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.　©　2023　IEEE.