Research Article Collaborative Management of Complex Major … · 2019. 7. 30. · Research Article...

Research ArticleCollaborative Management of Complex Major ConstructionProjects AnyLogic-Based Simulation Modelling

Na Zhao and Shi An

School of Management Harbin Institute of Technology Heilongjiang 150001 China

Correspondence should be addressed to Shi An zhaonahiteducn

Received 9 September 2015 Revised 5 December 2015 Accepted 11 January 2016

Academic Editor Miguel Angel Lopez

Copyright copy 2016 N Zhao and S An This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Complex supply chain system collaborative management of major construction projects effectively integrates the differentparticipants in the construction project This paper establishes a simulation model based on AnyLogic to reveal the collaborativeelements in the complex supply chain management system and the modes of action as well as the transmission problems of theintent information Thus it is promoting the participants to become an organism with coordinated development and coevolutionThis study can help improve the efficiency and management of the complex system of major construction projects

1 Introduction

Major constructions are surged unimaginably in demandalong with the development of science technology and soci-ety According toMorgan Stanley research report the emerg-ing economies are expected to spend $217 trillion for majorinfrastructure projects between 2009 and 2019 Like mostcountries the Chinese government will spend $9 trillionwhich is the 12ofGDPon themajor constructions [1]How-ever the major constructions often have some urgent prob-lems in the collaborative management field and suffer manyproblems and shortcomings from the traditional mode ofproject management for example the project cost exceedingbudgets the project duration delays and the ownersrsquo dissat-isfaction

Some basic characteristics of modern major constructionprojects are long construction period large investment andcomplex organization relationship Although there is no lin-early proportional relationship between scale and complexityhigh construction cost is a common characteristic of complexmajor construction projects In general the more complexmajor construction projects have both a longer constructionperiod and a higher cost [2] At the same time the fieldsinvolved in major construction projects are increasing suchas transportation real estate and medical fields It leads to

the major construction project which involves more orga-nizations Therefore the major construction projects needto organize the organizations and people with differentfunctions and experiences which further increase the orga-nizational complexity

In modern major construction projects the externalcharacteristics of culture and environment are strongeruncertainty and turbulence The unforeseeable factors in theimplementation process of major construction projects haveincreased Not only are projects affected by the local govern-ments and the social economic and cultural environmentsbut they are restricted by local resources climate and geol-ogy In particularmultiple participants ofmajor constructionprojects such as the owner consulting party designer con-tractors suppliers and operators have different social psy-chologies cultures habits and specialties which increasesthe difficulty in communication [3 4] In addition with theintensifying international competition in major construc-tion projects and the increasingly internationally cooperatedmajor construction projects participants are often from dif-ferent countries It is becausemost of themajor constructionsof the tender are globally oriented They seek the mostsuitable contractor in the world For example throughout theworld many countries are actively striving for high-speed rail

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2016 Article ID 6195673 8 pageshttpdxdoiorg10115520166195673

2 Discrete Dynamics in Nature and Society

projects Some factors increase the risks of major construc-tion projects Major projects have different social systemscultures and legal backgrounds and are in different lan-guages which increase barriers to communication and thecomplexity of project management The increasing environ-mental uncertainty is the main source leading to the com-plexity of major construction project [5]

Based on the above analysis the traditional process ofmajor construction projects is needed to innovate and con-solidate the management It is difficult for traditional majorconstruction projects to use a production process similar tothat of other industries The owners cannot obtain completebuilding products and perfect serviceThey have no ability tomanagemajor construction projects but have to participate inthe construction process They must perform complex man-agement work and bear the resulting responsibility leading tomany entanglements [6] In addition due to the specialty lim-itation of major construction projects it has different span-ning periods or implementation parities So it is hard to coor-dinate between a superior and an inferior and this leads todiscontinuity of management at last

Major construction projects have their own generalobjectives and requirements but due to the different organi-zation tasks and persons responsible in different phases thetasks are undertaken by different enterprises resulting in theseparation of project organization inconsistent objectivesand discrete responsibilities Due to the inconsistent objec-tives among the participants they balance each other leadingto tense relationships and low working efficiency whichinhibits enthusiasm and creativity Significant costs time andenergy are spent on various working interfaces [7] Becausethe interests of the participants of a project have nothing to dowith its ultimate benefit peoplersquos short-term actions are moreserious than those in other organizations which easily pro-duce the ideal for all constructionThe participants pay atten-tion to the short-term local interests and ignore the operationstatus of the project and the requirement of continuousdevelopment thus failing to realize the general optimizationof the life cycle of a major construction project Moreoverthere are obvious blind areas in the organizational responsi-bility systemwhich increases the risks for all participants Forexample governments and manufacturers must use positivepolitical connections to achieve product protection andsupervision of safety throughout the supply chain [8] and theagentrsquos working efficiency is decreased which may erode thevalue of the company [9]

The long construction period large investment complexorganizational relationship uncertain cultural environmentand breaking in phase of major construction projects areobjective problems that are difficult to solve However com-plex objective and information isolation can be improvedthrough management The traditional management systemmanaging mode and idea of major construction projectscannot satisfy and adapt to the needs of complex key projectmanagement [10] The complexity of a major constructionproject raises new requirements onmanagementThus it hasimportant theoretical and realistic significance in the researchof the collaboration of the complex system ofmajor construc-tion projects [11]

2 Literature Review

The following subsections are talking about collaborativemanagement of complex major construction projects whichare based on AnyLogic The research subject is a complexsystem of major construction project The research perspec-tives of collaborative management are from the relation-ship among the participants through mathematical analysisadopting the research methods of simulation modelling Inthis paper the existing research as theoretical basis stands ina new perspective to discuss the coordinated management ofmajor constructions

21 Complex Supply Chain of Major Construction Projects Amajor construction project supply chain is called CPSC Thesimulationmodels are applied to study a specific coordinationmechanism where coordination requirements are producedin different departments with complex relationships in keyorganizations In addition it is considered that the VDT(Virtual Design Team) model is more suitable for research ofprojects with unpredictable factors It is a formal method fordeveloping the newmicrolevel behavioral mechanisms as theprimary point of departure from the aspect of informationprocessing And the microcontingency model generates a setof testable hypotheses related to these theorized microlevelbehaviors [12] Mihm et al studied the impact of the hierar-chical organizational structure on the speed of the searchingdecision-making plan and the stability and quality of theproblem solutions by combining mathematical analysis andsimulation models [13] Cope et al pointed out that NASAfaced the difficulty of how to effectively manage and coordi-nate the experts in different places and proposed to design acase study where the approach was implemented to modelsimulate and analyse NASArsquos Space Exploration SupplyChain [14]

22 Collaborative Management of Major ConstructionProjects For the relationship among the participants Ruffet al noted that due to the greater uncertainty of majorconstruction projects it is easier to cause discordance amongthe participants leading to project delays cost exceedingand disputes The authors analysed the relationship amongthe participants of those projects and presented the problemsto address in project management [15] Hinze and Traceystudied the relationship between principal contractors andsubcontractors from the perspective of the subcontractorand noted that some behaviour of principal contractors maycause harm to the industry [16] Cheung analysed the keyfactors of the Alternative Dispute Resolution (ADR) methodfor solving disputes with the analytic hierarchy process andnoted that the disputes would be solvedmore efficiently usingthe ADR method if attention was paid to those key factors[17] Bond and Naus studied the communication issue ofengineering projects and put forward six factors affecting thecommunication efficiency of project participants and a wayto improve communication [18] Therefore the collaborativemanagement of major construction projects has importantsignificance Appropriate application of collaborativemanagement can improve the flexibility in the physical

Discrete Dynamics in Nature and Society 3

distribution and minimize the inefficiency of major con-struction projects [19 20]

23 Supply Chain Simulation Management Based on SystemDynamics The application of system dynamics to supplychain management can be traced back to 1958 Senge andForrester used system dynamics to solve some operation andmanagement problems in industry such as demand ampli-fication stock volatility instability between production andemployees influence of advertising strategies on productionchange and impact of information technology on manage-ment [21] The earliest application of system dynamics in thesupply chain was the research on the bullwhip effect Towillet al studied the changing range of demand informationwith the supply chain using system dynamics and foundthat the demand information was doubled at each link andamplified eightfold when the manufacturers received ordersfrom the distributors [22] Anderson and Morrice took themachine tool industry as an example to explore the content ofdemand amplification of themachine tool supply chain in thelead time inventory productivity and human with systemdynamics tested several strategies for improving the perfor-mance of the supply chain and created simulations with thestatistical fitting data [23] The results showed that marketvolatility and investment acceleration led to improvementof the production capacity and significant amplification ofdemandThe flexible order strategy and employment strategycould help overcome demand amplification and improve theoperation of the entire supply chain [24]

Given all that major construction projects are a complexadaptive system with complexity as an important feature Sofar few studies specifically consider the impact of complexityon major construction projects because major constructionprojects can be neither copied nor repeated In additionthe local complex environment cannot be copied Thereforea simulation modelling method based on the principle ofsystem dynamics can simulate the complex situation in thecomplex supply chain system of major construction projectswhich is conducive to the research of the collaborativemanagement of the complex supply chain system of majorconstruction projects [25]

3 Modelling

This paper classifies the population into the following 4 typesPotential Recipient of informative intention 119875 recipient ofinformative intention 119877 recipient of delivering informativeintention and forgetter of informative intention 119865 then theresearch sets up a complex system information deliveringmodel TRANSFER as follows

119889119875 (119905)

119889119905= minus120573119892 (119863 (119905)) 119875 (119905) + ] minus ]119875 (119905) + 120575119865 (119905)

119889119877 (119905)

119889119905= 120573119892 (119863 (119905)) 119875 (119905) minus (120576 + ]) 119877 (119905)

119889119863 (119905)

119889119905= 120576119877 (119905) minus (120574 + ])119863 (119905)

119889119865 (119905)

119889119905= 120574119863 (119905) minus (120575 + ]) 119865 (119905)

(1)

When119892(0) = 0119892 isin 1198621 (0 1) and119863 isin (0 1)119892(119863) gt 0 If120575 rarr 0 or 120576 rarr infin model (1) can be simplified into a complexsystem information delivering model The complex systemsupply chain that collaborated with the equilibrium point ofmodel (1) can be overall asymptotically stable when 120575 is suffi-ciently small or 120576 is sufficiently large Considering the relativefactors during information delivery this paper establishesthe following general nonlinear function of the TRANSFERcomplex system information delivering model (2)

In the complex SCM of critical engineering the numberof participants is dynamic Some people pull out of theconstruction link once they finish a certain portion and anew craft takes their place and continues construction

The proficiency and work duration of each participantdiffer hence the paper presumes that 119890(119905 120591) represents thenumber of potential recipients of informative intention attime 119905 on the condition of 120591 working years where 120576(120591)

and 120573(120591) are respectively working year 120591rsquos receiving rateand the delivering rate of potential recipients of informativeintention Λ 120583 120572 120575 120574 are critical engineering participantsrsquoincreasing and decreasing coefficients 120583 is the natural failurerate of information 120572 is failure rate of information 120575 is thesuccess rate of delivering information and 119862(119875 119877119863 119865) isthe delivering rate Then [119862(119875(119905) 119877(119905) 119863(119905) 119865(119905))119873(119905)] sdot

119875(119905) intinfin

0

120573(120591)119890(119905 120591)119889120591 are the new recipients at the time of 119905in different stages of working years as well as the number ofsecluded recipients at time 119905 [120590(119875(119905) 119877(119905) 119863(119905) 119865(119905))119873(119905)] sdot

intinfin

0

119890(119905 120591)119889120591 Consider

119873(119905) = 119875 (119905) + 119877 (119905) + 119863 (119905) + 119865 (119905)

119890 (119905 119900) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905))

119873 (119905)119875 (119905)

sdot int

infin

0

120573 (120591) 119890 (119905 120591) 119889120591

119875 (0) = 1198750

119890 (0 120591) = 120578 (120591)

119863 (0) = 1198630

119865 (0) = 1198650

(2)

By applying fixed point theory and the continuationtheorem of the solution this research can prove the existenceof a global nonnegative solution This paper emphasizes theexistence and stability of critical engineering complex SCMthat collaborated with the equilibrium point Therefore theresearch develops the following fundamental assumption forits parameters120590 119862 are nonnegative continuous differentiablefunctions of 1198774 and 120597119862120597119875 120597119862120597119877 120597119862120597119863 120597119862120597119865 120597120590120597119875

120597120590120597119877 120597120590120597119863 120597120590120597119865 isin 119871infin

([0infin)times[0infin)times[0infin)times[0infin))


that nonnegative functions 120576 and 120573meet the condition 120576(sdot) isin1198621

[0infin) cap 119871infin

[0infin) 1205761015840(sdot) isin 119871infin

[0infin) 120573(sdot) isin 1198622

[0infin) cap

119871infin

[0infin) as well as 1205731015840(sdot) 12057310158401015840(sdot) isin 119871infin

[0infin) Λ 120583 120572 120574 120575are positive constants recorded as sdot

1and sdot

infin These

two constants are respectively the Banach spacersquos 1198711[0infin)

and 119871infin

[0infin) norms If the paper records 1198711+[0infin) as the

positive cone of Banach space 1198711[0infin) 120578(sdot) isin 1198711+[0infin)

31 Asymptotic Stability of the Equilibrium Point The equi-librium point of the complex SCM information deliveringmodel represents the final condition of information deliv-ering and coordination The stability decides the ability ofinformation delivering for the final conditionNext the paperstudies the existence and stability of model (2)rsquos equilibriumpoint If it assumes (119875lowast 119890lowast(120591) 119863lowast 119865lowast) as systemrsquos equilibriumpoint it is necessary and sufficient that condition of existenceshould satisfy the following integrodifferential equations

Λ minus 120583119875lowast

minus 119861lowast

+ 120575119861lowast

= 0

119889119890lowast

(120591)

119889120591

= minus (120583 + 120576 (119905)) 119890lowast

(120591) minus120590 (119875lowast

119877lowast

119863lowast

119865lowast

)

119873lowast119890lowast

(120591)

int

infin

0

120576 (120591) 119890lowast

(120591) 119889 minus 119898119863lowast

= 0

120574119863lowast

minus 119899119865lowast

+120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


= 0

119861lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 119890lowast

(120591) 119889120591

(3)

from which we can conclude that 119877lowast = intinfin

0

119890lowast

(120591)119889120591 119873lowast =119875lowast

+ 119877lowast

+ 119863lowast

+ 119865lowast 119898 = 120583 + 120572 + 120574 and 119899 = 120583 + 120575 and the

system always contains the unique null information equi-librium point (Λ120583 0 0 0) Then the paper discusses theexistence of the complex system SCM that collaborated withthe equilibrium point Consider

119872(119905) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905)) 119875 (119905)

119873 (119905)

119872lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

) 119875lowast

119873lowast

119872lowast

1=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119875lowast

119872lowast

2=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119877lowast

119872lowast

3=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119863lowast

119872lowast

4=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119865lowast

119886 (sdot) = 120583 + 120576 (sdot) +120590 (119875lowast

119877lowast

119863lowast

119865lowast

)

119873lowast

119873lowast

= 119875lowast

+ 119877lowast

+ 119863lowast

+ 119865lowast

119890lowast

(120591) = 119861lowast

120587119886(120591)

(4)

The research obtains (4) from the second equation thenplug (4) into (3)

119875lowast

=(Λ minus 119861

lowast

+ 120575119865lowast

)

120583

119877lowast

= 119861lowast

int

infin

0

120587119886(120591) 119889120591

119863lowast

=119861lowast

119898int

infin

0

120576 (120591) 120587119886(120591) 119889120591

119865lowast

=120574

119899119863lowast

+119876lowast

119899119877lowast

119861lowast

= 119872lowast

119861lowast

int

infin

0

120573 (120591) 120587119886(120591) 119889120591

(5)

From (5) we can regard119875lowast119877lowast119863lowast119865lowast as119861lowastrsquos continuousfunction and record it as 119875(119861lowast) = 119875

lowast 119877(119861lowast) = 119877lowast 119863(119861lowast) =

119863lowast and 119865(119861lowast) = 119865

lowast and then define it as follows

119866 (119861lowast

) =119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 120587119886(120591) 119889120591 (6)

Then 119866 will still be 119861lowastrsquos continuous

function If the design sets R0

= 119862(Λ120583 0 0

0)intinfin

0

120573(120591)119890minusint

120591

0(120583+120576(119904)+120583120590(Λ120583000)Λ)119889119904

119889120591 it can conclude thefollowing

Theorem 1 When R0gt 1 the system will have at least one

complex system SCM equilibrium point when R0le 1 and 119866

strictly decreases monotonically the system will no longer havean equilibrium point 119866 is defined by formula (6)

From (5) the necessary condition of existence of apositive equilibrium is a positive number 119861lowast which makesthe fourth equationrsquos validity of formula (5) The necessaryand sufficient condition of 119861lowast as the fourth solution offormula (5) is 119866(119861lowast) = 1

When 119861lowast is sufficiently large 119866(119861lowast) lt 0 Because 119866(0) =R0 there exists at least one positive number 119861lowast that makes

119866(119861lowast

) = 1 valid whenR0gt 1 Then the system will have at

least one positive equilibrium point based on formula (5)When R

0lt 1 (namely 119866(0) le 1) and 119866 is a strictly

decreasing function if forall119861lowast gt 0 119866(119861lowast) lt 1 Then the systemwill have a null information coordination equilibrium point

Next in order to study the stability of equilibrium point(2) At first the research need to discuss the global asymptoticstability of the null information coordination equilibriumpoint whenR

0lt 1

Theorem 2 Assume 119862(119875 119877119863 119865) = 119862(119873) 120590(119875 119877119863 119865) =

120590(119873) and 1198621015840

(119873) ge 0 (120590(119873)119873)1015840

le 0 Then systemrsquosnull information equilibrium point will have global asymptoticstability ifR

0lt 1


Theorem 3 If R ge 1 random nonnegative numbers 119875 119877119863119865

119862 (119875 119877119863 119865) le 119862(Λ

120583 0 0 0)

120590 (119875 119877119863 119865) ge 120590(Λ

120583 0 0 0)

(7)

can meet the systemrsquos null information equilibrium point whichwill have global asymptotic stability Then examining thestability (119875lowast 119890lowast(120591) 119863lowast 119865lowast) the critical engineering complexinformation synergy balance If the research assumes 119883(119905) =

(119875(119905) 119877(119905) 119863(119905) 119865(119905) 119861(119905))119879 the119883(119905)will satisfy the following

equation

119860119883 (119905) = int

119905

0

119870 (119905 minus 120591)119883 (120591) 119889120591 = 119891 (119905) (8)

It can then be proved that positive number 119867 makes 119870and its derivative satisfy

119870 (119905) 10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817

10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817le 119867119904minus120583119905

(9)

Analysing119870(119905)rsquos Laplace conversion (119904) in the right halfplane Re(119904) gt minus120583 of the complex plane and on the conditionthat lim

|119904|rarrinfin(119904) = 0 conclude lim

|119904|rarrinfindet(119860 + (119904)) = 1

Therefore all roots of det(119860 + (119904)) are isolated in the circlecentred at the origin If the design sets all roots of det(119860 +

(119904)) as having a negative real part there will exist 120583lowast 0 lt

120583lowast

lt 120583 that makes all roots in Re(119904) lt minus120583lowast When it sets

119871(119904) as 119860 + (119904)rsquos analytic inverse in Re(119904) ge minus120583lowast because 119860

is reversible and lim|119904|rarrinfin

(119904) = 0 for sufficiently large |119904| onthe condition that Re(119904) gt minus120583 the following can be obtained

119871 (119904) = 119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

infin

sum

119895=0

(119860minus1

(119904))119895

lim|119904|rarrinfin

119871 (119904) = lim|119904|rarrinfin

119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

(10)

By applying Taylorrsquos formula it can be concluded that(119904) = 119870(0)119904 + 119870(0)119904

2

+ 119900(119904minus2

) on the condition that 119904 isin119904 isin 119862 | Re(119904) ge minus120583

lowast

|119904| rarr infin Therefore when 119904 isin 119904 isin

119862 | Re(119904) ge minus120583lowast

|119904| rarr infin there exists a constant matrix 1198690

that makes 119871(119904) = 119860minus1

+ 1198690119904 + 119900(119904

minus2

) These results indicatethat (119904) = 119871(119904) minus 119860

minus1 is 119869(119905)rsquos Laplace conversion and 119869(119905) =(12120587)119890

minus120583lowast

119905

intinfin

minusinfin

119890119894120585119905

(minus120583lowast

+ 119894120585)119889120585 119905 ge 0Because 119894 is an imaginary unit by formula (9) there exists

a positive number1198671that makes 119869(119905) le 119867

1119890minus120583lowast

119905 119905 ge 0 Toinvestigate the asymptotic stability of the positive equilibriumpoint assume the following

(i) |119872(119905)minus119872lowast

minusnabla119872lowast

sdot(119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)|+

|119877(119905)|+|119863(119905)|+|119865(119905)|) When |119875(119905)|+|119877(119905)|+|119863(119905)|+|119865(119905)| rarr0 namely forall120598

0gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| +

|119863(119905)| + |119865(119905)| lt 120575(1205760) |119872(119905) minus 119872

lowast

minus nabla119872lowast

sdot (119875(119905) 119864(119905) 119877(119905)

119865(119905))| lt 1205760(|119875(119905)| |119864(119905)| |119877(119905)| |119865(119905)|)

(ii) |119876(119905) minus119876lowast minusnabla119876lowast sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)| +

|119877(119905)| + |119863(119905)| + |119865(119905)|)When |119875(119905)| + |119877(119905)| + |119863(119905)| + |119865(119905)| rarr 0 (namely

forall1205980gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| + |119863(119905)| +

|119865(119905)| lt 120575(1205760)) |119876(119905) minus 119876

lowast


sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| lt

1205760(|119875(119905)| |119877(119905)| |119863(119905)| |119865(119905)|)When 120590(119875(119905) 119877(119905) 119863(119905) 119865(119905)) = 120573

1119873(119905) 119862(119875(119905) 119877(119905)

119863(119905) 119865(119905)) = 1205732119873(119905) the above assumption is naturally avail-

able amongwhich1205731 1205732are positive numbers and119873(119905) is the

population size

4 Simulation

The complex supply chain of a major construction projectrefers to the construction process from the preliminary workincluding the definition of the project feasibility research anddesign key project implementation completion acceptanceand maintenance to all activities in the processes of expan-sion and building demolition as well as all organizationalinstitutions involved The complex system of a major con-struction project is an overall functional mode that combinesowners consultants designers construction parties andmaterial and equipment suppliers into a whole through thecontrol of information flow logistics and cash flow in whichthe owners are the investor supplier and final user as welland other node enterprises are driven by the demand infor-mation to realize the value of the whole supply chain throughthe division of labour and cooperation

Because there are many participants in the complex sys-temofmajor construction projects collaboration consistencyis bound to undergo severe tests in the overall operationThus the root cause of difficult collaboration is that differentparticipants have different objectives and the informationtransmission is obstructed This paper presents a model thatshows the transmission of the informative intention in theprocess of key project construction and seeks the key timepoints for collaborative consistency to strengthen the collabo-rative management of the complex system of major construc-tion projects

So this paper builds a model that constructed a visualsimulation model Figure 1 is this paper elaboration andit shows the process of the informative intention in thekey project construction intuitively It indicates a simulationmodel which is based on the above model of mathematicalbuilding and analysis And then the second part of Figure 1shows the application of this simulation model

41 Role Characteristics of Four Important Characters in theComplex System of Major Construction Projects As shown inFigure 1 participants are divided into four categories accord-ing to their respective stage characteristic which is from theintention information transmission of themajor constructionprojects They are specifically as follows

(i) Potential Recipient (potential intent informationreceiver) people who do not receive the intent infor-mation


Potential Receiving rate

Recipient Redelivery rate

Delivering Undelivery rate

Forgotten

Average Duration

Average Time

Delivery Rate

Multiple Delivery Rate

Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1

Potential receiverIntent receiver Forgotten receiver

Delivering receiver

(b)

Figure 1 The information simulation model of collaborative management

(ii) Intent Recipient (receiver who has received the intentinformation) people who have received the intentinformation but have not transmitted to others

(iii) Delivering Recipient (receiver in the process of intentinformation transmission) people who have receivedthe information and transmitted it to other potentialintent information receivers

(iv) Forgotten Recipient (people who have received theintent information but then forgotten it) [26]

42 Defining Parameters and Subordinates The parametersand subordinates are defined as follows

(i) Participants Considering a model of a key projectwith 10000 participants first the leader has intentinformation concerning the key project to be trans-mitted and other people become the potential intentinformation receivers

(ii) Delivery Rate In the initial stage of key project con-struction each person transmits the information toothers at the transmission and reception rate of 125

(iii) Multiple Delivery Rate If the receiver who hasreceived the information meets other receivers whomay have received the information the transmissionrate of the intent information by the latter is MultipleDelivery Rate

(iv) Average Time When a person receives informationthere is a thinking period that lasts 10 days In thisstage the information receiver becomes familiar withthe information

(v) Average Duration After the thinking period theintent information will last for a time period inthe consciousness of the information receiver Theaverage lasting time of the information is 15 days

(vi) Information receivers who have forgotten the intentinformation will not participate in the retransmissionof the information

Figures andTablesThepaper hypothesizes anddefines relatedindex (Table 1) The details are as follows

(i) Total Population = 10000(ii) Delivery Rate = 125(iii) Multiple Delivery Rate = 06(iv) Average Time = 10(v) Average Duration = 1

43 Analogy Simulation The research performs simulationmodelling of the complex supply chain coordinativemanage-ment process of critical engineering by adopting the simula-tion software AnyLogic Figure 1 depicts the system informa-tion synergy for the complex system of major constructionprojects It shows the transmission of the informative inten-tion in the process of key project construction and seeks thekey time points for collaborative consistency to strengthenthe collaborative management of the complex supply chainof major construction projects The result of the simulationmodel indicates that based on the TRANSFER modelrsquosadjustment applied to the system it can not only observe themacroscopic operational process of the whole supply chaincoordinative management but also measure certain links ofthe system microscopically

The Application The model can observe 4 kinds of differentparticipants visually (Potential Recipient Intent RecipientDelivering Recipient and Forgotten Recipient) It is helpful tounderstand the structure and dynamics of the intention infor-mation transmission in the major construction which was acomplex system And it can help the organization take theappropriate strategy in the process of major constructionsmanagement

5 Conclusions

This paper conducts innovation research on the complexsystem coordinative management of critical engineering anddevelops a mathematical modelThemathematical analytical


Table 1 Inflows and outflows

Stock Inflows OutflowsTotalPopulation Potential Receiving Rate = Delivering times Delivery Rate timesMultiple Delivery Rate times PotentialTotal Population + Delivery Rate

Delivery Rate Recipient Redelivery Rate = RecipientAverage TimeMultipleDelivery Rate Delivering Undelivery Rate = DeliveringAverage Duration

part proves the existence and stability of complex systemcoordinated with the equilibrium pointThen the simulationmodelling of the complex coordinative management processof critical engineering is performed by adopting the simula-tion software AnyLogic The result of the simulation modelindicates that based on the TRANSFER modelrsquos adjustmentapplied to the system it can not only observe themacroscopicoperational process of the whole supply chain coordinativemanagement but also measure certain links of the systemmicroscopically This study effectively integrates the par-ticipants of different critical engineering and it explicatessynergy elements and modes of action The study furtherproposes the informative intentionrsquos delivering problems inthe complex supply chain of critical engineering and promptsthe participants of the supply chain to act as an organism ofharmonious development and coevolutionThis paper is ben-eficial to increasing the efficiency of the critical engineeringcomplex supply chain to reform its management status

Conflict of Interests

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

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no 71390522) China Postdoc-toral Science Foundation and Hei Long Jiang PostdoctoralFoundation of China

References

[1] Building BRICs of growth The Economist June 2008 httpwwweconomistcomnode11488749

[2] P E D Love and Z Irani ldquoA project management quality costinformation system for the construction industryrdquo Informationamp Management vol 40 no 7 pp 649ndash661 2003

[3] J Uher ldquoConceiving lsquopersonalityrsquo psychologistrsquos challenges andbasic fundamentals of the transdisciplinary philosophy-of-science paradigm for research on individualsrdquo Integrative Psy-chological amp Behavioral Science vol 49 no 3 pp 398ndash458 2015

[4] Z Chen N Takeuchi and M Wakabayashi ldquoManagerial skillutilization work environment gender and training incentiverdquoInternational Journal of Human Resource Management vol 16no 5 pp 786ndash808 2005

[5] S Dougherty S Russo and D Freeman ldquoA successful strategyfor environmental permitting of an aggressively scheduledmajor water supply projectrdquo in Proceedings of the Pipelines

Conference pp 1338ndash1349 American Society of Civil EngineersKeystone Colo USA August-September 2010

[6] A Walker and R Newcombe ldquoThe positive use of power on amajor construction projectrdquo Construction Management andEconomics vol 18 no 1 pp 37ndash44 2000

[7] A Perez S Quintanilla P Lino and V Valls ldquoAmulti-objectiveapproach for a project scheduling problem with due dates andtemporal constraints infeasibilitiesrdquo International Journal ofProduction Research vol 52 no 13 pp 3950ndash3965 2014

[8] Z Na and W Fusheng ldquoThe game analysis of manufacturersrsquopolitical connections on product safety in supply Chain evi-dence from Chinardquo Discrete Dynamics in Nature and Societyvol 2013 Article ID 695384 5 pages 2013

[9] N Zhao F Wang and Q Tang ldquoGame analysis on the moti-vations for political connections in Chinarsquos listed companiesbased on a principal-agent modelrdquo Journal of ComputationalInformation Systems vol 9 no 10 pp 4155ndash4162 2013

[10] G-C Li L-Y Ding and J-T Wang ldquoConstruction projectcontrol in virtual reality a case studyrdquo Journal of AppliedSciences vol 6 no 13 pp 2724ndash2732 2006

[11] W Smew P Young and J Geraghty ldquoSupply chain analysisusing simulation gaussian process modelling and optimisa-tionrdquo International Journal of Simulation Modelling vol 12 no3 pp 178ndash189 2013

[12] M Boile and L Sdoukopoulos ldquoSupply chain visibility andsecuritymdashthe SMART-CMproject solutionrdquo International Jour-nal of Shipping and Transport Logistics vol 6 no 3 pp 280ndash2922014

[13] J Mihm C H Loch D Wilkinson and B A HubermanldquoHierarchical structure and search in complex organizationsrdquoManagement Science vol 56 no 5 pp 831ndash848 2010

[14] D CopeM S FayezMMollaghasemi andA Kaylani ldquoSupplychain simulationmodelingmade easy an innovative approachrdquoin Proceedings of the Winter Simulation Conference (WSC rsquo07)pp 1887ndash1896 IEEE Washington DC USA December 2007

[15] C M Ruff D A Dzombak and C T Hendrickson ldquoOwner-contractor relationships on contaminated site remediationprojectsrdquo Journal of Construction Engineering andManagementvol 122 no 4 pp 348ndash353 1996

[16] J Hinze and A Tracey ldquoThe Contractor-subcontractor rela-tionship the subcontractorrsquos viewrdquo Journal of ConstructionEngineering and Management vol 120 no 2 pp 274ndash287 1994

[17] S Cheung ldquoCritical factors affecting the use of alternativedispute resolution processes in constructionrdquo InternationalJournal of Project Management vol 17 no 3 pp 189ndash194 1999

[18] S R Bond and C C Naus ldquoRf-cloningorg an online tool forthe design of restriction-free cloning projectsrdquo Nucleic AcidsResearch vol 40 no 1 pp W209ndashW213 2012

[19] X Xue Q Shen and Z Ren ldquoCritical review of collaborativeworking in construction projects business environment andhuman behaviorsrdquo Journal of Management in Engineering vol26 no 4 pp 196ndash208 2010


[20] F T S Chan and T Zhang ldquoThe impact of collaborative trans-portation management on supply chain performance a simu-lation approachrdquo Expert Systems with Applications vol 38 no3 pp 2319ndash2329 2011

[21] P M Senge and N B Forrester Organizational Growth andManagement Overhead System Dynamics Group Sloan Schoolof Management Massachusetts Institute of Technology Cam-bridge Mass USA 1987

[22] D R Towill M M Naim and J Wikner ldquoIndustrial dynamicssimulationmodels in the design of supply chainsrdquo InternationalJournal of Physical Distribution and Logistics Management vol22 no 5 pp 3ndash13 1996

[23] E G Anderson Jr and D J Morrice ldquoA simulation game forteaching service-oriented supply chain management doesinformation sharing help managers with service capacity deci-sionsrdquo Production and Operations Management vol 9 no 1 pp40ndash55 2000

[24] J P C Kleijnen ldquoSupply chain simulation tools and techniquesa surveyrdquo International Journal of Simulation amp Process Mod-elling vol 1 no 1-2 2005

[25] D J Van Der Zee and J G A J Van Der Vorst ldquoA model-ing framework for supply chain simulation opportunities forimproved decision makingrdquoDecision Sciences vol 36 no 1 pp65ndash95 2005

[26] H L Lee V Padmanabhan and SWhang ldquoInformation distor-tion in a supply chain the bullwhip effectrdquoManagement Sciencevol 43 no 4 pp 546ndash558 1997

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


projects Some factors increase the risks of major construc-tion projects Major projects have different social systemscultures and legal backgrounds and are in different lan-guages which increase barriers to communication and thecomplexity of project management The increasing environ-mental uncertainty is the main source leading to the com-plexity of major construction project [5]

Based on the above analysis the traditional process ofmajor construction projects is needed to innovate and con-solidate the management It is difficult for traditional majorconstruction projects to use a production process similar tothat of other industries The owners cannot obtain completebuilding products and perfect serviceThey have no ability tomanagemajor construction projects but have to participate inthe construction process They must perform complex man-agement work and bear the resulting responsibility leading tomany entanglements [6] In addition due to the specialty lim-itation of major construction projects it has different span-ning periods or implementation parities So it is hard to coor-dinate between a superior and an inferior and this leads todiscontinuity of management at last

Major construction projects have their own generalobjectives and requirements but due to the different organi-zation tasks and persons responsible in different phases thetasks are undertaken by different enterprises resulting in theseparation of project organization inconsistent objectivesand discrete responsibilities Due to the inconsistent objec-tives among the participants they balance each other leadingto tense relationships and low working efficiency whichinhibits enthusiasm and creativity Significant costs time andenergy are spent on various working interfaces [7] Becausethe interests of the participants of a project have nothing to dowith its ultimate benefit peoplersquos short-term actions are moreserious than those in other organizations which easily pro-duce the ideal for all constructionThe participants pay atten-tion to the short-term local interests and ignore the operationstatus of the project and the requirement of continuousdevelopment thus failing to realize the general optimizationof the life cycle of a major construction project Moreoverthere are obvious blind areas in the organizational responsi-bility systemwhich increases the risks for all participants Forexample governments and manufacturers must use positivepolitical connections to achieve product protection andsupervision of safety throughout the supply chain [8] and theagentrsquos working efficiency is decreased which may erode thevalue of the company [9]

The long construction period large investment complexorganizational relationship uncertain cultural environmentand breaking in phase of major construction projects areobjective problems that are difficult to solve However com-plex objective and information isolation can be improvedthrough management The traditional management systemmanaging mode and idea of major construction projectscannot satisfy and adapt to the needs of complex key projectmanagement [10] The complexity of a major constructionproject raises new requirements onmanagementThus it hasimportant theoretical and realistic significance in the researchof the collaboration of the complex system ofmajor construc-tion projects [11]

2 Literature Review

The following subsections are talking about collaborativemanagement of complex major construction projects whichare based on AnyLogic The research subject is a complexsystem of major construction project The research perspec-tives of collaborative management are from the relation-ship among the participants through mathematical analysisadopting the research methods of simulation modelling Inthis paper the existing research as theoretical basis stands ina new perspective to discuss the coordinated management ofmajor constructions

21 Complex Supply Chain of Major Construction Projects Amajor construction project supply chain is called CPSC Thesimulationmodels are applied to study a specific coordinationmechanism where coordination requirements are producedin different departments with complex relationships in keyorganizations In addition it is considered that the VDT(Virtual Design Team) model is more suitable for research ofprojects with unpredictable factors It is a formal method fordeveloping the newmicrolevel behavioral mechanisms as theprimary point of departure from the aspect of informationprocessing And the microcontingency model generates a setof testable hypotheses related to these theorized microlevelbehaviors [12] Mihm et al studied the impact of the hierar-chical organizational structure on the speed of the searchingdecision-making plan and the stability and quality of theproblem solutions by combining mathematical analysis andsimulation models [13] Cope et al pointed out that NASAfaced the difficulty of how to effectively manage and coordi-nate the experts in different places and proposed to design acase study where the approach was implemented to modelsimulate and analyse NASArsquos Space Exploration SupplyChain [14]

22 Collaborative Management of Major ConstructionProjects For the relationship among the participants Ruffet al noted that due to the greater uncertainty of majorconstruction projects it is easier to cause discordance amongthe participants leading to project delays cost exceedingand disputes The authors analysed the relationship amongthe participants of those projects and presented the problemsto address in project management [15] Hinze and Traceystudied the relationship between principal contractors andsubcontractors from the perspective of the subcontractorand noted that some behaviour of principal contractors maycause harm to the industry [16] Cheung analysed the keyfactors of the Alternative Dispute Resolution (ADR) methodfor solving disputes with the analytic hierarchy process andnoted that the disputes would be solvedmore efficiently usingthe ADR method if attention was paid to those key factors[17] Bond and Naus studied the communication issue ofengineering projects and put forward six factors affecting thecommunication efficiency of project participants and a wayto improve communication [18] Therefore the collaborativemanagement of major construction projects has importantsignificance Appropriate application of collaborativemanagement can improve the flexibility in the physical





3 Modelling


119889119875 (119905)

119889119905= minus120573119892 (119863 (119905)) 119875 (119905) + ] minus ]119875 (119905) + 120575119865 (119905)

119889119877 (119905)

119889119905= 120573119892 (119863 (119905)) 119875 (119905) minus (120576 + ]) 119877 (119905)

119889119863 (119905)

119889119905= 120576119877 (119905) minus (120574 + ])119863 (119905)

119889119865 (119905)

119889119905= 120574119863 (119905) minus (120575 + ]) 119865 (119905)

(1)





119875(119905) intinfin

0


intinfin

0

119890(119905 120591)119889120591 Consider

119873(119905) = 119875 (119905) + 119877 (119905) + 119863 (119905) + 119865 (119905)

119890 (119905 119900) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905))

119873 (119905)119875 (119905)

sdot int

infin

0

120573 (120591) 119890 (119905 120591) 119889120591

119875 (0) = 1198750

119890 (0 120591) = 120578 (120591)

119863 (0) = 1198630

119865 (0) = 1198650

(2)


120597120590120597119877 120597120590120597119863 120597120590120597119865 isin 119871infin






[0infin) 120573(sdot) isin 1198622

[0infin) cap

119871infin



1and sdot

infin These


and 119871infin





minus 119861lowast

+ 120575119861lowast

= 0

119889119890lowast

(120591)

119889120591

= minus (120583 + 120576 (119905)) 119890lowast

(120591) minus120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


(120591)

int

infin

0

120576 (120591) 119890lowast

(120591) 119889 minus 119898119863lowast

= 0

120574119863lowast


+120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


= 0

119861lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 119890lowast

(120591) 119889120591

(3)


0

119890lowast

(120591)119889120591 119873lowast =119875lowast

+ 119877lowast

+ 119863lowast



119872(119905) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905)) 119875 (119905)

119873 (119905)

119872lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

) 119875lowast

119873lowast

119872lowast

1=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119875lowast

119872lowast

2=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119877lowast

119872lowast

3=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119863lowast

119872lowast

4=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119865lowast

119886 (sdot) = 120583 + 120576 (sdot) +120590 (119875lowast

119877lowast

119863lowast

119865lowast

)

119873lowast

119873lowast

= 119875lowast

+ 119877lowast

+ 119863lowast

+ 119865lowast

119890lowast

(120591) = 119861lowast

120587119886(120591)

(4)


119875lowast

=(Λ minus 119861

lowast

+ 120575119865lowast

)

120583

119877lowast

= 119861lowast

int

infin

0

120587119886(120591) 119889120591

119863lowast

=119861lowast

119898int

infin

0

120576 (120591) 120587119886(120591) 119889120591

119865lowast

=120574

119899119863lowast

+119876lowast

119899119877lowast

119861lowast

= 119872lowast

119861lowast

int

infin

0

120573 (120591) 120587119886(120591) 119889120591

(5)





119866 (119861lowast

) =119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 120587119886(120591) 119889120591 (6)



= 119862(Λ120583 0 0

0)intinfin

0

120573(120591)119890minusint

120591

0(120583+120576(119904)+120583120590(Λ120583000)Λ)119889119904







119866(119861lowast






0lt 1

Theorem 2 Assume 119862(119875 119877119863 119865) = 119862(119873) 120590(119875 119877119863 119865) =

120590(119873) and 1198621015840

(119873) ge 0 (120590(119873)119873)1015840


0lt 1



119862 (119875 119877119863 119865) le 119862(Λ

120583 0 0 0)

120590 (119875 119877119863 119865) ge 120590(Λ

120583 0 0 0)

(7)



equation

119860119883 (119905) = int

119905

0

119870 (119905 minus 120591)119883 (120591) 119889120591 = 119891 (119905) (8)


119870 (119905) 10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817

10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817le 119867119904minus120583119905

(9)



|119904|rarrinfindet(119860 + (119904)) = 1



120583lowast





119871 (119904) = 119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

infin

sum

119895=0

(119860minus1

(119904))119895


119871 (119904) = lim|119904|rarrinfin

119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

(10)


2

+ 119900(119904minus2


lowast




that makes 119871(119904) = 119860minus1

+ 1198690119904 + 119900(119904

minus2



minus120583lowast

119905

intinfin

minusinfin

119890119894120585119905

(minus120583lowast





(i) |119872(119905)minus119872lowast


sdot(119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)|+


0gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| +

|119863(119905)| + |119865(119905)| lt 120575(1205760) |119872(119905) minus 119872

lowast


sdot (119875(119905) 119864(119905) 119877(119905)

119865(119905))| lt 1205760(|119875(119905)| |119864(119905)| |119877(119905)| |119865(119905)|)


|119877(119905)| + |119863(119905)| + |119865(119905)|)When |119875(119905)| + |119877(119905)| + |119863(119905)| + |119865(119905)| rarr 0 (namely

forall1205980gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| + |119863(119905)| +

|119865(119905)| lt 120575(1205760)) |119876(119905) minus 119876

lowast


sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| lt

1205760(|119875(119905)| |119877(119905)| |119863(119905)| |119865(119905)|)When 120590(119875(119905) 119877(119905) 119863(119905) 119865(119905)) = 120573

1119873(119905) 119862(119875(119905) 119877(119905)



population size

4 Simulation










Forgotten

Average Duration

Average Time

Delivery Rate


Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1


Delivering receiver

(b)
















5 Conclusions









Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













3 Modelling


119889119875 (119905)

119889119905= minus120573119892 (119863 (119905)) 119875 (119905) + ] minus ]119875 (119905) + 120575119865 (119905)

119889119877 (119905)

119889119905= 120573119892 (119863 (119905)) 119875 (119905) minus (120576 + ]) 119877 (119905)

119889119863 (119905)

119889119905= 120576119877 (119905) minus (120574 + ])119863 (119905)

119889119865 (119905)

119889119905= 120574119863 (119905) minus (120575 + ]) 119865 (119905)

(1)





119875(119905) intinfin

0


intinfin

0

119890(119905 120591)119889120591 Consider

119873(119905) = 119875 (119905) + 119877 (119905) + 119863 (119905) + 119865 (119905)

119890 (119905 119900) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905))

119873 (119905)119875 (119905)

sdot int

infin

0

120573 (120591) 119890 (119905 120591) 119889120591

119875 (0) = 1198750

119890 (0 120591) = 120578 (120591)

119863 (0) = 1198630

119865 (0) = 1198650

(2)


120597120590120597119877 120597120590120597119863 120597120590120597119865 isin 119871infin






[0infin) 120573(sdot) isin 1198622

[0infin) cap

119871infin



1and sdot

infin These


and 119871infin





minus 119861lowast

+ 120575119861lowast

= 0

119889119890lowast

(120591)

119889120591

= minus (120583 + 120576 (119905)) 119890lowast

(120591) minus120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


(120591)

int

infin

0

120576 (120591) 119890lowast

(120591) 119889 minus 119898119863lowast

= 0

120574119863lowast


+120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


= 0

119861lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 119890lowast

(120591) 119889120591

(3)


0

119890lowast

(120591)119889120591 119873lowast =119875lowast

+ 119877lowast

+ 119863lowast



119872(119905) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905)) 119875 (119905)

119873 (119905)

119872lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

) 119875lowast

119873lowast

119872lowast

1=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119875lowast

119872lowast

2=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119877lowast

119872lowast

3=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119863lowast

119872lowast

4=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119865lowast

119886 (sdot) = 120583 + 120576 (sdot) +120590 (119875lowast

119877lowast

119863lowast

119865lowast

)

119873lowast

119873lowast

= 119875lowast

+ 119877lowast

+ 119863lowast

+ 119865lowast

119890lowast

(120591) = 119861lowast

120587119886(120591)

(4)


119875lowast

=(Λ minus 119861

lowast

+ 120575119865lowast

)

120583

119877lowast

= 119861lowast

int

infin

0

120587119886(120591) 119889120591

119863lowast

=119861lowast

119898int

infin

0

120576 (120591) 120587119886(120591) 119889120591

119865lowast

=120574

119899119863lowast

+119876lowast

119899119877lowast

119861lowast

= 119872lowast

119861lowast

int

infin

0

120573 (120591) 120587119886(120591) 119889120591

(5)





119866 (119861lowast

) =119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 120587119886(120591) 119889120591 (6)



= 119862(Λ120583 0 0

0)intinfin

0

120573(120591)119890minusint

120591

0(120583+120576(119904)+120583120590(Λ120583000)Λ)119889119904







119866(119861lowast






0lt 1

Theorem 2 Assume 119862(119875 119877119863 119865) = 119862(119873) 120590(119875 119877119863 119865) =

120590(119873) and 1198621015840

(119873) ge 0 (120590(119873)119873)1015840


0lt 1



119862 (119875 119877119863 119865) le 119862(Λ

120583 0 0 0)

120590 (119875 119877119863 119865) ge 120590(Λ

120583 0 0 0)

(7)



equation

119860119883 (119905) = int

119905

0

119870 (119905 minus 120591)119883 (120591) 119889120591 = 119891 (119905) (8)


119870 (119905) 10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817

10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817le 119867119904minus120583119905

(9)



|119904|rarrinfindet(119860 + (119904)) = 1



120583lowast





119871 (119904) = 119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

infin

sum

119895=0

(119860minus1

(119904))119895


119871 (119904) = lim|119904|rarrinfin

119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

(10)


2

+ 119900(119904minus2


lowast




that makes 119871(119904) = 119860minus1

+ 1198690119904 + 119900(119904

minus2



minus120583lowast

119905

intinfin

minusinfin

119890119894120585119905

(minus120583lowast





(i) |119872(119905)minus119872lowast


sdot(119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)|+


0gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| +

|119863(119905)| + |119865(119905)| lt 120575(1205760) |119872(119905) minus 119872

lowast


sdot (119875(119905) 119864(119905) 119877(119905)

119865(119905))| lt 1205760(|119875(119905)| |119864(119905)| |119877(119905)| |119865(119905)|)


|119877(119905)| + |119863(119905)| + |119865(119905)|)When |119875(119905)| + |119877(119905)| + |119863(119905)| + |119865(119905)| rarr 0 (namely

forall1205980gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| + |119863(119905)| +

|119865(119905)| lt 120575(1205760)) |119876(119905) minus 119876

lowast


sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| lt

1205760(|119875(119905)| |119877(119905)| |119863(119905)| |119865(119905)|)When 120590(119875(119905) 119877(119905) 119863(119905) 119865(119905)) = 120573

1119873(119905) 119862(119875(119905) 119877(119905)



population size

4 Simulation










Forgotten

Average Duration

Average Time

Delivery Rate


Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1


Delivering receiver

(b)
















5 Conclusions









Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













[0infin) 120573(sdot) isin 1198622

[0infin) cap

119871infin



1and sdot

infin These


and 119871infin





minus 119861lowast

+ 120575119861lowast

= 0

119889119890lowast

(120591)

119889120591

= minus (120583 + 120576 (119905)) 119890lowast

(120591) minus120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


(120591)

int

infin

0

120576 (120591) 119890lowast

(120591) 119889 minus 119898119863lowast

= 0

120574119863lowast


+120590 (119875lowast

119877lowast

119863lowast

119865lowast

)


= 0

119861lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 119890lowast

(120591) 119889120591

(3)


0

119890lowast

(120591)119889120591 119873lowast =119875lowast

+ 119877lowast

+ 119863lowast



119872(119905) =119862 (119875 (119905) 119877 (119905) 119863 (119905) 119865 (119905)) 119875 (119905)

119873 (119905)

119872lowast

=119862 (119875lowast

119877lowast

119863lowast

119865lowast

) 119875lowast

119873lowast

119872lowast

1=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119875lowast

119872lowast

2=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119877lowast

119872lowast

3=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119863lowast

119872lowast

4=120597119872(119875

lowast

119877lowast

119863lowast

119865lowast

)

120597119865lowast

119886 (sdot) = 120583 + 120576 (sdot) +120590 (119875lowast

119877lowast

119863lowast

119865lowast

)

119873lowast

119873lowast

= 119875lowast

+ 119877lowast

+ 119863lowast

+ 119865lowast

119890lowast

(120591) = 119861lowast

120587119886(120591)

(4)


119875lowast

=(Λ minus 119861

lowast

+ 120575119865lowast

)

120583

119877lowast

= 119861lowast

int

infin

0

120587119886(120591) 119889120591

119863lowast

=119861lowast

119898int

infin

0

120576 (120591) 120587119886(120591) 119889120591

119865lowast

=120574

119899119863lowast

+119876lowast

119899119877lowast

119861lowast

= 119872lowast

119861lowast

int

infin

0

120573 (120591) 120587119886(120591) 119889120591

(5)





119866 (119861lowast

) =119862 (119875lowast

119877lowast

119863lowast

119865lowast

)


int

infin

0

120573 (120591) 120587119886(120591) 119889120591 (6)



= 119862(Λ120583 0 0

0)intinfin

0

120573(120591)119890minusint

120591

0(120583+120576(119904)+120583120590(Λ120583000)Λ)119889119904







119866(119861lowast






0lt 1

Theorem 2 Assume 119862(119875 119877119863 119865) = 119862(119873) 120590(119875 119877119863 119865) =

120590(119873) and 1198621015840

(119873) ge 0 (120590(119873)119873)1015840


0lt 1



119862 (119875 119877119863 119865) le 119862(Λ

120583 0 0 0)

120590 (119875 119877119863 119865) ge 120590(Λ

120583 0 0 0)

(7)



equation

119860119883 (119905) = int

119905

0

119870 (119905 minus 120591)119883 (120591) 119889120591 = 119891 (119905) (8)


119870 (119905) 10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817

10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817le 119867119904minus120583119905

(9)



|119904|rarrinfindet(119860 + (119904)) = 1



120583lowast





119871 (119904) = 119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

infin

sum

119895=0

(119860minus1

(119904))119895


119871 (119904) = lim|119904|rarrinfin

119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

(10)


2

+ 119900(119904minus2


lowast




that makes 119871(119904) = 119860minus1

+ 1198690119904 + 119900(119904

minus2



minus120583lowast

119905

intinfin

minusinfin

119890119894120585119905

(minus120583lowast





(i) |119872(119905)minus119872lowast


sdot(119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)|+


0gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| +

|119863(119905)| + |119865(119905)| lt 120575(1205760) |119872(119905) minus 119872

lowast


sdot (119875(119905) 119864(119905) 119877(119905)

119865(119905))| lt 1205760(|119875(119905)| |119864(119905)| |119877(119905)| |119865(119905)|)


|119877(119905)| + |119863(119905)| + |119865(119905)|)When |119875(119905)| + |119877(119905)| + |119863(119905)| + |119865(119905)| rarr 0 (namely

forall1205980gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| + |119863(119905)| +

|119865(119905)| lt 120575(1205760)) |119876(119905) minus 119876

lowast


sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| lt

1205760(|119875(119905)| |119877(119905)| |119863(119905)| |119865(119905)|)When 120590(119875(119905) 119877(119905) 119863(119905) 119865(119905)) = 120573

1119873(119905) 119862(119875(119905) 119877(119905)



population size

4 Simulation










Forgotten

Average Duration

Average Time

Delivery Rate


Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1


Delivering receiver

(b)
















5 Conclusions









Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119862 (119875 119877119863 119865) le 119862(Λ

120583 0 0 0)

120590 (119875 119877119863 119865) ge 120590(Λ

120583 0 0 0)

(7)



equation

119860119883 (119905) = int

119905

0

119870 (119905 minus 120591)119883 (120591) 119889120591 = 119891 (119905) (8)


119870 (119905) 10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817

10038171003817100381710038171003817 (119905)

10038171003817100381710038171003817le 119867119904minus120583119905

(9)



|119904|rarrinfindet(119860 + (119904)) = 1



120583lowast





119871 (119904) = 119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

infin

sum

119895=0

(119860minus1

(119904))119895


119871 (119904) = lim|119904|rarrinfin

119860minus1

(119868 + 119860minus1

(119904))minus1

= 119860minus1

(10)


2

+ 119900(119904minus2


lowast




that makes 119871(119904) = 119860minus1

+ 1198690119904 + 119900(119904

minus2



minus120583lowast

119905

intinfin

minusinfin

119890119894120585119905

(minus120583lowast





(i) |119872(119905)minus119872lowast


sdot(119875(119905) 119877(119905) 119863(119905) 119865(119905))| = 119900(|119875(119905)|+


0gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| +

|119863(119905)| + |119865(119905)| lt 120575(1205760) |119872(119905) minus 119872

lowast


sdot (119875(119905) 119864(119905) 119877(119905)

119865(119905))| lt 1205760(|119875(119905)| |119864(119905)| |119877(119905)| |119865(119905)|)


|119877(119905)| + |119863(119905)| + |119865(119905)|)When |119875(119905)| + |119877(119905)| + |119863(119905)| + |119865(119905)| rarr 0 (namely

forall1205980gt 0 exist120575(120576

0) gt 0 which makes |119875(119905)| + |119877(119905)| + |119863(119905)| +

|119865(119905)| lt 120575(1205760)) |119876(119905) minus 119876

lowast


sdot (119875(119905) 119877(119905) 119863(119905) 119865(119905))| lt

1205760(|119875(119905)| |119877(119905)| |119863(119905)| |119865(119905)|)When 120590(119875(119905) 119877(119905) 119863(119905) 119865(119905)) = 120573

1119873(119905) 119862(119875(119905) 119877(119905)



population size

4 Simulation










Forgotten

Average Duration

Average Time

Delivery Rate


Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1


Delivering receiver

(b)
















5 Conclusions









Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Forgotten

Average Duration

Average Time

Delivery Rate


Total Population

RIntent

Connections

(a)

302010 40 50 60 70 80 90 10000

05

1


Delivering receiver

(b)
















5 Conclusions









Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Collaborative Management of Complex Major … · 2019. 7. 30. · Research Article...

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Transcript of Research Article Collaborative Management of Complex Major … · 2019. 7. 30. · Research Article...