Enforcing fair cooperation in production-inventory settings with heterogeneous agents. (English) Zbl 1477.90003
Summary: Production-inventory settings with heterogeneous agents appear frequently in the study of supply chain management. For instance, there are production-inventory situations in which certain agents are essential as they can reduce the costs of other agents (followers) when they cooperate with each other. The study of such a cooperation can be modelled by means of a cooperative game and studied finding fair cost allocations. These class of cooperative games was introduced in [L. A. Guardiola et al., Games Econ. Behav. 65, No. 1, 205–219 (2009; Zbl 1165.91341)] where it was also proposed the Owen point. This cost allocation is an appealing solution concept that for production-inventory games (PI-games) is always stable, in the sense of the core. The Owen point allows all the players in the game to operate at minimum cost but it does not take into account the cost reduction induced by essential players over their followers. Thus, it may be seen as an altruistic allocation for essential players what can be criticized. The aim of this paper is two-fold: to introduce new core allocations for PI-games improving the weaknesses of the Owen point and to study the structure and complexity of set of stable cost allocations (the core) of PI-games.
MSC:
| 90B05 | Inventory, storage, reservoirs |
| 90B06 | Transportation, logistics and supply chain management |
| 91A12 | Cooperative games |
| 91A80 | Applications of game theory |
| 91B69 | Heterogeneous agent models |
Citations:
Zbl 1165.91341References:
| [1] | Bondareva, ON, Some applications of linear programming methods to the theory of cooperative games, Problemy Kibernety, 10, 119-139 (1963) · Zbl 1013.91501 |
| [2] | Borm, PEM; Hamers, H.; Hendrickx, R., Operations research games: A survey, TOP, 9, 139-216 (2001) · Zbl 1006.91009 · doi:10.1007/BF02579075 |
| [3] | Cachon, G.; Netessine, S.; Simchi-Levi, D.; Wu, SD; Shen, ZJ, Game theory in supply chain analysis, Handbook of quantitative supply chain analysis: Modeling in the eBusiness era (2004), Amsterdam: Kluwer Academic Publishers, Amsterdam · Zbl 1138.91365 |
| [4] | Ciardiello, F.; Genovese, A.; Simpson, A., A unified cooperative model for environmental costs in supply chains: The Shapley value for the linear case, Annals of Operations Research, 290, 421-437 (2018) · Zbl 1447.91106 · doi:10.1007/s10479-018-3028-3 |
| [5] | Deng, X.; Ibaraki, T.; Nagamochi, H., Algorithmic aspect of the core of combinatorial optimization games, Mathematics of Operations Research, 24, 751-766 (1999) · Zbl 1064.91505 · doi:10.1287/moor.24.3.751 |
| [6] | Derks, J.; Kuipers, J., On the core of routing games, International Journal of Game Theory, 26, 193-205 (1997) · Zbl 0881.90139 · doi:10.1007/BF01295848 |
| [7] | Drechsel, J.; Kimms, A., Cooperative lot sizing with transshipments and scarce capacities: Solutions and fair cost allocations, International Journal of Production Research, 49, 9, 2643-2668 (2011) · doi:10.1080/00207543.2010.532933 |
| [8] | Faigle, U.; Kern, W.; Fekete, SP; Hochstättler, W., On the complexity of testing membership in the core of min-cost spanning tree games, International Journal of Game Theory, 26, 361-366 (1997) · Zbl 0885.90123 · doi:10.1007/BF01263277 |
| [9] | Fang, Q.; Zhu, S.; Cai, M.; Deng, X., On the computational complexity of membership test in flow games and linear production games, International Journal of Game Theory, 31, 39-45 (2002) · Zbl 1083.91017 · doi:10.1007/s001820200106 |
| [10] | Fiestras-Janeiro, MG; García-Jurado, I.; Meca, A.; Mosquera, MA, Cooperative game theory and inventory management, European Journal of Operational Research, 210, 459-466 (2011) · Zbl 1213.90048 · doi:10.1016/j.ejor.2010.06.025 |
| [11] | Goemans, M.; Skutella, M., Cooperative facility location games, Journal of Algorithms, 50, 194-214 (2004) · Zbl 1106.91009 · doi:10.1016/S0196-6774(03)00098-1 |
| [12] | Guajardo, M.; Ronnqvist, M., Cost allocation in inventory pools OS spare parts with service-differentiated demand cases, International Journal of Production Research, 53, 1, 220-237 (2015) · doi:10.1080/00207543.2014.948577 |
| [13] | Guardiola, LA; Meca, A.; Puerto, J., Production-inventory games and PMAS-games: Characterizations of the Owen point, Mathematical Social Sciences, 56, 96-108 (2008) · Zbl 1141.91321 · doi:10.1016/j.mathsocsci.2007.12.002 |
| [14] | Guardiola, LA; Meca, A.; Puerto, J., Production-inventory games: A new class of totally balanced combinatorial optimization games, Games and Economic Behavior, 65, 205-219 (2009) · Zbl 1165.91341 · doi:10.1016/j.geb.2007.02.003 |
| [15] | Guardiola, LA; Meca, A.; Timmer, J., Cooperation and profit allocation in distribution chains, Decision Support Systems, 44, 1, 17-27 (2007) · doi:10.1016/j.dss.2006.12.015 |
| [16] | Guardiola, L. A., Meca, A., & Puerto, J. (2021) Unitary owen points in cooperative lot-sizing models with backlogging. Mathematics, 9, 869. doi:10.3390/math9080869. |
| [17] | Hamers, H.; Klijn, F.; Solymosi, T.; Tijs, SH; Villar, JP, Assignment games satisfy the CoMa-property, Games and Economic Behavior, 38, 231-239 (2002) · Zbl 1018.91006 · doi:10.1006/game.2001.0882 |
| [18] | Kar, A.; Mitra, M.; Mutuswami, S., On the coincidence of the prenucleolus and the Shapley value, Mathematical Social Sciences, 57, 16-25 (2009) · Zbl 1155.91314 · doi:10.1016/j.mathsocsci.2008.08.004 |
| [19] | Kuipers, J., On the core of information graph games, International Journal of Game Theory, 21, 339-350 (1993) · Zbl 0801.90149 · doi:10.1007/BF01240149 |
| [20] | Perea, F.; Puerto, J.; Fernández, FR, Avoiding unfairness of Owen allocations in linear production processes, European Journal of Operational Research, 220, 125-131 (2012) · Zbl 1253.91021 · doi:10.1016/j.ejor.2012.01.013 |
| [21] | Sánchez-Soriano, J.; López, MA; García-Jurado, I., On the core of transportation games, Mathematical Social Sciences, 41, 215-225 (2001) · Zbl 0973.91005 · doi:10.1016/S0165-4896(00)00057-3 |
| [22] | Schmeidler, D., The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, 17, 1163-1170 (1969) · Zbl 0191.49502 · doi:10.1137/0117107 |
| [23] | Shapley, LS, A value for n-person games in contributions to the theory of games II, Annals of Mathematics Studies, 28, 307-317 (1953) · Zbl 0050.14404 |
| [24] | Shapley, LS, On balanced sets and cores, Naval Research Logistics, 14, 453-460 (1967) · doi:10.1002/nav.3800140404 |
| [25] | Shapley, LS, Cores of convex games, International Journal of Game Theory, 1, 11-26 (1971) · Zbl 0222.90054 · doi:10.1007/BF01753431 |
| [26] | Shapley, LS; Shubik, M., On market games, Journal of Economics Theory, 1, 9-25 (1969) · doi:10.1016/0022-0531(69)90008-8 |
| [27] | Sotomayor, M., Some further remarks on the core structure of the assignment game, Mathematical Social Sciences, 46, 261-265 (2003) · Zbl 1064.91011 · doi:10.1016/S0165-4896(03)00067-2 |
| [28] | Sprumont, Y., Population monotonic allocation schemes for cooperative games with transferable utility, Games and Economic Behavior, 2, 378-394 (1990) · Zbl 0753.90083 · doi:10.1016/0899-8256(90)90006-G |
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