Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

In this paper, we devise a framework for obtaining the optimal ordering policy in a single location, continuous-review inventory system with arbitrary inter-demand times. We show that it is optimal to order at demand arrival epochs only if the inter-demand time has a constant or decreasing failure rate. When the inter-demand time has an increasing failure rate, we show that the optimal policy is to delay the order. We then extend this policy to multi-echelon distribution systems consisting of one supplier and many retailers. Both decentralized and centralized systems are considered. We derive expressions and procedures for the evaluation of the total cost and the computation of optimal delay in all the considered settings. More importantly, we study the impact of our delay policy in all the settings. The numerical results indicate that for the single-location model, the optimal delay can significantly reduce the total cost. Results from the single-location model can be applied to the decentralized multi-echelon system, where the upstream supplier acts as a single-location system. The supplier order delay can also have a significant impact (either positive or negative) on the retailers' total cost as well as the system's total costs. Finally, the impact of supplier order delay is minimal in the centralized multi-echelon setting. We offer an intuitive explanation for this observation.