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Modelling robust closed loop supply chain network by applying the Benders decomposition algorithm

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  • Seyed Farid‎ Mousavi
  • Arash‎ Apornak

Abstract

This paper presents a mixed-integer linear optimisation programming for a 9-echelon closed-loop supply chain network design with seasonal raw materials and product demand. The objective function minimises total fixed and operational costs. Here, the demand, suppliers' capacities, and fixed setup costs are uncertain, and use is made of the robust optimisation based on the box and polyhedral uncertainty set to model uncertainties. Since closed-loop supply chain network design model is among NP-hard problems the solutions of which in large scales are very difficult, use has been made of the Benders exact solution algorithm to find the optimal solution of the proposed model. Results found from appliance industrial case study have revealed that the robust model performs worse than the deterministic model with nominal data. In addition, Benders algorithm has been quite efficient in reducing the computation time to find the exact optimal solution.

Suggested Citation

  • Seyed Farid‎ Mousavi & Arash‎ Apornak, 2026. "Modelling robust closed loop supply chain network by applying the Benders decomposition algorithm," International Journal of Management Concepts and Philosophy, Inderscience Enterprises Ltd, vol. 19(1), pages 104-129.
    • Handle: RePEc:ids:ijmcph:v:19:y:2026:i:1:p:104-129
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