Closed-loop food supply chain with returnable transport items and uncertain production capacity

Inspired by the fact that production capacity in the food industry is uncertain due to unexpected events, such as downtime, this work investigates a stochastic closed-loop supply chain for multiple perishable foods that are carried by returnable transport items, where production capacity is uncertain. For the new problem, we propose a non-linear chance-constrained model. Then it is transformed into a mixed-integer linear programming model via the sampling average approximation and the distribution-free methods such that it can be solved by commercial solvers, like CPLEX. Numerical experiments on randomly generated instances show that the distribution-free method performs better than the average approximation method. Some managerial insights are also presented and discussed.