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Closed-loop supply chains (CLSC) for food products mostly focus on the recovery of the residual value of food itself. Food packaging that plays an important role in food supply chain has rarely been studied. This paper aims to investigate an integrated multi-period closed-loop food supply chain planning problem with returnable transport items (RTIs) in which the total profit and the environmental impact are simultaneously considered. For the problem, an improved bi-objective mixed-integer linear program is formulated with obtained valid inequalities. Especially, the model with valid inequalities can reduce nearly 50% of the average computation time compared with the initial one. To solve the problem, a kernel-search heuristic based  ε -constraint method is developed to obtain an approximate Pareto front. Finally, a fuzzy logic-based technique is adapted to help decision makers select a preferred solution according to his/her preference. A real case study from a slaughterhouse illustrates that the proposed method can improve the company’s current strategy for a 7-day planning. Computational results of randomly generated instances demonstrate that the proposed method outperforms the exact  ε -constraint method in terms of computational time while providing good approximation.

Improved model and efficient method for bi-objective closed-loop food supply chain problem with returnable transport items