Mathematical Methods of Operations Research

, Volume 65, Issue 3, pp 499–517

A core-allocation family for generalized holding cost games

Original Article

DOI: 10.1007/s00186-006-0131-z

Cite this article as:
Meca, A. Math Meth Oper Res (2007) 65: 499. doi:10.1007/s00186-006-0131-z


Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied.


Generalized holding cost games Core-allocations Minimum square proportional rule Inventory situations Cooperative games 

Mathematics Subject Classification (2000))

91A12 90B05 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Operations Research CenterUniversidad Miguel HernándezElche (Alicante)Spain

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