A mixed integer linear programming approach for closed-loop food supply chain with returnable transport items

This paper studies a multi-period, single-manufacturer and single-retailer closed-loop food supply chain with returnable transport items (RTIs) which are used for shipping perishable products. The quality of the products is distinguished according to its age over time. After commodities delivered to the retailer, the emptied returnable transport items are returned to the manufacturer after certain disposes and will be reused in the subsequent shipments. During this process, the manufacturer has to decide when and how many new RTIs to be purchased so as to avoid their shortage and deterioration of products. The objective is to maximize the total expected profit of the supply chain. To cope with the problem, a mixed integer linear programming model is developed and commercial software CPLEX12.6 is applied to solve it. Computational results based on randomly generated instances illustrate the validity and effectiveness of the proposed model.