A Cooperative Game Approach to a Production Planning Problem

D. G. Ramírez-Ríos, D. C. Landinez, P. A. Consuegra, J. L. García, L. Quintana

Abstract

This paper deals with a production planning problem formulated as a Mixed Integer Linear Programming (MILP) model that has a competition component, given that the manufacturers are willing to produce as much products as they can in order to fulfil the market’s needs. This corresponds to a typical game theoretic problem applied to the productive sector, where a global optimization problem involves production planning in order to maximize the utilities for the different firms that manufacture the same type of products and compete in the market. This problem has been approached as a cooperative game, which involves a possible cooperation scheme among the manufacturers. The general problem was approached by Owen (1995) as the ``production game'' and the core was considered. This paper identifies the cooperative game theoretic model for the production planning MILP optimization problem and Shapley Value was chosen as the solution approach. The results obtained indicate the importance of cooperating among competitors. Moreover, this leads to economic strategies for small manufacturing companies that wish to survive in a competitive environment.

References

  1. Aydinliyim, T., Vairaktarakis, G. L., 2013. A cooperative savings game approach to a time sensitive capacity allocation and scheduling problem. Decision Sciences, 44(2), 357-376.
  2. Cadenillas, A., Lakner, P., Pinedo, M., 2013. Optimal production management when demand depends on the business cycle. Operations Research, 61(4), 1046- 1062.
  3. Chen, L. T., 2014. Optimal dynamic policies for integrated production and marketing planning in business-tobusiness marketplaces. International Journal of Production Economics, 153, 46-53.
  4. Das, B. C., Das, B., Mondal, S. K., 2014. Optimal transportation and business cycles in an integrated production-inventory model with a discrete credit period. Transportation Research Part E: Logistics and Transportation Review, 68, 1-13.
  5. Doulabi, S. H. H., Avazbeigi, M., Arab, S., Davoudpour, H., 2012. An effective hybrid simulated annealing and two mixed integer linear formulations for just-in-time open shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 59(9-12), 1143-1155.
  6. Ertugrul, I., Isik, A. T., 2009. Production Planning for a Winery With Mixed Integer Programming Model. Ege Academic Review, 9(2), 375-387.
  7. Gimenez, C., Ventura, E., 2005. Logistics-production, logistics-marketing and external integration: their impact on performance. International journal of operations & Production Management, 25(1), 20-38.
  8. Gong, X., Zhou, S. X., 2013. Optimal production planning with emissions trading. Operations Research, 61(4), 908-924.
  9. Guzman, L., Ramírez Ríos, D. G., Yie, R., Ucros, M., Acero, K., Paternina, C. D., 2008. Modelos de planificación cooperativa de recursos energéticos. Ediciones Uninorte, Barranquilla, 1'p.
  10. Hartman, B. C., Dror, M., 2003. Optimizing centralized inventory operations in a cooperative game theory setting. IIE Transactions, 35(3), 243-257.
  11. Hsiao, Y. C., Lin, Y., Huang, Y. K., 2010. Optimal multistage logistic and inventory policies with production bottleneck in a serial supply chain. International Journal of Production Economics, 124(2), 408-413.
  12. Jolayemi, J. K., 2012. Scheduling of projects under penalty and reward arrangements: a mixed integer programming model and its variants. Academy of Information & Management Sciences Journal, 15(2).
  13. Kang, S., Medina, J. C., Ouyang, Y., 2008. Optimal operations of transportation fleet for unloading activities at container ports. Transportation Research Part B: Methodological, 42(10), 970-984.
  14. Khaledi, H., Reisi-Nafchi, M., 2013. Dynamic production planning model: a dynamic programming approach. The International Journal of Advanced Manufacturing Technology, 67(5-8), 1675-1681.
  15. L'Heureux, G., Gamache, M., Soumis, F., 2013. Mixed integer programming model for short term planning in open-pit mines. Mining Technology, 122(2), 101-109.
  16. Li, P., Wendt, M., Wozny, G., 2003. Optimal operations planning under uncertainty by using probabilistic programming. Foundations of Computer-Aided Process Operations (FOCAPO 2003), Coral Springs, FL.
  17. Li, X., Gao, L., & Li, W., 2012. Application of game theory based hybrid algorithm for multi-objective integrated process planning and scheduling. Expert Systems with Applications, 39(1), 288-297.
  18. Lütke Entrup, M., Günther, H. O., Van Beek, P., Grunow, M., & Seiler, T., 2005). Mixed-Integer Linear Programming approaches to shelf-life-integrated planning and scheduling in yoghurt production. International Journal of Production Research, 43(23), 5071-5100.
  19. Manupati, V. K., Deo, S., Cheikhrouhou, N., Tiwari, M. K., 2012. Optimal process plan selection in networked based manufacturing using game-theoretic approach. International Journal of Production Research, 50(18), 5239-5258.
  20. Mattik, I., Amorim, P., Günther, H. O., 2014. Hierarchical scheduling of continuous casters and hot strip mills in the steel industry: a block planning application. International Journal of Production Research, 52(9), 2576-2591.
  21. Missbauer, H., Uzsoy, R., 2011. Optimization models of production planning problems. In Planning Production and Inventories in the Extended Enterprise (pp. 437-507). Springer US.
  22. Mukhopadhyay, S. K., Setoputro, R., 2004. Reverse logistics in e-business: optimal price and return policy. International Journal of Physical Distribution & Logistics Management, 34(1), 70-89.
  23. Okada, A. The Nash bargaining solution in general nperson cooperative games. Journal of Economic Theory 2010, Vol. 145, pp 2356-2379.
  24. Owen, G., 1995, Game Theory. In San Diego: Academic Press. 447p.
  25. Puello Pereira, N. & Ramírez Ríos, D.G., 2014. Un modelo de juegos cooperativos aplicado a cadenas de suministro para maximizar la competitividad de los clusters. In Revista Ingeniare, Paper submitted for publication.
  26. Roth, A., 1988. The Shapley Value. In Cambridge University Press, 1988. ISBN 0-521-36177-X.
  27. Shi, J., Zhang, G., Sha, J., 2011. Optimal production planning for a multi-product closed loop system with uncertain demand and return. Computers & Operations Research, 38(3), 641-650.
  28. Widyadana, G. A., Wee, H. M., 2011. Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time. Applied Mathematical Modelling, 35(7), 3495- 3508.
  29. Yin, S., Nishi, T., & Zhang, G., 2013. A Game Theoretic Model to Manufacturing Planning with Single Manufacturer and Multiple Suppliers with Asymmetric Quality Information. Procedia CIRP, 7, 115-120.
  30. Zamarripa, M., Aguirre, A., & Méndez, C., 2012. Integration of Mathematical Programming and Game Theory for Supply Chaina Planning Optimization in Multi-objective competitive scenarios. Computer Aided Chemical Engineering,30, 402-406.
  31. Zhou, G., Xiao, Z., Jiang, P., & Huang, G. Q., 2010. A game-theoretic approach to generating optimal process plans of multiple jobs in networked manufacturing. International Journal of Computer Integrated Manufacturing, 23(12), 1118-1132.
Download


Paper Citation


in Harvard Style

G. Ramírez-Ríos D., C. Landinez D., A. Consuegra P., L. García J. and Quintana L. (2015). A Cooperative Game Approach to a Production Planning Problem . In Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-075-8, pages 148-155. DOI: 10.5220/0005220201480155


in Bibtex Style

@conference{icores15,
author={D. G. Ramírez-Ríos and D. C. Landinez and P. A. Consuegra and J. L. García and L. Quintana},
title={A Cooperative Game Approach to a Production Planning Problem},
booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2015},
pages={148-155},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005220201480155},
isbn={978-989-758-075-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A Cooperative Game Approach to a Production Planning Problem
SN - 978-989-758-075-8
AU - G. Ramírez-Ríos D.
AU - C. Landinez D.
AU - A. Consuegra P.
AU - L. García J.
AU - Quintana L.
PY - 2015
SP - 148
EP - 155
DO - 10.5220/0005220201480155