Novel model and kernel search heuristic for multi-period closed-loop food supply chain planning with returnable transport items

Closed-loop supply chain (CLSC) is of utmost importance to sustainable development and has received increasing attention in recent decades. However, food CLSC with returnable transport items (RTIs) has been rarely studied although its growing applications in practice. This paper aims to investigate a multi-period CLSC planning problem that coordinates the flows of perishable food products and RTIs considering food quality. The objective is to maximise the total profit of the holistic supply chain over a finite planning horizon. To this end, a novel mixed integer linear programming model is first formulated. As the problem is proven NP-hard, an improved kernel search-based heuristic is then developed. A real case study deriving from a food manufacturer in China shows the applicability of the proposed model and method. The results indicate that the manufacturer’s profit can be improved by more than 10% with our method. Numerical experiments on randomly generated instances demonstrate that the proposed heuristic can yield high-quality solutions with much less computation time compared with the commercial solver CPLEX and an existing heuristic.