Journal Article

Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals

Chao, Xiuli, Zhou, Sean X

2009

Overview

In many production/distribution systems, materials flow in fixed lot sizes (e.g., in full truckloads or full containers) and under regular schedules (e.g., delivery every week). In this paper, we study a multiechelon serial system with batch ordering and fixed replenishment intervals. We derive the optimal inventory control policy, provide a distribution-function solution for its optimal control parameters, and present an efficient algorithm for computing those parameters. Further, we show that the optimal expected system cost is minimized when the ordering times for all stages are synchronized. In contrast to the known approach in the literature that develops a lower bound for the average cost of a given period for the classical serial system, we develop a lower bound for the average total cost over an appropriately defined cycle and then construct a policy that reaches the lower bound. We also discuss its extension to the nonlinear shortage cost case (i.e., the nonlinear cost case). This paper generalizes several recent results on the analysis of multiechelon systems.

• Publisher: INFORMS,Institute for Operations Research and the Management Sciences
• Subject: Analysis / Applied sciences / Average cost / Average total cost / batch ordering / Convexity / Cost efficiency / Cost functions / Exact sciences and technology / fixed replenishment intervals / Integers / Inventories / Inventory control / Inventory control, production control. Distribution / multiechelon system / nonlinear shortage costs / Operational research and scientific management / Operational research. Management science / Operations research / Optimal control / Optimal policy / Optimization algorithms / Order picking systems / Order processing / Order quantity / Random variables / Studies / synchronized ordering