Supplier selection and order allocation using two-stage hybrid supply chain model and game-based order price

  • Samuel Yousefi
  • Mustafa Jahangoshai RezaeeEmail author
  • Maghsud Solimanpur
Original Paper


Achieving an efficient supply chain is impossible without integrating supply chain processes and extending long-term relationships between its members. Evaluating the process, selecting a set of suppliers, and allocating orders are effective parameters in the coordination among supply chain members. In this study, to achieve an organized process, a two-stage hybrid model is presented to choose efficient suppliers, allocate order, and determine price in a supply chain with regard to coordination among members. First, an integrated Multi-Objective Mixed-Integer Nonlinear Programming (MOMINLP) model is provided to minimize costs and evaluate suppliers simultaneously. The proposed model includes a single-buyer multi-vendor coordination model and Data Envelopment Analysis (DEA). Then, the model is simplified and converted into a quadratic programming model. In the second stage, a model is presented to determine the price agreed upon by the buyer and the selected efficient suppliers using the bargaining game and the Nash equilibrium concept. The purpose of this model is to maximize the parties’ utilities considering the order quantity specified in the first stage. At the end of this paper, the data taken and adapted from the previous researches are applied to show the abilities of the proposed models.


Buyer-vendor coordination Supplier selection Order allocation Order price Data envelopment analysis Nash bargaining game 



The authors are also indebted to the anonymous reviewers who have provided professional aspects and constructive feedbacks. They help us to improve the paper according to the useful and valuable comments and suggestions on the technical and structural aspects of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Industrial EngineeringUrmia University of TechnologyUrmiaIran
  2. 2.Faculty of EngineeringUrmia UniversityUrmiaIran

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