A Specially Structured Nonlinear Integer Resource Allocation Problem Kurt M. Bretthauer, 1 Bala Shetty, 2 Siddhartha Syam 3 1 Department of Operations and Decision Technologies, Kelley School of Business, Indiana University, Bloomington, Indiana 47405 2 Department of Information and Operations Management, Lowry Mays College of Business, Texas A&M University, College Station, Texas 77843 3 Department of Management, College of Business Administration, Marquette University, Milwaukee, Wisconsin 53201 Received 22 January 2002; revised 13 March 2003; accepted 14 March 2003 DOI 10.1002/nav.10089 Abstract: We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one gener convex constraint, a set of block diagonal convex constraints, and boundson the integer variables. The continuous variable problem is also considered. The continuous problem is solve by taking advantage of the structure of the Karush-Kuhn-Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to sol the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc.Naval Research Logistics 50: 770 –792, 2003. Keywords: nonlinearesource allocation problem; nonlinear integerprogramming; block diagonal constraints 1. INTRODUCTION Nonlinear resource allocation problems have received a great deal of attention in the lit (see,for example, the textby Ibaraki and Katoh [23]). In its most widely studied form, the Correspondence to: K. M. Bretthauer (kbrettha@indiana.edu) © 2003 Wiley Periodicals, Inc.