A Multiagent Based System for Resource Allocation and Scheduling of Distributed Projects

Transcription

1 International Journal of Modelin and Optimization, Vol. 2, No., Auust 2012 A Multiaent Based System for Resource Allocation and Schedulin of Distributed Projects Sunil Adhau and M. L. Mittal Abstract In this paper, a multi aent based decentralized decision makin approach is presented for allocatin resources and schedulin of distributed multiple projects. The resource allocation and schedulin is performed cooperatively and collectively by a roup of autonomous project aents, resource aents and a mediator aent. We propose a price mechanism that allows project aents to bid for the needed resources. A new contract net protocol (CNP) concept is used for neotiations and coordination amon the aents. This approach is successfully applied on an example problem. Index Terms CNP; biddin; multiaent; multi project; schedulin. I. INTRODUCTION Multi-project schedulin is a process of the schedulin of two or more simultaneously runnin projects which demand the same scarce resources. These problems are referred to as the resource-constrained multi-project schedulin problems (RCMPSP). RCMPSP can be solved by exact procedures, metaheuristics, or simple priority rules. For real-world problems, however, exact procedures are impractical due to computational intractability and thus heuristic procedures are used. In most of the research on multi-project schedulin problems, plannin and control of projects is often considered centralized and manaed by a sinle manaer. This in practice is very limitin assumption. In decentralized multi-project schedulin problem the decision makin process is decentralized with as many local and autonomous decision makers (project manaers) as the projects. Confessor [1] refers to this problem as the decentralized resource constrained multi-project schedulin problem (DRCMPSP). This kind of environment is commonly found in automobile industry where supplier carries out several enineerin projects with different automobile manufacturers or oriinal equipment s manufacturers (OEM s). In the last decade, aent based systems for project schedulin has received a reat attention from the academic. An aent may be defined as an entity that is situated in some environment, and that is capable of autonomous action in this environment in order to meet its desin objectives [2]. An aent is considered intellient when it has the followin capabilities: reactivity, proactiveness, and social ability [3]. Manuscript received April 12, 2012; revised June 28, Sunil Adhau is with the Mechanical Enineerin Department, Government Polytechnic Pune INDIA ( * correspondin author mobile: ; fax: ; suniladhau@ mail.com). M. L. Mittal is with the Department of Mechanical Enineerin, Malaviya National Institute of Technoloy, JAIPUR INDIA. ( [email protected]). A multi aent system (MAS) is a distributed artificial intellience system composed of a number of autonomous aents capable of communicatin and collaboratin with each other to achieve common oals [3]. This paper is concerned with developin a multi aent based schedulin approach in which multiple distributed projects share a set of lobal resources. All the projects have to be planned simultaneously by a roup of local decision makers (project manaers, resource aent and mediator aent). A project aent PA i is responsible for a project i consistin of a set of activities. Activities in the projects need certain resources for their completion which are provided by the resource aents. A resource aent RA is responsible for a resource type ; that receives the resource requests from project aents and neotiates with the project aent for the allocation of the resources. The objective of the problem is to obtain a quality schedule of all the projects while respectin the resource availability and precedence constraints. The remainder of this paper is oranized as: Section II summarizes some related work on multi aent based project schedulin problems. Section III formally describes the distributed multi-project schedulin problem. Section IV presents the multi aent based model. Section V introduces the proposed system and describes implementation mechanism. Section VI illustrates the proposed work on simple problem. Finally, the paper presents conclusions. II. LITERATURE REVIEW Different methodoloies and techniques have been proposed in the literature for aent-based project schedulin. Knotts et al. [] develop eiht aent-based alorithms for solvin the multimode, resource-constrained project schedulin problem. Yan et al. [5] present a MAS as a technique to resource allocation problem in a distributed environment. For solvin decentralized multi-project schedulin problems, only a few methods are available in literature. Lee et al. [6] is probably the first who presented a dynamic economy model and a novel market based mechanism for dynamic resource allocation in a multi-project environment. Later on, Confessore et al. [1] developed a MAS model for schedulin of multiple projects. Authors assume that sinle unit of a shared resource is available in each period of plannin horizon. Both systems are based on modern electronic auctions for resource allocation and simple heuristics for schedulin activities. A coordination mechanism usin arumentation-based neotiation is introduced by Lau et al. [7],[8]. They propose a MAS consistin of a set of schedule aents and a set of contractor or resource aents with different local objective functions. Homberer [9] suested a MAS for the DRCMPSP with 52

2 International Journal of Modelin and Optimization, Vol. 2, No., Auust 2012 several lobal resources. Each sinle project is planned by one responsible schedule aent. An iterative coordination mechanism based on centrally imposed solutions is used. Adhau and Mittal [10] presented a new approach to solve the decentralized resource constrained dynamic multi-project schedulin problem usin a cooperative MAS. The brief review of the related literature shows that there are only a few studies concernin multi-project environment, usin multi-aent technoloy in particular. The current paper considers these problems and proposes a multi aent based solution approach for schedulin of distributed multiple projects. III. PROBLEM DESCRIPTION AND OBJECTIVES A DRCMPSP can be described as follows. There is a set of M projects runnin simultaneously at eoraphically different locations utilizin local (always available to the concerned project) and lobal (shared amon the projects) resources for their completion. The resources are available in limited quantity on per period basis. The projects are to be scheduled decentrally and autonomously. Each Project i {1,..., M} consists of n i non-preemptable activities a with a set j {1,...,n i }; Two fictitious activities a i0 and a in+1 each of duration zero are added to each project i for representin the start and the end of the project; E i is a set of precedence relations in project i. Pair (a, a ik ) means : a a ik ; Each project i has an earliest release time t ri, from which activity a i0 can be started; Each activity a has a non-preemptive processin duration p ; For each project i, a set of local renewable resources k (k = 1,..., K) are provided in an amount R kti in each period t (t = 1,..., T). Each activity a requires an amount r of resource type k [11]; k For each project i, a set of lobal renewable resources ( = 1,..., G) which is shared amon the projects is available in quantity R t in each period t (t= 1,..., T). An activity j of project i may require an amount r ; of resource type ; The performance of proposed method is evaluated for the Mean Project Delay (MPD) [1]; [12]; [13].MPD is defined as below, M 1 Mean project delay ( C D ) i i (1) M i 1 where, C i = Completion time of project i, D i = Desired due date of project i, as determined by initial schedulin with local resources. IV. AGENT- BASED MODELING FOR MULTI-PROJECT SCHEDULING In this study, we model a distributed multi-project schedulin problem as a multi aent system. An aent PA i is used to model the schedulin processes of a project i. It is implemented as a proram that is located at the individual project and aims at buildin initial feasible local schedule based on its capacity constraints. PA i also neotiates for lobal resources and determines the schedule of the activities with respect to resource availability of the lobal resources. Each project aent has its own schedulin objective and acts independently to each other. Objective of project aent PA i is to complete the project within a iven due date and at minimum total cost (TC i ). Total cost is the sum of the cost of performin, earliness and tardiness costs of the activities of the project. The earliness cost EC incurs when an activity j of project i is completed earlier to its due date d i (desired due date of activity a as determined by initial schedulin with local resources). The tardiness cost T incurs when an activity j of project i is completed later to its due date. The earliness cost penalizes idle time between consecutive activities [7]. The schedule S i of project i is referred to as the vector of start time (s i1,.., s in ). Let A t represent the set of activities in proress durin the time interval (t-1, t). Mathematical formulation of cost function for each project aent is as follows, n Min TC [ O E T i M (2) i j1 where, O = Operatin cost of activity a, E = Earliness cost of activity a, T = Tardiness cost of activity a Subject to, s p s i M, a a E (3) ik ik i At t 1,..,, 1,.., r R T G The objective function (2) is to minimize the total operatin cost of the solution schedule. The set of constraints (3) ensure the precedence constraints between activities of each project. Constraint () represents the capacity constraint with respect to different lobal resources of resource aent in each period. Each lobal resources has a correspondin resource aent RA who owns all available quantity of resources durin different time periods. The properties of resources and the utilization status are recorded in the memory of RA. The mediator aent (MA) will be responsible for identification of resource conflicts and allocate lobal resources to projects usin bid selection alorithm. Mediator aent updates the capacities of the available lobal resources allotted to current projects. It also stores the schedules of all projects into the database. V. CO-ORDINATION MECHANISM Contract net protocol (CNP) is used in this paper for distributed plannin and schedulin. Contracts are a powerful co-ordination mechanism in distributed systems. CNP specifies a biddin approach that enables resource allocation amon multiple aents [1]. Based on the cost functions derived in section IV, this paper proposes a new contract-net based neotiation mechanism for allocatin lobal resources to the projects. The neotiation process is coordinated by a () 525

3 International Journal of Modelin and Optimization, Vol. 2, No., Auust 2012 mediator aent. We apply economy-based biddin mechanism which coordinates resource allocation amon the project aents competin for specific amount of lobal resources. Fi. 1, depicts the communication scenario between project aent PA and resource aent RA concernin a slot reservation of lobal resources. The CNP neotiation process and the activities performed by different types of the aents are discussed as follows. PROJECT AGENT (PA) Start CNP Announcin activities for resource requirement for period τ NO / reply Awardin /select activities to schedule Schedule all activities YES Stop Fi. 1. CNP neotiation protocol. A. Project Aent In each schedulin period t the execution of protocol beins with project aents. PA i starts to schedule activity a when all its precedin activities of a have been scheduled. Each project aent do followin; 1.1. Project aent PA i announces resource requirement to the correspondin resource aent RA with the bid messae = {Project ID, Activity ID, p, r, time window} 1.2. PA i receives list of offers containin resource price P r for requested lobal resources as per step 2.3 and virtually reschedule the project Calculate bid prices for all the resources for time slot t usin followin expression; Biddin / offer prices Acknowlede / confirm RESOURCE AGENT (RA) B P p VC D (5) max pik r i i where, VC i = Completion time of virtually scheduled project i, 1.. Communicate bid = {B pik, r,time window} to mediator aent for evaluation PA i receives the cheapest slot for schedulin activity a as per step 3.1 to 3.3 of MA Send award messae to RA and schedules a on this selected slot Repeat steps 1.1 to 1.6 for each activity of project i in turn, settin t = t + 1. B. Resource Aent Resource aent RA receives bid messaes up to some expiration time from project aent PA i as per step 1.1 and prepare list of offers usin its own pricin model iven below (steps 2.1 and 2.2) for reservation of time slot on the resource requirements Calculate areate demand D t of lobal resources in each period t by the followin formula: D t n M r j1 i1 (6) where, 0 r R t Calculate P r on the basis of D t and constant availability of R t shared by all projects as below: n M r r j1 i1 P p r (7) where, p r = initial/reserve price of lobal resource per unit time RA announces resource price P r to project aent PA i throuh mediator aent. 2.. Receives award messae as per step 1.6. Checks the available capacity of recourses. In period t, reserve resource for project and send a commitment messae to the correspondin project. C. Mediator Aent The mediator aent apply the bid selection alorithm to choose the best bid as below, 3.1. Receives bids from all PA s as per step WHILE(t T) Make sequence of bids in ascendin order of bid price. Evaluate and select bid submittin hihest bid price for each resource Communicate selected bid to PA i and RA. 3.. Update the capacities until all activities with lobal resource requirement are finished. Update time period t = t + 1. VI. AN ILLUSTRATION This section presents a simple example to demonstrate how the proposed mechanism collaboratively allocate resources and schedule the distributed multiple projects. We consider a simple multi-project problem with three projects for clear demonstration of the interactions amon aents. Fi. 2 represent the activity-on-node networks of three different independent (sinle) projects i = 1, 2, and 3. The constituent activities for these project, their processin duration p and requirements for local r and lobal resources k r are iven in Table 1. The total availability of local (equal for all the projects) and lobal resources is 3 units respectively. The decisional process oes as iven below in two phases. 526

4 International Journal of Modelin and Optimization, Vol. 2, No., Auust 2012 Project 1 Project 2 Project Fi. 2. Project network of project 1, 2 and 3 TABLE I: DATA OF PROJECT 1, 2 AND 3 A. Phase I: Initialization The project aents perform the local schedulin usin a static project schedulin alorithm with minimum latest finish time (min LFT) priority rules and serial schedule eneration scheme [15]. At this phase we inore the lobal resource requirements and thus all the activities can be scheduled in projects by utilizin local resources only. Fi. 3 shows the Gantt chart for the schedules for projects 1, 2, and 3. Activity ID Fi. 3. Gantt chart for schedule with local resources. The x- axis of the chart is subdivided into equal units of periods (days in our case). The y-axis, on the other hand, lists the project activities. The dummy activities in each network are not shown in the chart. B. Phase II: Allocation of lobal resources As can be seen in Fi. 3 there are resource conflicts for lobal resources durin periods 3- (activity requires 2 units and activity 2- requires 2 addin to ) and period 6-8 (activity requires 2 units and activity requires 2 units). The resource conflicts for lobal resources are to be solved via the CNP neotiation process of the aents as described in section V. Each project aent sends request for resource requirement in bid massae (RFB) to resource aent RA.. Initial/ reserve price of lobal resource per unit time is assumed, p r =2. The resource prices is calculated as per the equation (7) and communicated to project aent. In biddin round the bid price are determined by project aent PA 1, PA 2 as 10 and 17 respectively. The mediator evaluates the bids and selects the activity 2- with hiher bid price (17) as per the bid selection alorithm. The procedure is repeated for the next time slot for allocation of the lobal resources to all activities. The start time of all activities which required the lobal resources from all projects are fixed and the remainin scheduled activities are rescheduled locally at each PA. With this interactive aent neotiation scheme, implemented on example projects, the resources are distributed successfully, and overall schedule of all projects emeres. The optimum sequence of activities for lobal resource allocation is emeres as 2-; ; ; considerin maximum bid price criteria for bid selection. Fi. shows the final multi project schedule of our sample problem. Activit y ID 2-3- Activit y ID Fi.. Final Multi-project Schedule. 527

5 International Journal of Modelin and Optimization, Vol. 2, No., Auust 2012 It is noted that project 1 shifted riht with three days delay. While project 2 and project 3 do not impact on its due date for shared resource requirement. Result shows that the optimal multi-project schedule has minimum mean project delay = The procedure can be validated considerin multiple local as well as lobal shared resources. VII. CONCLUSION In this paper we have considered distributed multi-project schedulin problem where each project utilizin limited amount of its own local and lobal (shared amon the projects) resources for their completion. A multi aent based decentralized decision makin approach is presented for schedulin of multiple projects. An aent based model is developed. The objective of the model is to minimize the makespan. We apply economy-based biddin and price mechanism in which multiple project aents compete for specific amount of resources supplied by resource aents. The biddin process is coordinated by mediator aent. We proposed a new neotiation mechanism on contract net protocol for allocatin lobal resources. This approach is successfully applied and simulated on an example problem to validate the proposed method. aent-based neotiation model, International Journal of Prod. Research, vol. 3(22), pp , [8] S. K. Lau, G. Q. Huan, K. L. Mak, and L. Lian, Aent-based modelin of supply chains for distributed schedulin, IEEE Trans Syst Man Cybern A Syst Hum, vol. 36(5), pp , [9] J. Homberer, A multi-aent system for the decentralized resource-constrained multi-project schedulin problem, Intern Trans. Oper. Res, vol. 1(6), pp , 2007 [10] S. Adhau and M. L Mittal, A multi-aent based approach for dynamic multi-project schedulin, Int. J. Advanced Operations Manaement, vol. 3, No. 3/, pp , Dec [11] A. Sprecher, R. Kolisch, and A. Drexl, Semi-active, active, and non-delay schedules for the resource constrained project schedulin problem, Eur. J. Oper Res,vol. 80(1), pp , 1995 [12] A. Lova and P. Tormos, Analysis of schedulin schemes and heuristic rules performance in resource-constrained multiproject schedulin, Annals of Operations Research, vol. 10(2), pp. 2686, [13] M. L. Mittal and A. Kanda, Two-phase Heuristics for Resource Constrained Multi-project Schedulin, International Journal of Operational Research, vol., no. 2, pp , [1] S. Adhau, M. L Mittal, and A. Mittal, A multi-aent system for distributed multi- project schedulin: An auction-based neotiation approach, Enineerin Appllications of Artificial. Intellient.,doi: /j.enappai , available online, Jan [15] R. Kolisch and S. Hartmann, Heuristic alorithms for solvin the resource-constrained project schedulin problem: Classification and computational analysis, in J. Welarz (Ed.), Project schedulin: Recent models, alorithms and applications, Dordrecht: Kluwer Academic, ACKNOWLEDGMENT The authors are thankful to the anonymous referee(s) and the editor for their constructive comments which resulted in the subsequent improvement of this article. The authors are also thankful to Department of Science and Technoloy, Government of India, New Delhi. REFERENCES [1] G. Confessore, S. Giordani, and S. Rismondo, A market-based multi-aent system model for decentralized multiproject schedulin, Annals of Operations Research, vol.150, pp , [2] M. Wooldride and N. R. Jennins, Intellient aents: Theory and practice, The Knowlede Enineerin Review, vol. 10(2), pp , [3] M. Wooldride, An Introduction to Multiaent Systems, second edition, John Wiley and Sons, UK, [] G. Knotts, M. Dror, and B.C. Hartman, Aent-based project schedulin, IIE Transactions, vol. 32, pp , 2000 [5] Y. Yan, T. Kuphal, and J. Bode, Application of multi aent systems in project manaement, Int. J. Production Economics, vol. 68, pp , 2000 [6] Y. H. Lee, S.R. Kumara, and K. Chatterjee, Multiaent based dynamic resource schedulin for distributed multiple projects usin a market mechanism, Journal of Intellient Manufacturin, vol. 1, pp. 71 8, 2003 [7] S. K. Lau, G. Q. Huan, K. L. Mak, and L. Lian, Distributed project schedulin with information sharin in supply chains: part I an S. Adhau was born in Wardha district of Maharashtra state (India), on May 15, He received his Bachelor of Enineerin in Production Enineerin from Amravati University in 1991 and Master of Enineerin in Manufacturin Technoloy from NITTTIR, Chandiarh (India) in He has submitted his Ph.D. in Mechanical Enineerin at Malaviya National Institute of Technoloy, Jaipur (India) in He is currently workin as a selection rade Lecturer in Department of Mechanical Enineerin at Government Polytechnic, Pune (India). He has over 20 years of teachin experience in India. He has published more than 10 papers in International journals and peer reviewed conference proceedins. His research interests are in artificial intellient systems and in, particular, distributed Multi aent system based manufacturin schedulin, operation manaement and project manaement. M. L. Mittal obtained his Bachelor of Enineerin in Mechanical Enineerin from University of Rajasthan (India) in 1988 and Master of Enineerin in Production Enineerin from M.S. University of Baroda (India) in He obtained his Ph.D. in Industrial Enineerin form Indian Institute of Technoloy, Delhi (India) in He worked in industry for about a year before joinin the academe. His area of interests includes production and operation manaement, total quality manaement and project manaement. He has published more than 20 papers in journals and conference proceedins. 528