, Volume 55, Issue 3–4, pp 721–748 | Cite as

Multi-objective bi-level supply chain network order allocation problem under fuzziness

  • Srikant GuptaEmail author
  • Irfan Ali
  • Aquil Ahmed
Application Article


In this paper we addressed supply chain network (SCN) as bi-level programming problem in which the primary objective is to determine optimal order allocation of products where the customer’s demands and supply for the products are fuzzy. In the proposed SCN model, we suppose that the first level (leader) and second level (follower) operate two separate groups of SCN. The leader, who moves first, determines quantities shipped to retailers, and then, the follower decides his quantities rationally. The leader’s objective is to minimize the total transportation costs, and similarly, the follower’s objective is to minimize the total delivery time of the SCN and at the same time balancing the optimal order allocation from each source, plant, retailer and warehouse respectively. The fuzzy goal programming approach has been used to achieve the highest degree of the membership goals by minimizing the deviational variables so that most satisfactory or the preferred solution for both the levels to be obtained. A numerical example is given to demonstrate the proposed methodology.


Supply chain network Multi-objective optimization Bi-level programming problem Trapezoidal fuzzy number \(\alpha\)-cut approach Fuzzy goal programming 


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Copyright information

© Operational Research Society of India 2018

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchAligarh Muslim UniversityAligarhIndia

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