Coordinated logistics: replenishment with capacitated transportation for a supply chain

In this study, we consider the integrated inventory replenishment and transportation operations in a supply chain where the orders placed by the downstream retailer are dispatched by the upstream warehouse via an in-house fleet of limited size. We first consider the single-item single-echelon case where the retailer operates with a quantity based replenishment policy, (r,Q), and the warehouse is an ample supplier. We model the transportation operations as a queueing system and derive the operating characteristics of the system in exact terms. We extend this basic model to a two-echelon supply chain where the warehouse employs a base-stock policy. The departure process of the warehouse is characterized in distribution, which is then approximated by an Erlang arrival process by matching the first two moments for the analysis of the transportation queueing system. The operating characteristics and the expected cost rate are derived. An extension of this system to multiple retailers is also discussed. Numerical results are presented to illustrate the performance and the sensitivity of the models and the value of coordinating inventory and transportation operations.