuristicalgorithm and simulation to solve the scheduling problemfor a combination of berths and quay cranes [17] Legato andMazza studied the problem of vessel arrival berthing andleaving using a queuing theory method [18] The main goalof all of these studies was to reduce the time that the ship

spends berthed while also decreasing the cost of berthingFor yard scheduling many researchers have undertakenthorough research into the overall yard distribution of importand export containers Zhang et al designed a storage modelto balance the number of containers loaded and unloadedin each block to achieve the shortest horizontal transportdistance across the yard [19] Chen et al proposed a hybridmethod that combines the Tabu search algorithm with anoptimization algorithm to solve the yard scheduling problem[20] Therefore yard scheduling has currently been theresearch priority for export containers Some problems stillexist for yard scheduling such as the scale of the models andlow solution efficiencies For yard crane scheduling manyresearchers have aimed to achieve high efficiency in the yardLinn et al established a scheduling model for yard cranesbased on integer programming [21] Additionally there aremany other similar methods in this area

Although current researchers have made certain progressin key resource scheduling of container terminals an energy-efficient and integrated scheduling method has not beeneffectively proposed Therefore there is no complete integra-tion of key resources scheduling systems nor any efficiencystudy including the objective set the decision-making vari-able set and the constraint set which defines the mappingrelationship between them In this paper an integrated keyresource scheduling systemwill be designed and themappingrelationship of the objective set the decision-making variableset and the constraint set will be defined

In Section 2 an energy-efficient evaluation model ofthe key resource scheduling will be proposed In Section 3the objective set decision variable set and constraint setof key resource scheduling of a container terminal forenergy-efficient operation are established and their mappingrelationship is carefully analyzedThe system structure of thekey resource scheduling for energy-efficient operation in thecontainer terminal will finally be proposed Conclusions willbe given in Section 4

2 An Energy-Efficient Evaluation Model

Energy-efficient scheduling of various types of core resourcesis the key to energy-efficient operation of a container termi-nal A container terminal includes four types of key resourcesa berth quay cranes a storage yard and yard cranesObviously the berth and storage yard are spatial resourcesand the quay cranes and yard cranes are equipment resourcesIn contrast with general resource scheduling problems theefficient scheduling of resources needs to consider not onlythe efficiency of the allocations but also the evaluation indexof the energy consumption

In this paper efficient operation of the container terminalrequires efficient scheduling of the four key resources theberth the quay cranes the storage yard and the yard cranesThe scheduling of each of these four types of key resourcesdepends on each other The scheduling results of one type ofresourcemay provide the initial conditions for the schedulingof another type of resource At the same time the results ofscheduling the second resource type may have an impact onscheduling of other resources

Scientific Programming 3

21 Parameter Setting In this section the parameters aredefined as follows

CT the time delay of the ship leaving the portBT the berthing time of the shipDT the planned departure time of the shipST the loading and unloading time of the quay craneD the offset of the berthing position (m)P the actual berthing position119875lowast the planned berthing locationTE119904 energy consumption of ships at the port120576 energy consumption of ships per unit of time at theportn total number of quay cranes allocated to the shipqn119894 loading and unloading quantity for the 119894th quaycrane120578 the handling efficiency of the quay crane119892 efficiency coefficient whenmultiple quay cranes areworkingst119894 starting working time of the 119894th quay craneTE119902 energy consumption of the quay crane120588 energy consumption of the quay crane per unit oftimeTd horizontal transport distanceb blocks allocated to the shipbn119894 the number of containers allocated to the 119894thblock119889119894 horizontal transport distance between the berthand the 119894th blockBP economic balance between the blocksbn119894 the handling quantity allocated to the 119894th blockBayd the distance between two baysba119894 the number of bays allocated to the 119894th block119875119894119895 the position of the jth bay in the 119894th blockBs the continuity of bays in the block119892119894119895119896 the serial number of the jth bay and kth roll inthe 119894th blockLpb the parallelism of the sending containersbnlp119894 the sum of the allocated blocks in the 119894th portlp the number of the port dischargeTE119905 energy consumption of horizontal transport120582 energy consumption of the truck per unit distanceDT the delay time of the task grouptn the number of the task groupST119894119895 starting working time of yard crane jNT119894119895 the allocated handling quantity of yard crane 119895in task group i

Et119901119894 the planned completion time of task group i

120590 the loading and unloading efficiency of the yardcrane

ny the total number of yard cranes

TM the total time of yard cranes to move from oneblock to another

1199051198941198941015840 time for a yard crane to move from task group 119894 totask group 1198941015840TE119910 the moving energy consumption of the yardcranes

Ls119894119895119896 the current position of yard crane 119895 for task 119896 intask group i

Lt119894119895119896 target position of yard crane 119895 for task 119896 in taskgroup 119894vt119895 quantity of task group i

120596 energy consumption of yard crane per unit dis-tance

TE119910 the energy consumption of the yard crane

120583 the handling energy consumption of the yard craneper unit time

22 Efficiency Evaluation for Berth Scheduling Primarily thescheduling of a berth requires decisions to be made on theberthing location and the berthing time of ships There aremany factors that can impact the results including the shipspecifications the ship arrival time the loading and unload-ing quantity required for each ship the currently mooredships and the length of each shoreline ship on the berthIn this efficiency evaluation model the objectives used formaking a decision are to ensure that a ship is at port for theshortest possible time while maintaining the lowest possibleenergy consumption for the ship at port and the shortesthorizontal transport distance The calculation models forenergy consumption and efficiency evaluation for berthscheduling can be illustrated as follows

(1) Efficiency Calculation Equation for Berth Scheduling Thetime delay of a ship leaving a port is calculated using (1) andthe offset of the berthing

CT = ST + (BT minus DT) (1)

119863 = 119875 minus 119875lowast (2)

(2) Energy Consumption Calculation Equation for BerthScheduling The energy consumption of a ship at a port isdetermined by its turnaround timeThe turnaround time of aship is determined by the shiprsquos berthing time and departuretime which is within the category of berth scheduling Theenergy consumption of a ship at port is calculated using

TE119904 = CT sdot 120576 (3)

4 Scientific Programming

23 Efficiency Evaluation for Quay Crane Scheduling Thescheduling of quay cranes depends mainly on the time wheneach quay crane starts service and the distribution of eachquay craneThere aremany factors that need to be consideredincluding the number of quay cranes the current positionof each quay crane the current state of each quay cranethe shipping carts the efficiency of each quay crane and theenergy consumption of each quay crane per unit of time Inthis paper the objectives that are used for decision-makingare based on obtaining the shortest service time of ships andthe minimum energy consumption of quay cranes duringloading and unloading operations

(1) Efficiency Calculation Equation for Quay Crane Schedul-ing The service time of a ship ends once loading andunloading operations have been completed at the quay sideThe acceptable service time of the ship is calculated as follows

ST = Max119894=12119899

( st119894 + qn119894(120578 (119899)119892)) minus BT (4)

(2) Energy Consumption Calculation Equation for QuayCrane Scheduling Equation (5) gives the energy consumptioncalculation equation for quay crane scheduling as follows

TE119902 = 119899sum119894=1

qn119894 sdot ( 120578(119899)119892) sdot 120588 (5)

24 Efficiency Evaluation for Yard Scheduling Generally thescheduling of a yard includes scheduling blocks and baysThere are some additional factors that have an impact on thescheduling of a yard such as the loading and unloading ofthe ship the division of blocks the location of blocks theposition of the berthing ship and the availability of the blocksin the container terminal The objectives used for decision-making aremainly based on achieving the shortest horizontaltransportation distance the highest economic balance ofthe blocks the shortest moving distance of the yard cranesand the minimum energy consumption for the horizontaltransportation

(1) Efficiency Calculation Equation for Yard Scheduling Equa-tion (6) can be used to obtain the horizontal transportationdistance as follows

Td = 119887sum119894=1

bn119894 sdot 119889119894 (6)

For yard scheduling there are two factors that influencethe moving distance of a yard crane the concentration ofbays in a block and the continuity of the block in the bayTherefore calculation of the moving distance of a yard cranecan be broken down into two steps The first step is the

calculation of the distance between distributed bays and thesecond step is calculation of the continuity assigned to thebay in the container terminal In (7) the economic balancebetween blocks is calculated The economic balance betweenblocks is based on the difference in production value betweenthe allocated blocks with the largest and smallest productionvalues As shown in (8) the distance between bays is includedin the calculations The continuity that is assigned to a bay inthe container terminal is expressed by (9)

BP = Max119894=12119887

(bn119894) minus Min119894=12119887

(bn119894) (7)

Bayd = 119887sum119894=1

ba119894sum119895=2

(119875119894119895 minus 119875119894(119895minus1)) (8)

Bs = 119887sum119894=1

ba119894sum119895=1

119897119894119895sum119896=1

10038161003816100381610038161003816119891119894119895119896 minus 110038161003816100381610038161003816

119891119894119895119896 =

119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816 if 119892119894119895119896 = 119892(119894119895119896minus1)1 otherwise

(9)

The continuity of the sending containers can be evaluatedbased on the continuity assigned to the bay The parallelismbetween the sending containers is mainly determined basedon whether the distribution of blocks in the same port isscattered or not as shown in

Lpb = lpsum119894=1

bnlp119894 (10)

(2) Energy Consumption Calculation Equation for YardScheduling The energy consumption of horizontal trans-portation is shown in

TE119905 = Td sdot 120582 (11)

25 Efficiency Evaluation for Yard Crane Scheduling Thescheduling of yard cranes requires decision-making on thetask group needing service the start time of that service andthe number of containers to be loaded and unloaded for thatservice There are many factors impacting this schedulingincluding the block and bay of the task group the handlingefficiency of the yard crane the current position of the yardcrane and the number of yard cranes The objectives fordecision-making are mainly based on achieving the mini-mumdelay in completing a task group theminimumnumberof transitions of yard cranes and the minimum energy con-sumption of yard cranes during both moving and handling

(1) Efficiency Calculation Equation for Yard Crane SchedulingThe time delay in finishing a task group is described by (12)and the transition time of yard cranes is described by (13)

DT = tnsum119894=1

( Max119895=12ny

(ST119894119895 +NT119894119895 sdot 120590) minus Et119901119894 ) (12)

Scientific Programming 5

TM = tnsum119894=1

tnsum1198941015840=1119894 =1198941015840

nysum119895=1

1199041198951198941198941015840sdot 1199051198941198941015840

1199041198951198941198941015840=

1 If the task group 119894 is finished by yard crane 119895 then the task group 1198941015840 will be done right now0 otherwise

(13)

(2) Energy Consumption Calculation Equation for Yard CraneScheduling Equation (14) represents the moving energyconsumption of a yard crane and (15) describes the handlingenergy consumption of a yard crane as follows

TE119910 = tnsum119894=1

nysum119895=1

vt119895sum119896=1

10038161003816100381610038161003816Ls119894119895119896 minus Lt11989411989511989610038161003816100381610038161003816 sdot 120596 (14)

TEyc = nysum119894=1

tnsum119895=1

NT119894119895 sdot 120590 sdot 120583 (15)

3 Framework of the Scheduling Model

In practice the scheduling of core resources in a containerterminal consists of a series of decision-making processesDecision-making is required for scheduling of the berth quaycranes storage yard and yard cranes Since the berthingposition of ships is required to make decisions on whento implement the scheduling of quay cranes the loadingand unloading time of ships must be considered for quaycrane scheduling which is decided by the berth schedulingTherefore integration is required between the schedulingproblems for quay cranes and berths In this paper theyare considered to be a unified problem for the purposes ofdecision-making and optimization The decision objectivesfor the core resource allocation in traditional container ter-minals are mainly based on time (T such as the turnaroundtime of a ship and the delay time of a task group) and distance(D such as the offset distance of the berthing position thehorizontal transport distance and the moving distance of theyard crane) In this paper not only is the efficiency objectivetaken into consideration but also the energy consumption (119864)is taken into consideration

31 Parameter Setting Theparameters are defined as follows

BQ the decision-making variable set for integratedscheduling of the berth and quay cranesBL the decision-making variable set for yard schedul-ingYC the decision-making variable set for yard craneschedulingTC the time constraint setSC the space constraint setEC the equipment constraint set

32 Modeling of the Objective Set The optimized objectiveset for efficient scheduling of key resources in a container

terminal consists of time (119879) distance (119863) and energyconsumption (119864) The mapping relationship between theobjective set and the decision-making problem is shownin Figure 2 These three decision-making objectives can befurther embodied based on the specific scheduling problemof key resources In addition each objective includes anumber of independent components Taking the energyconsumption objective119864 as an example119864 includes the energyconsumption of ships at port 1198641 the energy consumption ofthe loading and unloading operations of quay crane 1198642 theenergy consumption of horizontal transport 1198643 the energyconsumption of moving the yard crane 1198644 and the energyconsumption of the loading and unloading operations of theyard crane 1198645 Therefore each objective can be representedby a vector composed of various factors For example 119864 canbe expressed as a vector of n subobjects as shown in (16) Ina similar way the other objectives can be expressed as shownin (17) and (18)

= (1198641 1198642 119864119899) (16)

= (1198791 1198792 119879119899) (17)

= (1198631 1198632 119863119899) (18)

33 Modeling of the Decision Variable Set The schedulingof key resources in a container terminal consists of multi-ple optimization decision-making problems including theintegrated scheduling of the berth and quay cranes yardscheduling and yard crane schedulingThedecision variablesof each decision-making problem are shown in Figure 3

The decision-making problems of the application canbe regarded as being composed of many decision-makingsubquestions For this purpose each decision problem isregarded as a vector The decision-making variable vector forintegrated scheduling of the berth and quay cranes can beindicated by BQ = bq1 bq2 bq119898 Equation (19) showsthe decision-making variable set 119863 for the scheduling of keyresources within the overall container terminal

119863 = [[[[

BQ = (bq1 bq2 bq119898)BL = (bl1 bl2 bl119899)YC = (yc1 yc2 yc119896)

]]]] (19)

34 Modeling of the Constraint Set In the energy-efficientscheduling decision-making model of key resources in acontainer terminal the constraint set is quite complicatedThe optimization decision-making model of the constraintset usually includes time constraints space constraints andequipment constraints For example the berthing time of a

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

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Applied Computational Intelligence and Soft Computing

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 3

21 Parameter Setting In this section the parameters aredefined as follows

CT the time delay of the ship leaving the portBT the berthing time of the shipDT the planned departure time of the shipST the loading and unloading time of the quay craneD the offset of the berthing position (m)P the actual berthing position119875lowast the planned berthing locationTE119904 energy consumption of ships at the port120576 energy consumption of ships per unit of time at theportn total number of quay cranes allocated to the shipqn119894 loading and unloading quantity for the 119894th quaycrane120578 the handling efficiency of the quay crane119892 efficiency coefficient whenmultiple quay cranes areworkingst119894 starting working time of the 119894th quay craneTE119902 energy consumption of the quay crane120588 energy consumption of the quay crane per unit oftimeTd horizontal transport distanceb blocks allocated to the shipbn119894 the number of containers allocated to the 119894thblock119889119894 horizontal transport distance between the berthand the 119894th blockBP economic balance between the blocksbn119894 the handling quantity allocated to the 119894th blockBayd the distance between two baysba119894 the number of bays allocated to the 119894th block119875119894119895 the position of the jth bay in the 119894th blockBs the continuity of bays in the block119892119894119895119896 the serial number of the jth bay and kth roll inthe 119894th blockLpb the parallelism of the sending containersbnlp119894 the sum of the allocated blocks in the 119894th portlp the number of the port dischargeTE119905 energy consumption of horizontal transport120582 energy consumption of the truck per unit distanceDT the delay time of the task grouptn the number of the task groupST119894119895 starting working time of yard crane jNT119894119895 the allocated handling quantity of yard crane 119895in task group i

Et119901119894 the planned completion time of task group i

120590 the loading and unloading efficiency of the yardcrane

ny the total number of yard cranes

TM the total time of yard cranes to move from oneblock to another

1199051198941198941015840 time for a yard crane to move from task group 119894 totask group 1198941015840TE119910 the moving energy consumption of the yardcranes

Ls119894119895119896 the current position of yard crane 119895 for task 119896 intask group i

Lt119894119895119896 target position of yard crane 119895 for task 119896 in taskgroup 119894vt119895 quantity of task group i

120596 energy consumption of yard crane per unit dis-tance

TE119910 the energy consumption of the yard crane

120583 the handling energy consumption of the yard craneper unit time

22 Efficiency Evaluation for Berth Scheduling Primarily thescheduling of a berth requires decisions to be made on theberthing location and the berthing time of ships There aremany factors that can impact the results including the shipspecifications the ship arrival time the loading and unload-ing quantity required for each ship the currently mooredships and the length of each shoreline ship on the berthIn this efficiency evaluation model the objectives used formaking a decision are to ensure that a ship is at port for theshortest possible time while maintaining the lowest possibleenergy consumption for the ship at port and the shortesthorizontal transport distance The calculation models forenergy consumption and efficiency evaluation for berthscheduling can be illustrated as follows

(1) Efficiency Calculation Equation for Berth Scheduling Thetime delay of a ship leaving a port is calculated using (1) andthe offset of the berthing

CT = ST + (BT minus DT) (1)

119863 = 119875 minus 119875lowast (2)

(2) Energy Consumption Calculation Equation for BerthScheduling The energy consumption of a ship at a port isdetermined by its turnaround timeThe turnaround time of aship is determined by the shiprsquos berthing time and departuretime which is within the category of berth scheduling Theenergy consumption of a ship at port is calculated using

TE119904 = CT sdot 120576 (3)

4 Scientific Programming

23 Efficiency Evaluation for Quay Crane Scheduling Thescheduling of quay cranes depends mainly on the time wheneach quay crane starts service and the distribution of eachquay craneThere aremany factors that need to be consideredincluding the number of quay cranes the current positionof each quay crane the current state of each quay cranethe shipping carts the efficiency of each quay crane and theenergy consumption of each quay crane per unit of time Inthis paper the objectives that are used for decision-makingare based on obtaining the shortest service time of ships andthe minimum energy consumption of quay cranes duringloading and unloading operations

(1) Efficiency Calculation Equation for Quay Crane Schedul-ing The service time of a ship ends once loading andunloading operations have been completed at the quay sideThe acceptable service time of the ship is calculated as follows

ST = Max119894=12119899

( st119894 + qn119894(120578 (119899)119892)) minus BT (4)

(2) Energy Consumption Calculation Equation for QuayCrane Scheduling Equation (5) gives the energy consumptioncalculation equation for quay crane scheduling as follows

TE119902 = 119899sum119894=1

qn119894 sdot ( 120578(119899)119892) sdot 120588 (5)

24 Efficiency Evaluation for Yard Scheduling Generally thescheduling of a yard includes scheduling blocks and baysThere are some additional factors that have an impact on thescheduling of a yard such as the loading and unloading ofthe ship the division of blocks the location of blocks theposition of the berthing ship and the availability of the blocksin the container terminal The objectives used for decision-making aremainly based on achieving the shortest horizontaltransportation distance the highest economic balance ofthe blocks the shortest moving distance of the yard cranesand the minimum energy consumption for the horizontaltransportation

(1) Efficiency Calculation Equation for Yard Scheduling Equa-tion (6) can be used to obtain the horizontal transportationdistance as follows

Td = 119887sum119894=1

bn119894 sdot 119889119894 (6)

For yard scheduling there are two factors that influencethe moving distance of a yard crane the concentration ofbays in a block and the continuity of the block in the bayTherefore calculation of the moving distance of a yard cranecan be broken down into two steps The first step is the

calculation of the distance between distributed bays and thesecond step is calculation of the continuity assigned to thebay in the container terminal In (7) the economic balancebetween blocks is calculated The economic balance betweenblocks is based on the difference in production value betweenthe allocated blocks with the largest and smallest productionvalues As shown in (8) the distance between bays is includedin the calculations The continuity that is assigned to a bay inthe container terminal is expressed by (9)

BP = Max119894=12119887

(bn119894) minus Min119894=12119887

(bn119894) (7)

Bayd = 119887sum119894=1

ba119894sum119895=2

(119875119894119895 minus 119875119894(119895minus1)) (8)

Bs = 119887sum119894=1

ba119894sum119895=1

119897119894119895sum119896=1

10038161003816100381610038161003816119891119894119895119896 minus 110038161003816100381610038161003816

119891119894119895119896 =

119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816 if 119892119894119895119896 = 119892(119894119895119896minus1)1 otherwise

(9)

The continuity of the sending containers can be evaluatedbased on the continuity assigned to the bay The parallelismbetween the sending containers is mainly determined basedon whether the distribution of blocks in the same port isscattered or not as shown in

Lpb = lpsum119894=1

bnlp119894 (10)

(2) Energy Consumption Calculation Equation for YardScheduling The energy consumption of horizontal trans-portation is shown in

TE119905 = Td sdot 120582 (11)

25 Efficiency Evaluation for Yard Crane Scheduling Thescheduling of yard cranes requires decision-making on thetask group needing service the start time of that service andthe number of containers to be loaded and unloaded for thatservice There are many factors impacting this schedulingincluding the block and bay of the task group the handlingefficiency of the yard crane the current position of the yardcrane and the number of yard cranes The objectives fordecision-making are mainly based on achieving the mini-mumdelay in completing a task group theminimumnumberof transitions of yard cranes and the minimum energy con-sumption of yard cranes during both moving and handling

(1) Efficiency Calculation Equation for Yard Crane SchedulingThe time delay in finishing a task group is described by (12)and the transition time of yard cranes is described by (13)

DT = tnsum119894=1

( Max119895=12ny

(ST119894119895 +NT119894119895 sdot 120590) minus Et119901119894 ) (12)

Scientific Programming 5

TM = tnsum119894=1

tnsum1198941015840=1119894 =1198941015840

nysum119895=1

1199041198951198941198941015840sdot 1199051198941198941015840

1199041198951198941198941015840=

1 If the task group 119894 is finished by yard crane 119895 then the task group 1198941015840 will be done right now0 otherwise

(13)

(2) Energy Consumption Calculation Equation for Yard CraneScheduling Equation (14) represents the moving energyconsumption of a yard crane and (15) describes the handlingenergy consumption of a yard crane as follows

TE119910 = tnsum119894=1

nysum119895=1

vt119895sum119896=1

10038161003816100381610038161003816Ls119894119895119896 minus Lt11989411989511989610038161003816100381610038161003816 sdot 120596 (14)

TEyc = nysum119894=1

tnsum119895=1

NT119894119895 sdot 120590 sdot 120583 (15)

3 Framework of the Scheduling Model

In practice the scheduling of core resources in a containerterminal consists of a series of decision-making processesDecision-making is required for scheduling of the berth quaycranes storage yard and yard cranes Since the berthingposition of ships is required to make decisions on whento implement the scheduling of quay cranes the loadingand unloading time of ships must be considered for quaycrane scheduling which is decided by the berth schedulingTherefore integration is required between the schedulingproblems for quay cranes and berths In this paper theyare considered to be a unified problem for the purposes ofdecision-making and optimization The decision objectivesfor the core resource allocation in traditional container ter-minals are mainly based on time (T such as the turnaroundtime of a ship and the delay time of a task group) and distance(D such as the offset distance of the berthing position thehorizontal transport distance and the moving distance of theyard crane) In this paper not only is the efficiency objectivetaken into consideration but also the energy consumption (119864)is taken into consideration

31 Parameter Setting Theparameters are defined as follows

BQ the decision-making variable set for integratedscheduling of the berth and quay cranesBL the decision-making variable set for yard schedul-ingYC the decision-making variable set for yard craneschedulingTC the time constraint setSC the space constraint setEC the equipment constraint set

32 Modeling of the Objective Set The optimized objectiveset for efficient scheduling of key resources in a container

terminal consists of time (119879) distance (119863) and energyconsumption (119864) The mapping relationship between theobjective set and the decision-making problem is shownin Figure 2 These three decision-making objectives can befurther embodied based on the specific scheduling problemof key resources In addition each objective includes anumber of independent components Taking the energyconsumption objective119864 as an example119864 includes the energyconsumption of ships at port 1198641 the energy consumption ofthe loading and unloading operations of quay crane 1198642 theenergy consumption of horizontal transport 1198643 the energyconsumption of moving the yard crane 1198644 and the energyconsumption of the loading and unloading operations of theyard crane 1198645 Therefore each objective can be representedby a vector composed of various factors For example 119864 canbe expressed as a vector of n subobjects as shown in (16) Ina similar way the other objectives can be expressed as shownin (17) and (18)

= (1198641 1198642 119864119899) (16)

= (1198791 1198792 119879119899) (17)

= (1198631 1198632 119863119899) (18)

33 Modeling of the Decision Variable Set The schedulingof key resources in a container terminal consists of multi-ple optimization decision-making problems including theintegrated scheduling of the berth and quay cranes yardscheduling and yard crane schedulingThedecision variablesof each decision-making problem are shown in Figure 3

The decision-making problems of the application canbe regarded as being composed of many decision-makingsubquestions For this purpose each decision problem isregarded as a vector The decision-making variable vector forintegrated scheduling of the berth and quay cranes can beindicated by BQ = bq1 bq2 bq119898 Equation (19) showsthe decision-making variable set 119863 for the scheduling of keyresources within the overall container terminal

119863 = [[[[

BQ = (bq1 bq2 bq119898)BL = (bl1 bl2 bl119899)YC = (yc1 yc2 yc119896)

]]]] (19)

34 Modeling of the Constraint Set In the energy-efficientscheduling decision-making model of key resources in acontainer terminal the constraint set is quite complicatedThe optimization decision-making model of the constraintset usually includes time constraints space constraints andequipment constraints For example the berthing time of a

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

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Applied Computational Intelligence and Soft Computing

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httpwwwhindawicom Volume 2014

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Advances in

Computer EngineeringAdvances in

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4 Scientific Programming

23 Efficiency Evaluation for Quay Crane Scheduling Thescheduling of quay cranes depends mainly on the time wheneach quay crane starts service and the distribution of eachquay craneThere aremany factors that need to be consideredincluding the number of quay cranes the current positionof each quay crane the current state of each quay cranethe shipping carts the efficiency of each quay crane and theenergy consumption of each quay crane per unit of time Inthis paper the objectives that are used for decision-makingare based on obtaining the shortest service time of ships andthe minimum energy consumption of quay cranes duringloading and unloading operations

(1) Efficiency Calculation Equation for Quay Crane Schedul-ing The service time of a ship ends once loading andunloading operations have been completed at the quay sideThe acceptable service time of the ship is calculated as follows

ST = Max119894=12119899

( st119894 + qn119894(120578 (119899)119892)) minus BT (4)

(2) Energy Consumption Calculation Equation for QuayCrane Scheduling Equation (5) gives the energy consumptioncalculation equation for quay crane scheduling as follows

TE119902 = 119899sum119894=1

qn119894 sdot ( 120578(119899)119892) sdot 120588 (5)

24 Efficiency Evaluation for Yard Scheduling Generally thescheduling of a yard includes scheduling blocks and baysThere are some additional factors that have an impact on thescheduling of a yard such as the loading and unloading ofthe ship the division of blocks the location of blocks theposition of the berthing ship and the availability of the blocksin the container terminal The objectives used for decision-making aremainly based on achieving the shortest horizontaltransportation distance the highest economic balance ofthe blocks the shortest moving distance of the yard cranesand the minimum energy consumption for the horizontaltransportation

(1) Efficiency Calculation Equation for Yard Scheduling Equa-tion (6) can be used to obtain the horizontal transportationdistance as follows

Td = 119887sum119894=1

bn119894 sdot 119889119894 (6)

For yard scheduling there are two factors that influencethe moving distance of a yard crane the concentration ofbays in a block and the continuity of the block in the bayTherefore calculation of the moving distance of a yard cranecan be broken down into two steps The first step is the

calculation of the distance between distributed bays and thesecond step is calculation of the continuity assigned to thebay in the container terminal In (7) the economic balancebetween blocks is calculated The economic balance betweenblocks is based on the difference in production value betweenthe allocated blocks with the largest and smallest productionvalues As shown in (8) the distance between bays is includedin the calculations The continuity that is assigned to a bay inthe container terminal is expressed by (9)

BP = Max119894=12119887

(bn119894) minus Min119894=12119887

(bn119894) (7)

Bayd = 119887sum119894=1

ba119894sum119895=2

(119875119894119895 minus 119875119894(119895minus1)) (8)

Bs = 119887sum119894=1

ba119894sum119895=1

119897119894119895sum119896=1

10038161003816100381610038161003816119891119894119895119896 minus 110038161003816100381610038161003816

119891119894119895119896 =

119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816119892119894119895119896 minus 119892(119894119895119896minus1)10038161003816100381610038161003816 if 119892119894119895119896 = 119892(119894119895119896minus1)1 otherwise

(9)

The continuity of the sending containers can be evaluatedbased on the continuity assigned to the bay The parallelismbetween the sending containers is mainly determined basedon whether the distribution of blocks in the same port isscattered or not as shown in

Lpb = lpsum119894=1

bnlp119894 (10)

(2) Energy Consumption Calculation Equation for YardScheduling The energy consumption of horizontal trans-portation is shown in

TE119905 = Td sdot 120582 (11)

25 Efficiency Evaluation for Yard Crane Scheduling Thescheduling of yard cranes requires decision-making on thetask group needing service the start time of that service andthe number of containers to be loaded and unloaded for thatservice There are many factors impacting this schedulingincluding the block and bay of the task group the handlingefficiency of the yard crane the current position of the yardcrane and the number of yard cranes The objectives fordecision-making are mainly based on achieving the mini-mumdelay in completing a task group theminimumnumberof transitions of yard cranes and the minimum energy con-sumption of yard cranes during both moving and handling

(1) Efficiency Calculation Equation for Yard Crane SchedulingThe time delay in finishing a task group is described by (12)and the transition time of yard cranes is described by (13)

DT = tnsum119894=1

( Max119895=12ny

(ST119894119895 +NT119894119895 sdot 120590) minus Et119901119894 ) (12)

Scientific Programming 5

TM = tnsum119894=1

tnsum1198941015840=1119894 =1198941015840

nysum119895=1

1199041198951198941198941015840sdot 1199051198941198941015840

1199041198951198941198941015840=

1 If the task group 119894 is finished by yard crane 119895 then the task group 1198941015840 will be done right now0 otherwise

(13)

(2) Energy Consumption Calculation Equation for Yard CraneScheduling Equation (14) represents the moving energyconsumption of a yard crane and (15) describes the handlingenergy consumption of a yard crane as follows

TE119910 = tnsum119894=1

nysum119895=1

vt119895sum119896=1

10038161003816100381610038161003816Ls119894119895119896 minus Lt11989411989511989610038161003816100381610038161003816 sdot 120596 (14)

TEyc = nysum119894=1

tnsum119895=1

NT119894119895 sdot 120590 sdot 120583 (15)

3 Framework of the Scheduling Model

In practice the scheduling of core resources in a containerterminal consists of a series of decision-making processesDecision-making is required for scheduling of the berth quaycranes storage yard and yard cranes Since the berthingposition of ships is required to make decisions on whento implement the scheduling of quay cranes the loadingand unloading time of ships must be considered for quaycrane scheduling which is decided by the berth schedulingTherefore integration is required between the schedulingproblems for quay cranes and berths In this paper theyare considered to be a unified problem for the purposes ofdecision-making and optimization The decision objectivesfor the core resource allocation in traditional container ter-minals are mainly based on time (T such as the turnaroundtime of a ship and the delay time of a task group) and distance(D such as the offset distance of the berthing position thehorizontal transport distance and the moving distance of theyard crane) In this paper not only is the efficiency objectivetaken into consideration but also the energy consumption (119864)is taken into consideration

31 Parameter Setting Theparameters are defined as follows

BQ the decision-making variable set for integratedscheduling of the berth and quay cranesBL the decision-making variable set for yard schedul-ingYC the decision-making variable set for yard craneschedulingTC the time constraint setSC the space constraint setEC the equipment constraint set

32 Modeling of the Objective Set The optimized objectiveset for efficient scheduling of key resources in a container

terminal consists of time (119879) distance (119863) and energyconsumption (119864) The mapping relationship between theobjective set and the decision-making problem is shownin Figure 2 These three decision-making objectives can befurther embodied based on the specific scheduling problemof key resources In addition each objective includes anumber of independent components Taking the energyconsumption objective119864 as an example119864 includes the energyconsumption of ships at port 1198641 the energy consumption ofthe loading and unloading operations of quay crane 1198642 theenergy consumption of horizontal transport 1198643 the energyconsumption of moving the yard crane 1198644 and the energyconsumption of the loading and unloading operations of theyard crane 1198645 Therefore each objective can be representedby a vector composed of various factors For example 119864 canbe expressed as a vector of n subobjects as shown in (16) Ina similar way the other objectives can be expressed as shownin (17) and (18)

= (1198641 1198642 119864119899) (16)

= (1198791 1198792 119879119899) (17)

= (1198631 1198632 119863119899) (18)

33 Modeling of the Decision Variable Set The schedulingof key resources in a container terminal consists of multi-ple optimization decision-making problems including theintegrated scheduling of the berth and quay cranes yardscheduling and yard crane schedulingThedecision variablesof each decision-making problem are shown in Figure 3

The decision-making problems of the application canbe regarded as being composed of many decision-makingsubquestions For this purpose each decision problem isregarded as a vector The decision-making variable vector forintegrated scheduling of the berth and quay cranes can beindicated by BQ = bq1 bq2 bq119898 Equation (19) showsthe decision-making variable set 119863 for the scheduling of keyresources within the overall container terminal

119863 = [[[[

BQ = (bq1 bq2 bq119898)BL = (bl1 bl2 bl119899)YC = (yc1 yc2 yc119896)

]]]] (19)

34 Modeling of the Constraint Set In the energy-efficientscheduling decision-making model of key resources in acontainer terminal the constraint set is quite complicatedThe optimization decision-making model of the constraintset usually includes time constraints space constraints andequipment constraints For example the berthing time of a

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 5

TM = tnsum119894=1

tnsum1198941015840=1119894 =1198941015840

nysum119895=1

1199041198951198941198941015840sdot 1199051198941198941015840

1199041198951198941198941015840=

1 If the task group 119894 is finished by yard crane 119895 then the task group 1198941015840 will be done right now0 otherwise

(13)

(2) Energy Consumption Calculation Equation for Yard CraneScheduling Equation (14) represents the moving energyconsumption of a yard crane and (15) describes the handlingenergy consumption of a yard crane as follows

TE119910 = tnsum119894=1

nysum119895=1

vt119895sum119896=1

10038161003816100381610038161003816Ls119894119895119896 minus Lt11989411989511989610038161003816100381610038161003816 sdot 120596 (14)

TEyc = nysum119894=1

tnsum119895=1

NT119894119895 sdot 120590 sdot 120583 (15)

3 Framework of the Scheduling Model

In practice the scheduling of core resources in a containerterminal consists of a series of decision-making processesDecision-making is required for scheduling of the berth quaycranes storage yard and yard cranes Since the berthingposition of ships is required to make decisions on whento implement the scheduling of quay cranes the loadingand unloading time of ships must be considered for quaycrane scheduling which is decided by the berth schedulingTherefore integration is required between the schedulingproblems for quay cranes and berths In this paper theyare considered to be a unified problem for the purposes ofdecision-making and optimization The decision objectivesfor the core resource allocation in traditional container ter-minals are mainly based on time (T such as the turnaroundtime of a ship and the delay time of a task group) and distance(D such as the offset distance of the berthing position thehorizontal transport distance and the moving distance of theyard crane) In this paper not only is the efficiency objectivetaken into consideration but also the energy consumption (119864)is taken into consideration

31 Parameter Setting Theparameters are defined as follows

BQ the decision-making variable set for integratedscheduling of the berth and quay cranesBL the decision-making variable set for yard schedul-ingYC the decision-making variable set for yard craneschedulingTC the time constraint setSC the space constraint setEC the equipment constraint set

32 Modeling of the Objective Set The optimized objectiveset for efficient scheduling of key resources in a container

terminal consists of time (119879) distance (119863) and energyconsumption (119864) The mapping relationship between theobjective set and the decision-making problem is shownin Figure 2 These three decision-making objectives can befurther embodied based on the specific scheduling problemof key resources In addition each objective includes anumber of independent components Taking the energyconsumption objective119864 as an example119864 includes the energyconsumption of ships at port 1198641 the energy consumption ofthe loading and unloading operations of quay crane 1198642 theenergy consumption of horizontal transport 1198643 the energyconsumption of moving the yard crane 1198644 and the energyconsumption of the loading and unloading operations of theyard crane 1198645 Therefore each objective can be representedby a vector composed of various factors For example 119864 canbe expressed as a vector of n subobjects as shown in (16) Ina similar way the other objectives can be expressed as shownin (17) and (18)

= (1198641 1198642 119864119899) (16)

= (1198791 1198792 119879119899) (17)

= (1198631 1198632 119863119899) (18)

33 Modeling of the Decision Variable Set The schedulingof key resources in a container terminal consists of multi-ple optimization decision-making problems including theintegrated scheduling of the berth and quay cranes yardscheduling and yard crane schedulingThedecision variablesof each decision-making problem are shown in Figure 3

The decision-making problems of the application canbe regarded as being composed of many decision-makingsubquestions For this purpose each decision problem isregarded as a vector The decision-making variable vector forintegrated scheduling of the berth and quay cranes can beindicated by BQ = bq1 bq2 bq119898 Equation (19) showsthe decision-making variable set 119863 for the scheduling of keyresources within the overall container terminal

119863 = [[[[

BQ = (bq1 bq2 bq119898)BL = (bl1 bl2 bl119899)YC = (yc1 yc2 yc119896)

]]]] (19)

34 Modeling of the Constraint Set In the energy-efficientscheduling decision-making model of key resources in acontainer terminal the constraint set is quite complicatedThe optimization decision-making model of the constraintset usually includes time constraints space constraints andequipment constraints For example the berthing time of a

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Scientific Programming

Objectives set for thescheduling of key resources

Energyconsumption

E

EfficiencyP

TimeT

DistanceD

Energy-efficientproductionobjectivessystem in

the containerterminal

Ships in port

Handling operationby quay crane

Horizontal transport

Yard crane

Vertical handlingoperation byyard crane

Turnround of a ship

Service time ofthe ship

Delay time

Berth offset

Horizontaltransport distance

Economic balance

Distance betweentwo bays

Continuity ofblock in bays

Parallelism ofsending containers

Number oftransitions

Scheduling ofberth

Scheduling ofquay crane

Scheduling ofblock

Scheduling ofbay

Scheduling ofyard crane

Decision-making problemfor the scheduling of

key resources

Integratedscheduling of

berth andquay crane

Scheduling ofyard

Decision-makingproblem

in thecontainerterminal

Figure 2 Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient schedulingof a container terminal

ship must be greater than or equal to the arrival time of theship Then the berthing location of a ship must be withinthe quay side line Additionally the number of assigned quaycranes must be less than or equal to the total number ofquay cranes in the wharf Therefore the constraint set of theschedulingmodel can be expressed as119862 in (20)119862 is made upof the time constraint set TC the space constraint set ST andthe equipment constraint set EC Each constraint is expressedwithin this equation and the inequality constraints are givenin (21)

119862 = [[[[

TC = (tc1 tc2 tc119898)SC = (sc1 sc2 sc119899)EC = (ec1 ec2 ec119896)

]]]]

(20)

st 119862119906 = 0119862V le 0 (21)

35 Modeling of Decisions As previously discussed in theefficient decision-making scheduling model of key resources

a mapping relationship exists between the decision-makingvariable set the constraint set and the objective set In thismodel the calculation model for the objective functions andthe constraint conditions is comprised of decision-makingvariables and constants Equation (22) proposes the mappingrelationship between the objective set and the decision-making variable set Additionally the mapping relationshipbetween the constraint set and the decision-making variableset is expressed in (23)

[[[

119864 = 119864 (BQBLYC)119879 = 119879 (BQBLYC)119871 = 119871 (BQBLYC)

]]]

(22)

[[[

TC = TC (BQBLYC)SC = SC (BQBLYC)EC = EC (BQBLYC)

]]] (23)

The mapping relationship between the decision-makingvariable set the constraint set and the objective set in the

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 7

Decisionvariables

set

of block

Allocated blocks

Allocated handling quantity

Integrated schedulingof berth and quay

crane

Berthing time of ship

Berthing location of ship

Quay crane serving ship

Start working time of quay crane

Handling quantity of quay crane

The schedulingof bay

Allocated bays

Bays should be stocked

Thescheduling

The scheduling

of yard

Thescheduling

of yard

crane

Yard crane doing task

Start working of yard crane

Handling quantity of yard crane

Figure 3 Decision variable set for key resource energy-efficient scheduling of the container terminal

efficient decision-making scheduling model of key resourcesin the container terminal is shown in Figure 4 Based on care-ful discussion of the decision-making variable set the con-straint set and the objective set an overall and efficientscheduling model for the core resources was finally obtainedas shown in (24) 1205961 1205962 and 1205963 represent the differentweights of the objective function in (24)

objective function Min119891

= [[[[

1205961 sdot 119864 (BQBLYC)1205962 sdot 119879 (BQBLYC)1205963 sdot 119871 (BQBLYC)

]]]]

(24)

constraint condition[[[[

TC119906 (BQBLYC)SC119906 (BQBLYC)EC119906 (BQBLYC)

]]]]= 0 (25)

[[[[

TCV (BQBLYC)SCV (BQBLYC)ECV (BQBLYC)

]]]]le 0 (26)

Mapping relationship

Constraint set anddecision variable set

Objective set anddecision variable set

Objective setConstraint setDecisionvariable set

[[[[[

E

T

D

]]]]]

[[[[

]]]]

TC

SC

EC

[[[[

]]]]

E = E(BQ BLYC)

T = T(BQ BLYC)

L = L(BQ BLYC)

BQ

BL

YC

[[[[

]]]]

TC = TC(BQ BLYC)

SC = SC(BQ BLYC)

EC = EC(BQ BLYC)

[[[[

]]]]

Figure 4 Mapping relationship between the objective set con-straint set and decision variable set for key resource energy-efficientscheduling of a container terminal

4 Conclusions

This paper has firstly described the combination of keyresources scheduling and energy-efficient operation in a con-tainer terminal An energy-efficient evaluation model for keyresource scheduling has then been proposed The objectiveset decision variable set and constraint set of key resource

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Scientific Programming

scheduling of container terminals for energy-efficient opera-tion are then established in this paper At the same time theirmapping relationship is carefully analyzed and the systemstructure of the key resource scheduling for energy-efficientoperation in a container terminal is finally proposed

In future studies we will establish an efficient operationprocess analysis framework for container terminals and sub-division of the evaluation objective will be studied on thisbasis In addition an evaluation index system for an efficientoperation process will be established which will includecarbon load properties

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by funding from Shanghai Scienceand Technology Committee (16DZ2349900 16DZ120140216DZ2340400 16040501500 15590501700 14DZ2280200and 14170501500) National Natural Science Foundation ofChina (61540045 and 71602114) Shanghai Municipal Educa-tion Commission (14CG48) and Shanghai Talent Develop-ment Fund

References

[1] S Wang X Qu and Y Yang ldquoEstimation of the perceivedvalue of transit time for containerized cargoesrdquo TransportationResearch Part A Policy and Practice vol 78 pp 298ndash308 2015

[2] B Prindle M Eldridge M Eckhardt and A Frederick ldquoThetwin pillars of sustainable energy synergies between energy effi-ciency and renewable energy technology and policyrdquo 2008httpaceeeorg

[3] A B Lovins ldquoEnergy strategy the road not takenrdquo ForeignAffairs vol 55 no 1 pp 65ndash96 1976

[4] S Breukers and E Heiskanen ldquoInteraction schemes for 16successful demand-side managementrdquo Deliverable 5 of theChanging Behaviour project Funded by the EC 2009

[5] IMC Services ldquoStrategic planning and port operations plan-ningrdquo Tech Rep IMC Services Paitilla Panama 2009

[6] M Grunow H-O Gunther and M Lehmann ldquoStrategies fordispatching AGVs at automated seaport container terminalsrdquoOR Spectrum vol 28 no 4 pp 587ndash610 2006

[7] D Briskorn A Drexl and S Hartmann ldquoInventory-based dis-patching of automated guided vehicles on container terminalsrdquoOR Spectrum vol 28 no 4 pp 611ndash630 2006

[8] S Wang ldquoA novel hybrid-link-based container routing modelrdquoTransportation Research Part E Logistics and TransportationReview vol 61 pp 165ndash175 2014

[9] SWang ldquoEfficiency and equity of speed limits in transportationnetworksrdquo Transportation Research Part C Emerging Technologies vol 32 pp 61ndash75 2013

[10] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[11] X Qu J Zhang SWang and Z Liu ldquoModelling follow up timeat a single-lane roundaboutrdquo Journal of Traffic and Transporta-tion Engineering vol 1 no 2 pp 97ndash102 2014

[12] D Steenken S Voszlig and R Stahlbock ldquoContainer terminaloperation and operations researchmdasha classification and litera-ture reviewrdquo OR Spectrum vol 26 no 1 pp 3ndash49 2004

[13] A Imai E Nishimura and S Papadimitriou ldquoThe dynamicberth allocation problem for a container portrdquo TransportationResearch Part B Methodological vol 35 no 4 pp 401ndash417 2001

[14] K H Kim and K C Moon ldquoBerth scheduling by simulatedannealingrdquo Transportation Research Part B Methodological vol37 no 6 pp 541ndash560 2003

[15] K T Park andK H Kim ldquoBerth scheduling for container term-inals by using a sub-gradient optimization techniquerdquo Journalof the Operational Research Society vol 53 no 9 pp 1054ndash10622002

[16] Y Guan W-Q Xiao R K Cheung and C-L Li ldquoA multipro-cessor task scheduling model for berth allocation heuristic andworst-case analysisrdquo Operations Research Letters vol 30 no 5pp 343ndash350 2002

[17] D Chang W Yan C-H Chen and Z Jiang ldquoA berth alloca-tion strategy using heuristics algorithm and simulation opti-misationrdquo International Journal of Computer Applications inTechnology vol 32 no 4 pp 272ndash281 2008

[18] P Legato and R MMazza ldquoBerth planning and resources opti-misation at a container terminal via discrete event simulationrdquoEuropean Journal of Operational Research vol 133 no 3 pp537ndash547 2001

[19] C Q Zhang J Y Liu Y-W Wan K G Murty and R J LinnldquoStorage space allocation in container terminalsrdquo Transporta-tion Research Part BMethodological vol 37 no 10 pp 883ndash9032003

[20] P Chen Z H Fu and L Adrew ldquoThe yard allocation problemrdquoin Proceedings of the 18th National Conference on Artificial Intel-ligence pp 56ndash65 Edmonton Canada 2002

[21] R Linn J-Y Liu Y-WWan C Zhang and K G Murty ldquoRub-ber tired gantry crane deployment for container yard opera-tionrdquo Computers amp Industrial Engineering vol 45 no 3 pp429ndash442 2003

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014