STABILITY IN SUPPLY CHAIN NETWORKS: AN APPROACH BY DISCRETE CONVEX ANALYSIS

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Author(s)

Abstract

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<sup>♮</sup>-concave functions, which are variants of M<sup>♮</sup>-concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M<sup>♮</sup>-concave value functions of the agents, we analyze the time-complexity of our algorithm.

Journal

  • Journal of the Operations Research Society of Japan

    Journal of the Operations Research Society of Japan 58(3), 271-290, 2015

    The Operations Research Society of Japan

Codes

  • NII Article ID (NAID)
    130005096753
  • NII NACSIS-CAT ID (NCID)
    AA00703935
  • Text Lang
    ENG
  • ISSN
    0453-4514
  • NDL Article ID
    026744764
  • NDL Call No.
    Z53-M226
  • Data Source
    NDL  J-STAGE 
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