Stability in supply chain networks: An approach by discrete convex analysis

Yoshiko T. Ikebe, Akihisa Tamura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Ostrovsky generalized the stable marriage model of Gale and Shapley to a model on an acyclic directed graph, and showed the existence of a chain stable allocation under the conditions called same-side substitutability and cross-side complementarity. In this paper, we extend Ostrovsky's model and the concepts of same-side substitutability and cross-side complementarity by using value functions which are defined on integral vectors and allow indifference. We give a characterization of chain stability under the extended versions of same-side substitutability and cross-side complementarity, and develop an algorithm which always finds a chain stable allocation. We also verify that twisted M♮-concave functions, which are variants of M♮-concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M♮-concave value functions of the agents, we analyze the time-complexity of our algorithm.

Original languageEnglish
Pages (from-to)271-290
Number of pages20
JournalJournal of the Operations Research Society of Japan
Issue number3
Publication statusPublished - 2015 Jul


  • Acyclic networks
  • Discrete convex analysis
  • Economics
  • Stability

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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