Vol.:(0123456789) OPSEARCH https://doi.org/10.1007/s12597-018-0340-2 1 3 APPLICATION ARTICLE Multi‑objective bi‑level supply chain network order allocation problem under fuzziness Srikant Gupta 1  · Irfan Ali 1  · Aquil Ahmed 1 Accepted: 21 September 2018 © Operational Research Society of India 2018 Abstract 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 frst level (leader) and second level (follower) operate two separate groups of SCN. The leader, who moves frst, deter- mines 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. Keywords Supply chain network · Multi-objective optimization · Bi-level programming problem · Trapezoidal fuzzy number · -cut approach · Fuzzy goal programming * Srikant Gupta operation.srikant@hotmail.com Irfan Ali irfi.st@amu.ac.in Aquil Ahmed aquilstat@gmail.com 1 Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, UP, India