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.