Joint replenishment problem in two echelon inventory systems with transportation capacity

In this study, we examine the stochastic joint replenishment problem in the presence of a transportation capacity. We first study the multi-retailer and singleechelon setting under a quantity based joint replenishment policy. A limited fleet of capacitated trucks is used for the transportation of the orders from the ample supplier in our setting. We model the shipment operations of the trucks as a queueing system, where the customers are the orders and trucks are the servers. Consequently, different transportation limitation scenarios and methods of approach for these scenarios are discussed. We then extend our model to a two-echelon inventory system, where the warehouse also holds inventory. We characterize the departure process of the warehouse inventory system, which becomes the arrival process of the queueing system that models the shipment operations between the warehouse and the retailers. This arrival process is then approximated to an Erlang Process. Several numerical studies are conducted in order to assess the sensitivity of the total cost rate to system and cost parameters as well as the performance of the approximation.