Food supply chain (FSC) management has attracted increasing attention from academics and practitioners in recent years.
Although the closed-loop FSC (CLFSC) with returnable transport items (RTIs) has many applications, it is rarely studied. This paper studies a new production-transportation planning problem for a closed-loop perishable FSC with shared RTIs, in which the RTIs can be used by different manufacturer partners to improve the overall supply chain performance. The problem consists of determining the production, transportation and inventory quantities for each period of a considered planning horizon to maximize the total profit of the whole supply chain. For the problem, we first formulate it as a mixed-integer linear program (MILP). To efficiently solve the NP-hard problem, we then develop a three-phase heuristic algorithm (TPHA). Numerical experimental results of 225 randomly generated instances up to 10 manufacturers, 150 retailers and 15 periods show that the performance of TPHA outperforms the direct use of a commercial solver CPLEX. Finally, the benefit of the shared RTIs strategy in a CLFSC is verified.