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Optimal Control of Serial Inventory Systems with Fixed Replenishment Intervals

Department of Technology Management, Technische Universiteit Eindhoven, 5600 MB, Eindhoven, The Netherlands
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
SAS Institute Inc., Cary, North Carolina 27513
g.j.v.houtum{at}tm.tue.nl
awolf{at}andrew.cmu.edu
jinxin.yi{at}sas.com

We consider a single-item, periodic-review, serial inventory/production system, with linear inventory-holding and penalty costs. To facilitate shipment consolidation and capacity planning, we assume that the system has implemented fixed replenishment intervals; each stage is allowed to order only at given equidistant times. Further, for each stage except the most downstream one, the replenishment interval is assumed to be an integer multiple of the replenishment interval of the next downstream stage. This reflects the fact that the further upstream in a supply chain, the higher setup times and costs tend to be, and thus larger batches are desired. Our model with fixed replenishment intervals is a direct generalization of the serial model of Clark and Scarf (1960). For this generalized model, we prove the optimality of base-stock policies, we derive newsboy equations for the optimal base-stock levels, and we describe an efficient exact solution procedure for the case with mixed Erlang demands. Finally, we present extensions to assembly systems and to systems with a modified fill-rate constraint instead of backorder costs.

Subject classifications: inventory/production; multiechelon; stochastic demand; fixed replenishment intervals; optimal policies.
History: Received December 2003; revision received June 2006; accepted July 2006.

This article has been cited by other articles:

				X. Chao and S. X. Zhou Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals Operations Research, March 1, 2009; 57(2): 377 - 390. [Abstract] [PDF]