Performance Analyses of Production Inventory Systems Considering Service Time and Product Returns of Online Shopping

This paper considers a production inventory system with service time and product returns, dependent on the characteristics of online shopping behaviors. The customers arrive according to a Poisson process, in which the arriving customer requires an item in the inventory, as well as a server service that the service time is exponentially distributed. Moreover, there is one production facility to produce items according to (s, S) policy, and the production time also follows an exponential distribution. In the beginning, the stationary joint distribution is obtained in the product form for the queue length and the on-hand inventory level. Additionally, the resulting distribution is applied to derive some performance measures, which can be adopted to numerically calculate the optimal (s, S) policy. Finally, numerical analyses are processed to investigate the effects of some system parameters on the performance measures. The numerical results clearly indicate that the product return rate has a significantly monotonic effect on the optimal policy and optimal cost.