Cooperation in stochastic inventory models with continuous review

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Abstract

Consider multiple companies that continuously review their inventories and face Poisson demand. We study cooperation strategies for these companies and analyse if there exist allocations of the joint cost such that any company has lower costs than on its own; such allocations are called stable cost allocations. We start with two companies that jointly place an order for replenishment if their joint inventory position reaches a certain reorder level. This strategy leads to a simple expression of the joint costs. However, these costs exceed the costs for non-cooperating companies. Therefore, we examine another cooperation strategy. Namely, the companies reorder as soon as one of them reaches its reorder level. This latter strategy has lower costs than for non-cooperating companies. Numerical experiments show that the gametheoretical distribution rule — a cost allocation in which the companies share the procurement cost and each pays its own holding cost — is a stable cost allocation. These results also hold for situations with multiple companies.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages30
Publication statusPublished - Jun 2010

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1922
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • Continuous review
  • Cost allocation
  • IR-71682
  • METIS-270834
  • Joint replenishment
  • Distribution rule
  • Inventory model
  • Game Theory
  • Stochastic demand
  • EWI-17929

Cite this

Boucherie, R. J., Chessa, M., & Timmer, J. B. (2010). Cooperation in stochastic inventory models with continuous review. (Memorandum / Department of Applied Mathematics; No. 1922). Enschede: University of Twente, Department of Applied Mathematics.