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A variational inequality formulation for designing a multi-echelon, multi-product supply chain network in a competitive environment

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Abstract

In a competitive environment, supply chains are competing with each other to gain the market share and competition is a critical factor influencing the supply chain network structure. The current paper presents a variational inequality formulation and provides the results for a competitive supply chain network design model. The new-entrant supply chain competes against an existing one in a non-cooperative behavior. The networks include raw material suppliers, manufacturers, retailers, and the same demand markets. The manufacturers produce multiple products with deterministic, price-dependent demand. The goal is to maximize the future revenue of both chains. The problem is modeled by mathematical programming and the governing Nash equilibrium conditions are derived. Then, a finite-dimensional variational inequality formulation is presented to solve the equilibrium problem. Qualitative properties of the equilibrium pattern are provided to establish existence and uniqueness results under reasonable conditions. The modified projection algorithm is used to solve the variational inequality problem. A numerical example is presented in order to show the efficiency of the proposed model and to investigate the behavior of the model under different conditions.

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Authors and Affiliations

  1. School of Industrial Engineering, College of Engineering, University of Tehran, P.O. Box 11155-45632, Tehran, Iran

    Isa Feyzian-Tary & Jafar Razmi

  2. Faculty of Fouman, College of Engineering, University of Tehran, P.O. Box 43515-1155, Fouman, 43516-66456, Iran

    Mohamad Sadegh Sangari

Authors
  1. Isa Feyzian-Tary
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  2. Jafar Razmi
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  3. Mohamad Sadegh Sangari
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Correspondence to Mohamad Sadegh Sangari.

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Feyzian-Tary, I., Razmi, J. & Sangari, M.S. A variational inequality formulation for designing a multi-echelon, multi-product supply chain network in a competitive environment. Ann Oper Res 264, 89–121 (2018). https://doi.org/10.1007/s10479-017-2737-3

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