Decision Sciences Volume 33 Number zyxwvutsr 3 Summer 2002 Printed in the U.S.A. The Critical Few Minutes in Scheduling Time-Varying Queuing Systems zy Joseph S. Martinich School ofBusiness Administration, University zyxwv of Missouri zyxwv - St. Louis, 8001 Natural Bridge zyx Road, St. Louis, MO 63141, e-mail: Joseph.Martinich@umsl.edu ABSTRACT For nonstationary queuing systems where demand varies over time, zyx an important prac- tical issue is scheduling the number of servers to be available at various times of the day. Widely used scheduling procedures typically involve adding servers at natural time points (e.g., on the hour or at half past the hour) during peak demand periods. Schedul- ing is often complicated by restrictions on the minimum amount of time (human) servers must work, the earliest (or latest) time a server is available, and limits on the maximum number of servers that can be used at any one time. This paper was motivated by expe- rience with actual queuing systems that embodied such complications. For these sys- tems common scheduling methods that used “natural” starting times for servers resulted in needlessly long customer waits. This research demonstrates that changing the starting times of servers by only a few minutes can have dramatic impacts on customer waiting times for extended periods. In addition, the results highlight the importance of server punctuality. Subject Areas: Queuing Theory, Service Operations, Simulation Applications, and Workforce Scheduling. INTRODUCTION Competition for customers in retail service industries, such as the fast-food, gro- cery, and banking industries, is often fierce. This competition occurs not only in price, but especially in perceived customer service, and according to Bennett (1990, p. B l), “no aspect of customer service is more important than the wait in line to be served.” Consultant David Maister has stated that waiting “has a dispro- portionately high impact” on customers. “The wait can destroy an otherwise per- fect service experience” (Bennett, 1990, p. B2). Consequently, even small reductions in waiting time will improve service quality and lead to increased cus- tomer demand and sales. Increasing the (maximum) number of service channels is one way to reduce waiting, but it comes at a cost. Some researchers (Davis, 1991; Ittig, 1994;Maggard, 1981)have investigated this option to determine the optimal number of servers to use so as to maximize profits. For example, Ittig found that increasing the number of servers zyxwv at a grocery store from six to eight reduced cus- tomer waiting enough that volume increased by 19%, complaints decreased by 415