European Journal of Operational Research 54 (1991) 163-175 163 North-Holland Theory and Methodology System.planning and configuration problems for optimal system design Christopher S. Tang and Seuck-Cheun Yoo Anderson Graduate School of Management, University of California-Los Angeles, Los Angeles, CA 90024, USA Received July 1989; revised November 1989 Abstract: This paper addresses the issues of server allocation and customer partition that arise from designing a service system. The service system is modelled as a GI/G/m queueing system. In order to provide meaningful insights for system design, we consider two system design problems: the system planning problem and the system configuration problem. The former problem analyzes the tradeoff between investment cost and performance level while the latter problem examines the tradeoff between the system operating cost and the customer waiting cost. Both problems are formulated as dynamic programs that can be solved within polynomial number of operations. Keywords: System design, resource allocation, dynamic programming, combinatorial optimization, queue- ing system 1. Introduction Queueing models have been recognized as an effective approach for evaluating system performance in the areas of computer science, operations research, and production management since the early 70's. For example, Gerla and Kleinrock (1977), and Chapters 5 and 6 of Kleinrock (1976) have examined various queueing models for designing efficient computer communication networks. Kaplan (1987) has developed a queueing model for analyzing various tenant assignment policies for the government housing project in Texas while Green (1984) has analyzed another queueing model for designing a patrol system for the police in New York City. In the context of manufacturing system design, Bitran and Tirupati (1987, 1988a and 1988b), Boxma et al. (1988), Buzacott and Yao (1986), Dallery and Frein (1986), Rolfe (1971), Shanthikumar and Buzacott (1981), Shanthikumar and Yao (1987 and 1988), van Vliet and Rinnooy Kan (1989), and Weber (1978 and 1980) have considered various queueing network models for assigning servers to workstations. These models focused on the issue of server allocation while our model integrates the issues of server allocation and customer partition. Our model arises from various service systems in which customers are partitioned into various groups. Each group forms its own queue, and each queue is served by servers assigned to that group. (For example, the 'first class only' check-in counters at the airport terminals, the 'express' check-out counters at the supermarkets, the 'A-L' registration windows at the registry, and the 'Money orders only' windows at a 0377-2217/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved