Inventory Cost Impact of Order Processing Priorities Based on Demand Uncertainty Ananth. V. Iyer Krannert School of Management, 1310 Krannert Building, Room #541, Purdue University, West Lafayette, Indiana 47907-1310 Received November 1995; revised 26 June 1996; accepted 15 October 2001 Abstract: We evaluate an approach to decrease inventory costs at retail inventory locations that share a production facility. The retail locations sell the same product but differ in the variance of retail demand. Inventory policies at retail locations generate replenishment orders for the produc- tion facility. The production facility carries no finished goods inventory. Thus, production lead time for an order is the sojourn time in a single server queueing system. This lead time affects in- ventory costs at retail locations. We examine the impact of moving from a First Come First Served (FCFS) production rule for orders arriving at the production facility to a rule in which we provide non-preemptive priority (PR) to orders from retail locations with higher demand uncertainty. We provide three approximations for the ratio of inventory costs under PR and FCFS and use them to identify conditions under which PR decreases retail inventory costs over FCFS. We then use a Direct Approach to establish conditions when PR decreases retail inventory costs over FCFS. We extend the results to orders from locations that differ in the mean and variance of demand uncertainty. The analysis suggests that tailoring lead times to product demand characteristics may decrease system inventory costs. c  2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 376–390, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10016 Keywords: safety stock; lead time; priority; demand uncertainty 1. INTRODUCTION We consider a supply chain consisting of a single production facility that serves many retail locations. Demand at each retail location i each period follows a probability distribution with mean m i and standard deviation σ i = k i m, where k i is the coefficient of variation of demand at location i. Orders are generated by retail locations, each location uses a periodic review reorder point, reorder quantity inventory policy. Order arrivals to the production facility are random, reflecting the randomness of retail demand. Orders are processed one at a time on the single machine at the production facility, the processing time for an order (of size Q) is a constant (1/μ). The production facility carries no finished goods inventory, and orders are shipped to the corresponding retail location on completion. Thus, the lead time for a retail order is the system waiting time in a single machine queueing system. This lead time affects retail inventory costs. Our goal is to reduce retail inventory costs through the use of alternate scheduling rules at the production facility. c  2002 Wiley Periodicals, Inc.