SciELO - Scientific Electronic Library Online

 
vol.19 issue1A Scatter Search Algorithm for Solving a Bilevel Optimization Model for Determining Highway TollsSaving Time for Object Finding with a Mobile Manipulator Robot in 3D Environment author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.19 n.1 México Jan./Mar. 2015

http://dx.doi.org/10.13053/CyS-19-1-1921 

Artículos

 

Finding Pure Nash Equilibrium for the Resource-Constrained Project Scheduling Problem

 

Guillermo De Ita Luna, Fernando Zacarias-Flores and L. Carlos Altamirano-Robles

 

Computer Science Department, Autonomous University of Puebla (BUAP), México. deita@cs.buap.mx, altamirano@cs.buap.mx, fzflores@yahoo.com.mx

Corresponding author is Fernando Zacarias-Flores.

 

Article received on 12/12/2013.
Accepted on 27/11/2014.

 

Abstract

The paper focuses on solving the Resource-Constrained Project Scheduling (RCPS) problem with a method based on intelligent agents. Parallelism for performing the tasks is allowed. Common and limited resources are available to all agents. The agents are non-cooperative and compete with each other for the use of common resources, thereby forming instances of RCPS problem. We analyze the global joint interaction of scheduling via a congestion network and seek to arrive at stable assignments of scheduling. For this class of network, stable assignments of scheduling correspond to a pure Nash equilibrium, and we show that in this case there is a guarantee of obtaining a pure Nash equilibrium in polynomial time complexity. The pure Nash equilibrium point for this congestion network will be a local optimum in the neighborhood structure of the projects, where no project can improve its completion time without negatively affecting the completion time of the total system. In our case, each state of the neighborhood represents an instance of the RCPS problem, and for solving such problem, we apply a novel greedy heuristic. It has a polynomial time complexity and works similar to the well-knowing heuristic NEH.

Keywords: Intelligent agents, congestion network, pure Nash equilibrium, RCPS problem, multi-scheduling, greedy heuristic NEH.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

1. Agnetis, A., Briand, C., Billaut, J., & Sucha, P. (2014). Nash equilibria for the multi-agent project scheduling problem with controllable processing times problem. Journal of Scheduling, Vol. 1, pp. 125-142.         [ Links ]

2. Artigues, C., Michelon, P., & Reusser, S. (2003). Insertion techniques for static and dynamic resource constrained project scheduling. European journal of Operational Research, Vol. 149, pp. 249-267.         [ Links ]

3. Averbakh, I. (2010). Nash equilibrium in competitive project scheduling. European journal of Operation Research, Vol. 205, pp. 552-556.         [ Links ]

4. Baar, T., Brucker, P., & Knust, S. (1998). Meta heuristics: Advances and Trends in local search paradigms for optimizatiion, chapter Tabu search algorithms and lower bounds for the resource constrained project scheduling problem. Kluwer, pp. 118.         [ Links ]

5. Bautista, J. & Pereira, J. (2002). Ant colonies for the RCPS problem. Lecture notes in computer science, Springer.         [ Links ]

6. Bouleimen, K. & Lecocq, H. (1998). Technical report, service de robotique et automatisation, chapter A new efficient simulated annealing algorithm for the resource constrained project scheduling problem. Universitde Lisge, pp. 1-20.         [ Links ]

7. Davis, E. & Patterson, J. (1975). A comparison of heuristics and optimum solutions in resource constrained project scheduling. Management Science, Vol. 21, pp. 944-955.         [ Links ]

8. Deckro, R., Winkofsky, E., Herbert, J., & Gangon, R. (1991). Decomposition approach to multi project scheduling. European journal of Operation Research, Vol. 51, pp. 110-118.         [ Links ]

9. Drwal, M., W., R., Ganzha, M., & Paprzycki, M. (2014). Equilibria in concave non-cooperative games and their applications in smart energy allocation. Internet and Distributed Computing Systems, LNCS, volume 8729, pp. 409-421.         [ Links ]

10. Elsasser, R., Gairing, M., Lucking, T., Mavronicolas, M., & Monien, B. (2005). A simple graph theoric model for selfish restricted scheduling. Lectures notes in computer science, Springer.         [ Links ]

11. Fabrikant, A., Papdimitriou, C., & Talwar, K. (2004). The complexity of pure Nash equilibria. Proceedings 34th ACM Symposium on Theory of Computing, STOC04, ACM.         [ Links ]

12. Garrido, A., M.A. Salido, Baber, F., & Lopez, M. (2000). Heuristic methods for solving job shop scheduling problems. Proc. ECAI-2000 Workshop on New Results in Planning, Scheduling and Design (PuK2000), pp. 44-49.         [ Links ]

13. Kim, S. & Leachman, R. (1993). Multi project scheduling with explicit lateness costs. IIE Transactions, Vol. 25, pp. 98-108.         [ Links ]

14. Kolisch, R. (1996). Serial and parallel resource constrained project scheduling methods resisited: Theory and computation. European journal of Operation Research, Vol. 90, pp. 320-333.         [ Links ]

15. Kolisch, R. & Hartmann, S. (1998). Handbook on recent advances in project shceduling, chapter Heuristic algorithms for solving the resource constrained project scheduling problem: Classification and computational analysis. Kluwer, pp. 1-20.         [ Links ]

16. Liefooghe, A., Basseur, M., Jourdan, L., & El-Ghazali, T. (2007). Combinatorial optimization of stochastic multi objective problems: and application to the flow-shop scheduling problem. Lecture notes in computer science, Springer.         [ Links ]

17. Ma, Y., Gao, Y., & Wang, L. (2009). A pcu resource scheduling algorithm based on Nash equilibrium. Proceedings of the future information networks, FIN.         [ Links ]

18. Mittal, M. & Kanda, A. (2009). Scheduling of multiple projects with resource transfers. International journal of mathematics in operational research, Vol. 1, pp. 303-325.         [ Links ]

19. Naphade, K., Wu, S., & Storer, R. (1997). Problem space search algorithms for resource constrained project scheduling. Annals of operations research, Vol. 70, pp. 307-326.         [ Links ]

20. Nawaz, M., Enscore Jr., E., & Ham, I. (1983). A heuristic algorithm forthe m-machine n-job flowshop sequencing problem. OMEGA International Journal of Management Science, Vol. 11, pp. 91-95.         [ Links ]

21. Nguyen, K. T. (2009). NP-Hardness of pure Nash equilibrium in scheduling and connection games. Lecture notes in computer sciences, Springer.         [ Links ]

22. Orlin, J., Punnen, A., & Schulz, A. (2004). Approximate local search in combinatorial optimization. Proceedings of SODA, SODA.         [ Links ]

23. Patterson, J. (1984). A comparasion of exact approaches for solving the multiple constrained re-sourve project scheduling problem. Management Science, Vol. 30, pp. 854-867.         [ Links ]

24. Pereyrol, F., Dupas, R., Alix, T., & Bourrieres, J. (1996). Serial and parallel resource constrained project scheduling methods resisited: Theory and computation. European journal of Operation Research, Vol. 90, pp. 320-333.         [ Links ]

25. Ravetti, M., Nakamura, F., Meneses, C., Resende, M., Mateus, G., & Pardatlos, P. (2006). Hybrid heuristics for the permutation flow shop problem. Technical report, AT & T Labs., AT & T Labs TD-6V9MEV.         [ Links ]

26. Simpson, W. & Patterson, J. (1996). A multiple tree search procedure for the resource constrained project scheduling problem. European journal of Operation Research, Vol. 89, pp. 525-542.         [ Links ]

27. Venkataramana, M. & Raghavan, N. (2010). Ant colony based algorithms for scheduling parallel batch processors with incompatible job families. International journal of mathematics in operational research, Vol. 2, pp. 73-98.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License