Robust supply chain network equilibrium model

Tatsuya Hirano, Yasushi Narushima

Research output: Contribution to journalArticle

Abstract

An important and often researched area of management science is mathematical modeling of a supply chain. Competitive situations can occur in supply chains owing to the involvement of multiple decision makers (players) that independently decide their behaviors. To investigate competitive supply chain networks, a supply chain network equilibrium (SCNE) model was proposed. Recently, particular attention has been paid to risk management of a supply chain. In equilibrium models, it is vital to consider players' decisions and interdependence relations. Thus, we consider competitive supply chain networks with uncertainties in the other players' strategies. In the proposed model, each player cannot know exactly the other players' strategies, and they decide their strategy using the minimax principle (that is, assuming the worst case). We call it the robust SCNE model. We formulate the robust SCNE model as a variational inequality problem (VIP) in which the set associated with the VIP is constructed by second-order cone constraints. We show the existence and uniqueness of the equilibrium under mild assumptions. In addition, we give, in a special case, some relations between players' strategies in the equilibrium and magnitudes of uncertainties. Finally, some numerical results are provided.

Original languageEnglish
Pages (from-to)1196-1212
Number of pages17
JournalTransportation Science
Volume53
Issue number4
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes

Keywords

  • Existence
  • Robust optimization
  • Supply chain network equilibrium model
  • Transportation
  • Uniqueness
  • Variational inequality problem

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

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