Abstract
Consider a set N of n (> 1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et al. 2000, Games Econ Behav 31:26–49; Muller et al. 2002, Games Econ Behav 38:118–126). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror 2005, IIE Trans Scheduling Logistics 37:93–107). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a, Int J Game Theor 31:341–351). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer’s rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players’ demands at different stages.
Similar content being viewed by others
References
Anupindi R, Bassok Y (1999) Centralization of stocks: retailers vs. manufacturer. Manage Sci 45:178–191
Blackwell D (1956) An analog of the MinMax Theorem for vector payoffs. Pacific J Math 6:1–8
Burer S, Dror M (2007) Convex optimization of centralized inventory operation (submitted)
Chen M-S, Lin C-T (1989) Effects of centralization on expected costs in a multi-location newsboy problem. J Oper Res Soc 40:597–602
Eppen GD (1979) Effects of centralization on expected costs in a multi-location newsboy problem. Manage Sci 25:498–501
Feller W (1966) An introduction to probability. Theory and its applications, vol. II. Wiley, New York
Fernandez FR, Puerto J, Zafra MJ (2002) Cores of stochastic cooperative games. Int Game Theory Rev 4(3):265–280
Granot D (1977) Cooperative games in stochastic function form. Manage Sci 23:621–630
Hartman BC, Dror M (1996) Cost allocation in continuous review inventory models. Naval Res Logistics J 43:549–561
Hartman BC, Dror M (2003) Optimizing centralized inventory operations in a cooperative game theory setting. IIE Trans Oper Eng 35:243–257
Hartman BC, Dror M (2005) Allocation of gains from inventory centralization in newsvendor environments. IIE Trans Scheduling Logistics 37:93–107
Hartman BC, Dror M, Shaked M (2000) Cores of inventory centralization games. Games Econ Behav 31:26–49
Lehrer E (2002a) Allocation process in cooperative games. Int J Game Theory 31:341–351
Lehrer E (2002b) Approachability in infinite dimensional spaces. Int J Game Theory 31:253–268
Muller A, Scarsini M, Shaked M (2002) The newsvendor game has a nonempty core. Games Econ Behav 38:118–126
Naurus JA, Anderson JC (1996) Rethinking distribution. Harvard Bus Rev 74(4):113–120
Parlar M (1988) Game theoretic analysis of the substitutable product inventory problem with random demands. Naval Research Logistics 35:397–409
Ruiz LM, Valenciano F, Zarzuelo JM (1998) The family of least square values for transferable utility games. Games Econ Behav 24:109–130
Slikker M, Fransoo J, Wouters M (2005) Cooperation between multiple news-vendors with transshipment. Eur J Oper Res 167:370–380
Suijs J (2000) Cooperative decision-making under risk. Kluwer, Boston
Timmer J (2006) The compromise value for cooperative games with random payoffs. Math Methods Oper Res 64:95–106
Timmer J, Borm P, Tijs S (2003) On three Shapley-like solutions for cooperative games with random payoffs. Int J Game Theory 32:595–613
Timmer J, Borm P, Tijs S (2005) Convexity in stochastic cooperative situations. Int Game Theory Rev 7:25–42
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dror, M., Guardiola, L.A., Meca, A. et al. Dynamic realization games in newsvendor inventory centralization. Int J Game Theory 37, 139–153 (2008). https://doi.org/10.1007/s00182-007-0102-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-007-0102-5