A closed-loop supply chain for deteriorating products under stochastic container return times

• A model of a two-stage supply chain for a deteriorating product is developed.
• Finished products are transported in containers to the buyer, container return times are stochastic.
• An analytical model of the supply chain is developed and solved.
• The supply chain can influence both the risk of RTI stockouts and the deterioration rate by changing the value of the return lot size.
• Realizing the optimal value for the RTI return lot size is especially important in case the mean return time of RTIs is short.

This paper studies a two-stage supply chain where returnable transport items (RTIs) are used to ship finished products from the supplier to the buyer. Empty RTIs are collected at the buyer and returned to the supplier. The return time of RTIs is considered to be stochastic in this paper, and further finished products are assumed to deteriorate during potential delivery delays. First, the paper develops an analytical model of this supply chain, and then it discusses the properties of the model. Secondly, it presents the results of a simulation study in which the behaviour of the model is analysed. The results of our analysis indicate that the supply chain can influence both the risk of RTI stockouts at the supplier and the deterioration rate by changing the value of the return lot size of RTIs. Further, the results indicate that realising the optimal value for the RTI return lot size is especially important in case the mean return time of RTIs is short, while in case of a long RTI return lead time, an approximation of the optimal RTI return lot size is also acceptable.