Loughborough University
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A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm

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journal contribution
posted on 2018-10-08, 09:20 authored by Javid Ghahremani-Nahr, Ramez Kian, Ehsan SabetEhsan Sabet
The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental-related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time.


The research described in this paper was funded by Iran’s National Elites Foundation, I.R. IRAN which is gratefully acknowledged here.



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Expert Systems with Applications




454 - 471


GHAHREMANI-NAHR, J., KIAN, R. and SABET, E., 2019. A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm. Expert Systems with Applications, 116, pp.454-471.


© Elsevier


  • AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Expert Systems with Applications and the definitive published version is available at https://doi.org/10.1016/j.eswa.2018.09.027.

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