A Branch-and-Cut Algorithm for Solving an Intraring Synchronous Optical Network Design Problem Youngho Lee Department of Industrial Engineering, Korea University, Sung-Buk Ku Anam Dong 5-1, Seoul 136-701, South Korea Hanif D. Sherali Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Junghee Han Department of Industrial Engineering, Korea University, Sung-Buk Ku Anam Dong 5-1, Seoul 136-701, South Korea Seong-in Kim Department of Industrial Engineering, Korea University, Sung-Buk Ku Anam Dong 5-1, Seoul 136-701, South Korea In this paper, we deal with a network design problem arising from the deployment of synchronous optical networks (SONET), a standard of transmission using optical fiber technology. The problem is to find an op- timal clustering of traffic demands in the network such that the total number of node assignments (and, hence, add–drop multiplexer equipment requirements) is mini- mized, while satisfying the ring capacity and node cardi- nality constraints. This problem can be conceptualized as an edge-capacitated graph partitioning problem with node cardinality constraints. We formulate the problem as a mixed-integer programming model and develop a new branch-and-cut algorithm along with preprocess- ing routines for optimally solving the problem. We also prescribe an effective heuristic procedure. Promising computational results are obtained using the proposed method. © 2000 John Wiley & Sons, Inc. Keywords: telecommunications networks; survivable network design; SONET ring; valid inequality; branch-and-cut 1. INTRODUCTION In this paper, we consider a network design problem arising from the deployment of synchronous optical net- Received February 19, 1999; revised September 23, 1999 Correspondence to: Y. Lee; e-mail: yhlee@kuccnx.korea.ac.kr Contract grant sponsor: Korea Science and Engineering Foundation; contract grant number: 981-1015-084-2 Contract grant sponsor: National Science Foundation; contract grant number: DMI9812047 Contract grant sponsor: Air Force Office for Scientific Research; contract grant number: F49620-96-1-0274 c  2000 John Wiley & Sons, Inc. works (SONET). The SONET is a standard of optical fiber transmission technology. The typical capacity of current SONET technology permits the transmission of 2.4 Gbps over a single fiber, which is equivalent to over 38,000 voice circuits (see Wu [11] for technical details). Thus, a failure in even a single link may result in a sig- nificant loss in customer service. In response, telecom- munication companies are adopting SONET ring archi- tectures, where the structure of the ring promotes an en- hanced survivability of the network. In this context, the issue of determining cost-effective topological designs and deployment strategies of SONET rings is important for network planners of telecommunication companies. Moreover, due to the inherent computational complexity of the problem of designing survivable networks, plan- ners resort to tools such as Bellcore’s SONET Planning Tool (SPT) and U S WEST’s SONET Planning System (SPS). This paper addresses a SONET design problem faced by network planners at any regional Bell operat- ing company (RBOC) providing for new SONET service in its territory. To focus on the optimization aspect of deploying a SONET architecture in a real telecommunication net- work, let us briefly describe the relevant background. As depicted in Figure 1, the routing of traffic between the nodes on a ring requires a special type of equipment at each node that is capable of adding and dropping the traffic. This device is called a SONET add–drop multi- plexer (ADM). Additionally, when the two nodes of a de- mand pair are located on different rings, we need to use a NETWORKS, Vol. 35(3), 223–232 2000