Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T14:36:19.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Solving multi-agent scheduling problems on parallel machineswith a global objective function

Published online by Cambridge University Press:  07 March 2014

F. Sadi ,
A. Soukhal  and
J.-C. Billaut
F. Sadi
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
A. Soukhal
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
J.-C. Billaut
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
Get access

Abstract

In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines.The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs isassociated with one agent. The K agents compete to perform their jobs on commonresources. The objective is to find a schedule that minimizes a global objective functionf 0, while maintaining the regularobjective function of each agent, f k, at a level nogreater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This problem is a multi-agent schedulingproblem with a global objective function. In this study, we consider the casewith preemption and the case without preemption. If preemption is allowed, we propose apolynomial time algorithm based on a network flow approach for the unrelated parallelmachine case. If preemption is not allowed, we propose some general complexity results anddevelop dynamic programming algorithms.

Keywords

Schedulingmulti-agentcomplexitydynamic programming
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 2: Isco 2012, guest editors Nelson Maculan, A. Ridha Mahjoub, Eduardo Uchoa , April 2014 , pp. 255 - 269
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agnetis, A., Mirchandani, P., Pacciarelli, D. and Pacifici, A., Nondominated schedules for a job-shop with two competing users. Comput. Math. Organ. Theor. 6 (2000) 191–217. Google Scholar
Agnetis, A., Pacciarelli, D. and Pacifici, A., Multi-agent sincle machine scheduling. Ann. Oper. Res. 150 (2007) 3–15. Google Scholar
Agnetis, A., Mirchandani, P., Pacciarelli, D. and Pacifici, A., Scheduling problems with two competing agents. Oper. Res. 52 (2004) 229–242. Google Scholar
Agnetis, A., Pascale, G. and Pacciarelli, D., A Lagrangian approach to single-machine scheduling problems with two competing agents. J. Scheduling 12 (2010) 401–415. Google Scholar
Baker, K.R. and Smith, J.C., A multiple-criteria model for machine scheduling. J. Scheduling 6 (2003) 7–16. Google Scholar
Balasubramanian, H., Fowler, J., Keha, A. and Pfund, M., Scheduling interfering job sets on parallel machines. Eur. J. Oper. Res. 199 (2009) 55–67. Google Scholar
J. Blazewicz, K.H. Ecker, E. Pesch, G. Schmidt and J. Weglarz, Handbook on scheduling: From Theory to Applications. International handbooks on information systems. Springer (2007).
P. Brucker, Scheduling algorithms. Fifth Edition. Springer (2005).
Cheng, T.C.E., Ng, C.T., Yuan, J.-J., Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theor. Comput. Sci. 362 (2006) 273–281. Google Scholar
Cheng, T.C.E., Ng, C.T. and Yuan, J.-J., Multi-agent scheduling on a single machine with max-form criteria. Eur. J. Oper. Res. 188 (2008) 603–609. Google Scholar
Cheng, T.C.E., Cheng, S.-R., Wu, W.-H., Hsu, P.-H. and Wu, C.-C., A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations. Comput. Ind. Engrg. 60 (2001) 534–541. Google Scholar
Cho, Y. and Sahni, S., Preemptive scheduling of independent jobs with release and due times on open, flow and job shops. Oper. Res. 29 (1981) 511–522. Google Scholar
D. Cordeiro, P.-F. Dutot, G. Mounié and D. Trystram, Tight Analysis of Relaxed Multi-Organization Scheduling Algorithms. In Proceedings of the 25th IEEE International Parallel & Distributed Processing Symposium (IPDPS), Anchorage, AL, USA, IEEE Comput. Soc. (2011) 1177–1186.
Elvikis, D., Hamacher, H.W. and T’kindt, V., Scheduling two interfering job sets on uniform parallel machines with makespan and cost functions. J. Scheduling 14 (2011) 471–481. Google Scholar
D. Elvikis and V. T’kindt, Two-agent scheduling on uniform parallel machines with min-max criteria. Ann. Oper. Res. (2012) 1–16.
Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnooy Kan, A.H.G., Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5 (1979) 287–326. Google Scholar
Hoogeveen, H., Multicriteria scheduling. Eur. J. Oper. Res. 167 (2005) 59–623. Google Scholar
Hopcroft, J.E. and Karp, R.-M., A n 5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2 (1973) 22–231. Google Scholar
Huynh Tuong, N., Soukhal, A. and Billaut, J.-C., Single-machine multi-agent scheduling problems with a global objective function. J. Scheduling 15 (2012) 311–321. Google Scholar
Lawler, E.L., Optimal sequencing of a single machine subject to precedence constraints. Manage. Sci. 19 (1973) 544–546. Google Scholar
Lee, K., Choi, B.-C., Leung, J.Y.-T. and Pinedo, M., Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Inform. Process. Lett. 16 (2009) 913–917. Google Scholar
Lee, W.-C., Chen, S.-k. and Wu, C.-C., Branch-and-bound and simulated annealing algorithms for a two-agent scheduling problem. Exp. Syst. Appl. 37 (2010) 6594–6601. Google Scholar
Leung, J.Y.-T., Pinedo, M. and Wan, G., Competitive two agent scheduling and its applications. Oper. Res. 58 (2007) 458–469. Google Scholar
Peng, L., Na, Y. and Xiaoye, Z., Two-agent single-machine scheduling problems under increasing linear deterioration. Appl. Math. Model. 35 (2011) 2290–2296. Google Scholar
Sedeno-Noda, A., Alcaide, D. and Gonza-Martin, C., Network flow approaches to pre-emptive open-shop scheduling problems with time-windows. Eur. J Oper. Res. 18 (2005) 1501–1518. Google Scholar
Soltani, R., Jolai, F. and Zandieh, M., Two robust meta-heuristics for scheduling multiple job classes on a single machine with multiple criteria. Exp. Syst. Appl. 37 (2010) 5951–5959. Google Scholar
A. Soukhal, N. Huynh Tuong and Z. Dao, Parallel machine scheduling with interfering jobs, in 8th International Conference on Multiple Objective and Goal Programming (MOPGP’08), Portsmouth, UK (2008).
A. Soukhal, N. Huynh Tuong and Z. Dao, Méthodes exactes et approchées pour l’ordonnancement de travaux interférant (in French), in Int. Symposium on Oper. Res., ISOR’08 Algers, Algeria (2008).
V. T’kindt and J.-C. Billaut, Multicriteria scheduling. Second Edition. Springer (2006).
Wan, G., Leung, J.-Y. and Pinedo, M., Scheduling two agents with controllable processing times. Eur. J. Oper. Res. 205 (2007) 528–539. Google Scholar
Yuan, J., Shang, W.-P. and Feng, Q., A note on the scheduling which two families of jobs. J. Scheduling 8 (2005) 537–542. Google Scholar