Journal of Materials Processing Technology 139 (2003) 178–186

Advances in e-manufacturing: foundations of market-basedcollaborative planning and control of distributed

multiple product development projectsYong-Han Lee, Soundar R.T. Kumara∗

Department of Industrial and Manufacturing Engineering, The Pennsylvania State University,310 Leonhard Building, University Park, PA 16802, USA

Abstract

e-Manufacturing is becoming popular with the increased use of the internet. Due the widespread availability of the Internet large-scaledistributed projects in manufacturing are becoming popular. The authors present a distributed, collaborative, and adaptive planning andcontrol approach for distributed multiple product development projects (DMPDPs), which is a representative project environment in moderne-enterprises. In DMPDP environment, multiple project groups share and compete for limited resources to achieve their own goals. Onthe other hand, the shared resource divisions intent to efficiently utilize their resources. It is suggested that this kind of situation can bewell modeled and efficiently solved by using two novel approaches: multiagent based information infrastructure and market-based controlmechanism. In this paper, the authors (i) formalize the DMPDP planning and control problem, and (ii) propose a market-based negotiationmechanism called unified-sequential market-clearing (U-SMC) protocol. The theoretical foundations of this novel concept are dealt with.© 2003 Published by Elsevier Science B.V.

Keywords:Unified-sequential market clearing; Distributed multiple product development project; e-Manufacturing

1. Introduction

The rapid change in both technology and the marketplacein recent years has called for a new paradigm for manag-ing large distributed projects. e-Manufacturing has lead toglobalization and large-scale distributed projects are verycommon to see. In order to compete in the highly competi-tive marketplace, modern enterprises are forced to compresstheir product development lead-time. In addition, projectshave become more and more distributed due to economicreasons and project fulfillment processes are overlapped.Internet is demanding rapid generation of information forimmediate availability to all the participants globally. There-fore project management has become harder. In these sit-uations, traditional project management techniques cannotprovide the required functionality to react effectively to thechanges and to support collaborative project managementprocesses in dispersed project environments. For the sakeof clarity of problem definition, we wish to characterize arepresentative project environment in modern and futuristicvirtual enterprises, called distributed multiple product de-

∗ Corresponding author.E-mail address:skumara@psu.edu (S.R.T. Kumara).

velopment projects (DMPDP). The unique characteristicsof DMPDP environments are as follows:

1. Frequent change inevitability. Due to the dynamicchanges in the market situation and a company’s mar-keting strategy, product designs, and product launchschedules frequently change.

2. Tightly coupled development process. Component partsof a final product and accordingly the individual tasksare tightly coupled.

3. Disciplinary self-interestedness. The functional divisionshave their own self-interests, for example, allproject ori-ented divisionswant their products or component partsto be scheduled on time;resource oriented divisionsaremore interested in efficient resource utilization and workload leveling. As a result, a great deal of coordination isrequired to solve conflicts between divisions. Accordingto Petrie[1], a result from a survey at Boeing showedthat 60% of the labor is devoted to task coordination.

4. Information/control distribution. As divisions get dis-tributed organizationally, geographically and/or compu-tationally, local divisions maintain local information—not only factual data but also process and planning knowl-edge. In addition, as the scale of a project grows, moreand more decisions are made by local organizations.

0924-0136/03/$ – see front matter © 2003 Published by Elsevier Science B.V.doi:10.1016/S0924-0136(03)00217-6

Y.-H. Lee, S.R.T. Kumara / Journal of Materials Processing Technology 139 (2003) 178–186 179

Fig. 1. Process centered project vs. component centered project.

5. Component part orientation. The product develop-ment projects are basically component oriented unlikeother processes or task centered projects such as R&Dprojects, construction projects and ship building projects.Typically a project in a DMPDP comprises of a setof multiple subprojects, each of which is to develop acomponent part or a module.Fig. 1 illustrates the differ-ences betweenprocess centered projectsandcomponentcentered projects.

1.1. Problem definition

In this paper the authors will address the problem ofeffective resource allocation in DMPDP environment. Thisproblem asplanning and control of DMPDP. Althoughthis can be thought of as scheduling and re-scheduling ofdistributed projects, the authors make a clear distinctionin the sense that the initial scheduling is planning for theuncertain future and short-term re-scheduling is executioncontrol. In our context, control is more frequent comparedto occasional rescheduling. Hence,planningandcontrol inthe current research means the initial scheduling and theshort-term scheduling or adaptation respectively.

1.1.1. A DMPDP exampleConsider an automotive manufacturing company having

four technical centers in Korea, Italy, UK and Germany, sayTCK, TCI, TCE and TCG, respectively. Every technicalcenter has multiple functional divisions internally and thefunctionality of each technical center is not mutually ex-clusive among the four technical centers. For example, TCIhas only a design studio and a prototyping division, TCEhas multiple body and chassis engineering design divisions,a prototyping division, and a testing division and TCG hasengine design and prototyping divisions. TCK has full func-

Fig. 2. An example of DMPDP organization.

tionality, namely it has all functional divisions required fora car development including the ones that other technicalcenters also have.Fig. 2 shows an example of the DMPDPorganizational structure. On the basis of the company’s plat-form line-up, four basic car programs are being carried outsimultaneously (projects a, b, c and d). Each car platform hasmajor-changeprojects once every 4 years andminor-changeprojects in between, meaning that a new project starts every6 months.

Now the question is how one can handle such a dynamicplanning and control problem in such an uncertain situation.In order to solve the DMPDP planning and control prob-lem, a distributed, collaborative, and adaptive planning andcontrol approach is required.

1.2. Basic approaches

The planning and control problem arises due to the self-interests of divisions, no matter whether they are projectoriented or resource oriented, conflicting with each other.Namely, each project group tries to secure enough resourcesto achieve their goals with higher probability. However, dueto the resource restriction one can rarely come up with a solu-tion satisfying every group. In addition, it is even unclear thatwhich solution is better than the others from the enterprise’sperspective. So, it is very natural to model this problem asa negotiation process between competitive participants whoneed to acquire some resources to achieve their individualgoals. And the prices of the commodities must be deter-mined based on the market principle—higher is the demand,higher is the price. In other words, the planning and controlproblem can be formulated as amarket-based resource al-location problem. In order to facilitate the market-based ap-proach it is necessary to have a computational architecture.The DMPDP can be facilitated through amultiagent system(MAS).

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1.3. Objectives of the paper

In this paper the authors propose a solution methodo-logy for the DMPDP problem. In specific, the objectivesof the paper are to develop a market-based planning andcontrol mechanism. Important research issues include: (i)modeling a resource allocation economy including the def-initions of goods, producers and consumers, (ii) an utilityfunction that incorporates the relative value of a goodfrom the individual project perspective, and (iii) marketprotocol consisting of an auction mechanism and biddingpolicies.

2. Background literature

Some of the most important literature related to this workin this section, are discussed.

2.1. Decomposition methods for distributed projectscheduling

Resource constrained project scheduling problems are ageneralization of the NP-hard job-shop scheduling problems.Hence, major efforts to solve this problem inoperationsresearch(OR) have concentrated on developing heuristicprocedures to obtainnear optimalsolutions. Luh et al.[2,3]formulated the scheduling problem of multiple distributeddesign projects as aninteger programming(IP) model, andproposed efficient solution procedure based onLagrangianrelaxation (LR) along with a stochastic dynamic program-ming method and some heuristics. They assume that thesubprojects are de-coupled in theprocess centeredprojectconfiguration as shown inFig. 1(a). This assumption, whichis not adequate for DMPDP, makes the problem formulationseparable so that LR can be successfully applied.

2.2. Distributed artificial intelligence/MAS for distributedproject planning and control

Distributed artificial intelligence (DAI) community hasaddressed the distributed project planning and controlproblem. Chang et al.[4] modeled the distributed projectplanning problem as a set of distributedassumption-basedtruth maintenance system(ATMS). Although each ATMS,as a decision support system(DSS), helps a distributedplanner to maintain his/her local plan consistently, conflictresolution among the participants’ plans still is based onface-to-face negotiations. Petrie[1] investigated the projectmanagement problem from the viewpoint ofprocess coor-dination and pointed out the importance ofchange prop-agation in distributed project environment. His research isconcentrated on modeling the dependency among the ele-mentary project activities rather than resource planning andcontrol. Drabble[5] pointed out that the desirable frame-work for intelligent project planning and control tool in

wide area project managementproblem would be based ona multiagent framework.

2.3. MAS for design projects

Although MAS based project planning and controlresearch can hardly be found, MAS applications for designprocess coordination have been frequently reported. Mul-tiagent design system (MADS) is a design application thatincorporates multiple software agents[6]. Some researchersdemonstrated that MADS can be successfully applied in thelarge-scale, distributed design environments by integratinghuman engineers and a set of application software usingmultiagent framework[7–10].

2.4. Market-based distributed resource allocation

Market-based controlis a paradigm for controlling com-plex systems that would otherwise are very difficult tohandle, by taking advantage of some desirable features ofa marketincluding decentralization, interacting agents, andsome notion of a resource that needs to be allocated[11].This approach has been applied to a wide range of fieldssuch as computer resource allocation, network bandwidthcontrol, power grid control and factory scheduling. Becauseof the similarity in problem formulation, we review someof literature in factory scheduling area.

2.4.1. Market-based contract net-bid for tasksBaker [12] and Tilley [13] showed the market-based

control is well applicable to real-time factory schedulingproblem in aheterachicalsituation. In their models eachagent controls one or more manufacturing resources suchas machines, material handling systems, inventory stor-age, and manual operations. Responding to the arrivals ofnew orders, the machine agents recursively bid for the re-maining tasks in a quite straightforward way. Hence theirresearch can be seen as a market-based extension ofcon-tract net. The limitation of their problem formulation isthat they did not seriously take into account the commonscheduling constraints such as strict due dates or resourceconstraints.

2.4.2. Market-based distributed scheduling-bid forresources

Walsh et al.[14] modeled the factory scheduling problemas a discrete allocation problem by seeing the resource’stime slots as discrete resources. In theirfactory schedulingeconomy, the time slots of a factory (as a single machine)are bought by and sold to the agents, who need the factoryfor a given period of time, through a simple auction mech-anism. Although the model is too simple, which cannot bedirectly applied to any practical problems, their theoreti-cal analysis of auction mechanisms gives good theoreticalinsights.

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2.5. Market-based software project scheduling

Qian[15] suggested the possibility of market-based soft-ware development project scheduling in his master’s the-sis. In the project scheduling economy, he introduced twotypes of goods: (i) resource time slots, which representthe employee’s working time just like Walsh et al.[14]did, and (ii) project time slots, which represent the prece-dence relation between consecutive tasks. The task agents(TAs) bid for the both types of time slots, and the priceof each slot is adjusted every bidding iteration based onthe number of bids to the slot. Because of the tight cou-pling between two time slots prices, the mechanism couldnot generate convergent solutions for a practical size of theproblems.

3. DMPDP planning and control problem

In this section the authors formally define fundamentalterms related to DMPDP planning and control problem.On the basis of these definitions, the planning and controlproblem of DMPDP is defined clearly.

3.1. DMPDP environment

Two elements are defined that constitute the DMPDPproblem domain: (i) a set of product development projects,and (ii) a set of functional divisions.

Definition 1 (product development project). Aproduct de-velopment project Pi is a quadruple〈Gi,Ci,Qi,Ni〉, whereGi is a set of milestones,Ci a set of all component parts,Qi a set of processes andNi the set of the precedenceconstraints.

As shown in the definition, a product developmentproject Pi may have multiple milestones or goals,Gi ={Gi1,Gi2, . . . ,Gi|Gi|, }, including the target project com-pletion dateGi1. For the sake of simplicity|Gi| = 1 for alli will be assumed in the remaining part of this paper. Tasks,denoted by a setTi, from the traditional project network’spoint of view, are defined by the component-process pairs,i.e.Ti ⊆ {Ci×Qi}. The examples of processes inQi includeengineering design, FEM analysis, prototype tooling, etc.The precedence constraints can be defined by task pairs,i.e.Ni = {(Tij , Tik) : j = k; Tij , Tik ∈ Ti}.

Definition 2 (functional division).A functional division Djis an organizational unit that comprises a set of resources,Rj = {Rj1, Rj2, . . . , Rj|Rj |}. All Rjk in Dj are located ata common place and under a common control exclusively,i.e. everyDj has its own manager or control.

Each resourceRjk has a capability to perform a specificprocessq ∈ Q, whereQ = ∪n

i=1Qi. Based on the abovetwo definitions, the DMPDP environment, can be defined asfollows.

Definition 3 (DMPDP). A DMPDP environment,Π, isdefined by a set of product development projects,P = {Pi},and a set of distributed functional divisions,D = {Dj}, i.e.Π = 〈P,D〉.

3.2. Cost function and project plans

In order to define the concept of a plan, one needs todefine beforehand a measure that decides on the superiorityof one plan with respect to another. For this purpose, a utilityfunction, called thedeviation cost function, is defined asfollows.

Definition 4 (deviation cost function). Adeviation costfunction, φi : R → R+, of a product development projectPi

is a function in time domain, representing the penalty costdue to the deviation of the project completion time from theoriginal completion target,Gi1. Obviously a smaller valueis preferable to a bigger value in this function, i.e. if thecompletion times of two plansA′

i andA′′i for a projectPi

are t(A′i) and t(A′′

i ), respectively,A′i � A′′

i if and only ifφi(t(A

′i)−Gi1) < φi(t(A

′′i )−Gi1), i.e. planA′

i is preferableto A′′

i .

Definition 5 (engagement). Anengagement, eil = (j, k, w),defines the assignment of a taskTil in Pi to a resourceRjk,wherew = (w1, w2) defines the time window in which thetask is to be allocated.

Definition 6 (project plan). Aproject planof Pi, denotedby Ai, is a set of engagements which covers all tasks inPi,i.e.Ai = {ei1, ei2, . . . , ei|Ti|}.

Definition 7 (DMPDP plan). ADMPDP plan (A) is a setof project plans within the DMPDP planning horizon, i.e.A = {Ai}.

Definition 8 (feasible DMPDP plan). Afeasible DMPDPplan is a DMPDP plan that satisfies all the constraints ofboth types—precedence and resource—for all projects in theDMPDP environment.

Definition 9 (efficient DMPDP plan). Anefficient DMPDPplan is a feasible DMPDP plan that isPareto optimalwith re-spect to the deviation costs of the individual projects, mean-ing that no project can improve its utility without worseningthe utility of any other project in the DMPDP.

Definition 10 (deviation cost range). Each project’s devia-tion cost can be calculated as defined inDefinition 4. Wecall the range of the all project’s deviation costsdeviationcost range(DCR), i.e.:

DCR(A) = maxi

(φi(t(Ai) − Gi1)) − mini(φi(t(Ai) − Gi1))

(1)

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Definition 11 (τ-balanced DMPDP plan). Aτ-balancedDMPDP plan is an efficient DMPDP plan that the rangeof the deviation costs of individual projects in a DMPDPis less than a given toleranceτ, i.e. DCR(A) ≤ τ for aDMPDP planA.

3.3. Planning and control

Now the planning and control of DMPDP is defined—the goal of this work. The planning procedure is carriedout every time a new product development project starts;control is a persistent procedure for maintaining the projectsas planned. Associating the concept of balance, we definethe plan and control as follows.

Definition 12 (DMPDP planning). ADMPDP planningisa procedure to generate a newτ-balanced DMPDP plan byadding a new product development project to the currentDMPDP plan, which has been alsoτ-balanced throughoutan ongoing DMPDP control procedure.

Definition 13 (DMPDP control). A DMPDP control isa persistent procedure to maintain a DMPDP plan to beτ-balanced all the time.

4. Multiagent based information system model

In this section, the authors present theDMPDP planningand control economymodel from the multiagent informationsystem’s viewpoint. The design and implementation issuesare not laborated open, as the focus is on the market-basedmodel and not on the IT infrastructure.

4.1. Agent organization

Five agent classes are defined—project manager (PM),component agent (CA), TA, resource manager (RM), andresource agent (RA)—along with some supportive mis-cellaneous agents. The following are the fundamentalroles of these agents and the key information entities theymaintain:

1. PM. This kind of agent is in charge of managing a projectplan by controlling the individual CAs. To achieve thesegoals, a PM is to (i) manage individual CAs belongingto the project and (ii) negotiate with RMs and/or otherPMs to resolve conflicts if required.

2. CA. Each CA is in charge of managing the devel-opment schedule of a component—a single part or amodule—based on so-calledcomponent process net-work (CPN), which is simply a component-wise projectnetwork.

3. TA. A TA is in charge of managing the schedule of a taskunder the control of the CA. This kind of agent works asa bidder in a resource time-slot market.

4. RM. Each RM is in charge of managing a set of resources,such as the manager of a computational analysis groupin a physical organization.

5. RA. Each RA is in charge of a unit of resource such asa machine, a worker and a tier of computer software.Each RA works as the auctioneer in a resource time-slotmarket. RAs maintain a few properties of the resourceincluding maintenance schedule, availability, capacityand cost of use.

In practice CAs usually form a hierarchical structurebased on theassembly part list(APL) or bill of material(BOM) information, causing the planning and control sit-uation much more complicated. Consider an example withthree components as shown inFig. 3. In this example,component-A is an assembly ofcomponent-B andcomponent-C. Although component-A’s CPN con-tains three processes (taskA1, taskA2 andtaskA3), thefirst two are just an aggregation of the task pairs (taskB1,taskC1) and (taskB2, taskC2), respectively. For the sakeof clarity, lettask∗1 denote anengineering design processof component-∗; let eachtask∗2 denote aprototypefabrication processof component-∗, and lettaskA3 de-note atesting process. Even though the engineering designand the prototype fabrication ofcomponent-A are undercontrol of TAs and a CA, these processes arevirtual, in thesense that they are not to be directly assigned to a specific re-source. The authors call this kind of tasks asaggregate tasksand the corresponding TAsaggregate TAs; call other kind oftasksassignable tasksand the corresponding TAsassignableTAs. Obviously, aggregate TAs do not bid for resource timeslots by themselves, instead they affect the bidding policiesof the TAs who are in charge of the “aggregated” tasks suchastaskB1, taskB2, taskC1 andtaskC2 in the example.

Besides the project group’s side, there is another part inDMPDP agent organization—resource or functional divi-sions. In contrast to the project groups, individual functionaldivisions are not under control of any higher organizationalentity. Each division has a single RM who coordinates theRAs, by affecting their pricing mechanism by some means.The RAs have central role in the resource time-slot markets.

Fig. 3. An example of hierarchical organization structure of CAs.

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4.2. Resource time-slot market

A resource time-slot market is established for every re-source, meaning that every RA will be an auctioneer for sell-ing the bundles of resource time slots to TAs—the bidders.Besides the resource time-slot markets, Qian[15] proposedanother type of market, calledproject time slot market, toensure the precedence between tasks in the software projectscheduling problem, as mentioned inSection 2.5. The ne-cessity of the project time slot markets, however, are notmuch appealing in DMPDP planning and control economymodel in that most of the precedence constraints are de-fined within the CPNs, meaning that the precedence couldbe coordinated explicitly by CAs and TAs without iterativemarket mechanisms. The details of the mechanism will bepresented inSection 5.

5. Market-based planning and control mechanism

In this section is presented the market-based DMPDPplanning and control mechanism. In the first section weinvestigate the problem structure from the market-basedcontrol perspective, and propose the fundamental designapproaches for the market-based resource allocation mech-anism. In the following sections, the details of the proposedmechanism are presented.

5.1. Mechanism design overview

5.1.1. Structure of abstract economyThe DMPDP planning and control environment is mod-

eled as an abstract economy, where multiple agents buyand sell the resource time slots. The overall DMPDP plan-ning and control economy is adynamic economyin thesense that multiple markets are dynamically established andcleared over time. This dynamic economy is called, as awhole,DMPDP economy. As shown inFig. 4, the DMPDPeconomye is an infinite sequence oftemporary economieset ’s, each of which is a set of uncleared time-slot markets ata specific timet. The individual time-slot market is calledthe local market, denoted bymj, which corresponds to theresourceRj. If every market in a economy has been cleared

Fig. 4. The structure of DMPDP planning and control economy.

and remains in the balanced and efficient status, the DM-PDP economy is calledstable. If there happens a changeat t that cannot be absorbed within the working window,the temporary economyet is established at this spot. In thistemporary economy, inter-related multiple local marketsmj ’s are established.

5.1.2. Mechanism design approachesIn order to design an efficient mechanism to generate a

desirable resource allocation, i.e. a DMPDP plan, one needsto designate approaches for each of three levels mentionedabove—DMPDP economy, temporary economy, and localmarket level:

1. For the DMPDP economy level control, aunifiedplan-ning and control loop is proposed, which keeps workingover time to maintain an efficient and balanced DMPDPplan.

2. For the temporary economy, asequential market clearingapproach is proposed for computational efficiency. Themain issue is how to design the mechanism to guaran-tee the efficiency or equilibrium in this multiple marketclearing problem.

3. For the local market, acombinatorial auctionmechanismis proposed to clear this time-slot market efficiently. Inorder for this mechanism to cause an emergent efficiencyand balancing in the higher level economies, we need tocarefully design the allocation rule, payment rule, andbid generation mechanism.

5.2. Overall planning and control procedure

As mentioned, adding a new project on a given runningDMPDP environment is just an extreme case ofchangesin a DMPDP environment. In this sense, the planning pro-cess and the control process can be combined in a unifiedplanning and control loop (seeFig. 5). The authors callthe overall planning and control mechanism based on thisloop unified-sequential market clearing (U-SMC) mecha-nism. In the U-SMC, the only differences between a newproject planning and routine control processes exist in thescale of re-planning horizon, the number of resources to bere-scheduled, and accordingly the number of inner-loop it-erations. The steps and issues in the U-SMC mechanismdesign are explained below:

1. Detect changes. Various types of changes in DM-PDP environment can be detected by different types ofagents. The detected changes must be reported to PMsor RMs depending on the type of changes.

2. Generate relevant RA list. When an RM isasked to adjust the schedules of its resources by a PM oran RA, the RM starts generating a list of RAs that are incharge of the resources to be re-scheduled. The authorscall this list the relevant RA list (RRAL), which is theset of sellers in a temporary market.

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Fig. 5. The DMPDP planning and control loop.

3. Sort the RRAL. The resource schedules are relatedeach other in a temporary market, so the change of aresource schedule may affect others’ through the prece-dence relations. For the sake of efficient implementation,the resource allocation (or market clearing) are donesequentially rather than simultaneously using a set ofordering rules mainly based on the due dates and prece-dence relationships.

4. Form a local market. The RA in charge of aresource to be re-scheduled initiates the correspondinglocal market, by broadcasting or selectively sendingmessages to the relevant TAs. A detailed speech-actdesign between agents is necessary to accomplish this.

5. Clear market through auction. An efficienttime-slot allocation is achieved through an auction mech-anism, which is formulated as an combinatorial auction.

6. Update DMPDP plan. According to the result ofthe auction, the DMPDP plan is updated. Because theplans are maintained by RMs and PMs in a distributedway, an information forwarding mechanism needs tobe developed to maintain the individual agents’ beliefsconsistently. The updated DMPDP plan can possibly bedetected as a change by other agents, thereby causinganother iteration of the DMPDP planning and controlloop.

5.2.1. Change detectionThe changes, which activate a planning and control pro-

cess in a DMPDP environment, can occur and be detectedin various ways such as adding a new project is informed toa PM directly from the top management; re-designing of apart due to some design failure may be detected by the corre-sponding CA and reported to itsmanger PM; re-schedulingof a task due to any execution failure may be detected by anRA and reported to the RM and the CA. The authors define

significant change, which causes any market establishment,as follows.

Definition 14 (significant change). Asignificant changeisthe change in DMPDP environment, which requires any re-source re-allocations, caused by either precedence violationor working window violation.

Any further detailed analysis and design of change detec-tion and reporting mechanism will be addressed in the cur-rent research. At this point, however, we just propose that(i) any change requiring new tasks must be reported to thePM, and (ii) any change regarding any resource failure mustbe reported to the RM.

5.2.2. RRAL generation and orderingThe RRAL defines the scope of re-scheduling by includ-

ing the RAs who are in charge of resources that are affectedby the detected change. In order to generate the RRAL,precedence relationships defined in the CPNs and compo-nent hierarchy defined in APL are used. We call the RRALthat consists of directly (i.e. through a single precedence re-lationship) affected RAs asfirst order RRAL. In the samesense, we can definenth orderRRAL by counting the depthof the RRAL search. Let us define these concepts below, fol-lowed by a simple example of first order RRAL generation.

Definition 15 (RRAL). An RRAL, L, is a list of RAs, i.e.L = [RA1, . . . ,RA|L|],where each RAi is in charge of aresource that is selected to be re-scheduled due to a changein DMPDP environment.

Definition 16 (origin RA). An RA, RA0, in an RRAL,L, iscalled anorigin RAof the RRAL, if RA0 is in charge of theresource that is directly affected by the change that causedthe formation ofL.

Definition 17 (order of RRAL). An RRAL,L, is callednthorder RRAL, if and only if every RAi; i = 1, . . . , |L|, canbe reached from any of the origin RAs inL within n stepsof precedence relationships.

Example 1 (a local market: RRAL generation). Consider asingle local market, which is established due to a resourcefailure, as shown inFig. 6. In the example, a resourceR22 indivision-2 failed and accordinglyRA22 reports a changein schedule to theRM22, and start searching the relevantRAs by askingTAA1 andTAB1 to search relevant RAs undertheir ownbranches. TheRA22 is obviously included as anorigin RA or zero order relevant RA, andRA12 andRA33are included in the RRAL through out the first order RRALsearch. Hence, the RRAL=[RA22, RA12, RA33].

In the proposed DMPDP planning and control loop(U-SMC), the authors solve the resource re-schedulingproblems sequentially based on the sorted RRAL, ratherthan solve the multiple markets simultaneously in order toget any kind of multiple market equilibrium. Obviously, the

Y.-H. Lee, S.R.T. Kumara / Journal of Materials Processing Technology 139 (2003) 178–186 185

Fig. 6. Generating a first order RRAL (in case of resource failure).

proposed approach has computational advantage; the laterapproach (simultaneous multiple markets clearing) has anadvantage in solution quality. However, it is suggested thatthe proposed sequential market-clearing approach can get asgood solutions as the later approach if one design the RRALordering rules carefully, because the change propagationis mainly based on the precedence between tasks. Further-more, it is proposed to use the first order RRAL basedon the assumption that furtherchange propagationcan beachieved through out the outer loop in the next iteration.

5.2.3. Local market formulationAs shown inFig. 5, the proposed mechanism has to form

and clear the local markets in the inner loop. There are threemajor approaches for solving the market-based discreteresource allocation problems: (i) iterative price-adjustmentmechanisms for generatinggeneralized equilibriumsolu-tions, including Walras’ originaltatonnement algorithm[16] and its distributed implementation—Walras algo-rithm [17]; (ii) simple ascending auction mechanisms forgenerating competitive equilibrium in efficient and simpleway (see Walsh et al.[14] and Ausubel[18]); (iii) combi-natorial auction mechanisms for maximizing revenue forbundles of discrete resources. In discrete resource timescheduling formulation, the value of each time slots cannotbe decided independently each other. However, the first twoapproaches cannot handle thiscomplementaritybetweenindividual time slots. Hence, the combinatorial auction isthe obvious choice for formulating the resource time slotmarket (i.e. a local market) in the current research.

Before presenting the detailed issues of the auction mech-anism in the following sections, we formulate a local marketas a special type of combinatorial auction. Suppose that wehavemTAs, andn consecutive time slots to be allocated in aresource time slot market. LetX {i : i = 1, . . . , n} be the setof time slots, where the time slots are ordered in chronolog-ical order. The authors allow combined bids for any set ofconsecutive time slots (bundle),Bij = {x ∈ X : i ≤ x ≤ j},which can be interpreted as a time interval. LetB be the setof all possible bundles, soB = {Bij : 1 ≤ i ≤ j ≤ n}. Thewinning bundles in the auction must be disjointed because

no time slot can be allocated twice. Anallocation is anyS ⊂ B such thatB ∩ B′ = ; for everyB, B′ ∈ S.

Assume that the goal of the RA is to maximize his rev-enue, for example, the sum of winning bids (more generalargument on this issue will be presented inSection 5.4). Letvi(B) be the bid submitted by TAi. Letw(B) = maxi{vi(B) :TAi bids forB}. If no bid is submitted forB, setw(B) = 0.Using this notation, one can define the goal of the RA, find-ing anoptimal allocation S∗, such as:

S∗ = arg maxS

∑

B∈Ss(B). (2)

Recall the optimal allocationS∗ is an optimal choice for thesingle time slot auction problem. However, it may not meanthat this is optimal from the global DMPDP planning andcontrol perspective. Now think about the meaning of theoptimal allocation in the global perspective. InSection 3, wedefined the efficiency andτ-balance of a DMPDP plan. Thequestion is whether and how the optimal allocations workfor generating aτ-balanced (or efficient, at least) DMPDPplans. The following three design parameters do the mainrole in designing a mechanism for generating such solutions.These three design factors are presented in the followingsections:

1. utility function, v(•), which represents theproject group’spreferenceon a specific bundle.

2. allocation rule, which represents theresource division’spreferenceon bundles. In the above example,S∗ calculat-ing function is an example of allocation rule (seeEq. (2)).

3. payment rule, which controls the incentive for bidders toattend the auction in a desirable manner.

5.3. Utility function

When a TA,Mi, receives an invitation to a local marketfrom an RA,Mi has to prepare a bid, denoted byXi. The invi-tation message contains the re-scheduling horizonh, withinwhich the tasks will be re-scheduled. Within this time hori-zon, Mi generates the bid, which is a set of bundle-utilitypairs, i.e.Xi = {(Bjk, vi(Bjk)) : 1 ≤ j ≤ k ≤ n}, where there-scheduling horizonh = [1, n]. The pattern of the utilityfunction v(•) is a critical and sensitive factor determiningthe auction result, so it must be carefully designed and tunedup in practice. The following are requirements for designingthe utility function:

1. It must work for the overall mechanism to generate andmaintain the global efficiency,τ-balance of the DMPDPplan, as an emergent property.

2. Penalty must be assigned to the bundles that violateprecedence and working window constraints so that thosebundles cannot be allocated.

The main factor to be taken into account for generatinga utility on a time-slot bundle must be the resultant slack-ness of the task schedule when the task is allocated on the

186 Y.-H. Lee, S.R.T. Kumara / Journal of Materials Processing Technology 139 (2003) 178–186

time-slot bundle. This measure may be determined based onPERT/CPM type critical path analysis with respect to goals.

5.4. Auction mechanism

Suppose that the RA already decided the set of TAsM = {Mi} and re-scheduling horizonh = [1, n], and sentinvitations to allMi ∈ M, thereby, forming a local mar-ket. Using the formulation explained inSection 5.2.3, theauction mechanism can be summarized as follows:

(1) Each agentMi ∈ M generates a bid:Xi = {(Bjk,

vi(Bjk)) : 1 ≤ j ≤ k ≤ n}.(2) The RA computes the optimal allocation:

S∗ = arg maxS⊂B

{W(S;X) : B ∩ B′

= \O; for everyB,B′ ∈ S} (3)

(3) Allocate the time-slot bundles of winning bids, and paynegative or positive rewards to the winning bidders.

5.4.1. Allocation ruleEq. (3) generalizesEq. (2) by introducing a function

W(S; X). The functionW(S; X) defines the preference ofthe RA. The most desirable goal of the resource division isto maximize an aggregate utility, which can be defined asa function that maps the set of bidders’ individual utilitiesto a single real-valuedsocial utility. The authors call thisfunction, W(S; X), aswelfare function. If one chooses thewelfare function as an increasing function with respect tothe individual utilities, the welfare maximizing allocationS∗ is Pareto efficient. The present approach is to maximizethe social welfare, which also ensures Pareto efficiency.

5.4.2. Payment ruleIn a simple mechanism, the winning bidders get rewarded

only through the goods (resource allocations). It means awinning bidder’s pay-off is exactly the bid (utility) itself.However, we can design different payment rules in order togive bidders some incentives to behave in desirable ways.

6. Summary

In this paper the authors proposed a MAS architectureand a market-based mechanism for DMPDP planning andcontrol problem. The discussion in this paper is novel and itis believed that they are the first to propose such a solutionstrategy. Although the arguments are theoretically validated,

one needs to implement them to ensure convergence, effi-ciency and scalability of the proposed information infras-tructure and control mechanism. Currently the present areimplementing our schemes are being implemented Java.

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