Algorithms for Separable Nonlinear Resource Allocation Problems

• Published in: Operations research Vol. 46; no. 2; pp. 272 - 284
• Main Authors: Kodialam, Muralidharan S, Luss, Hanan
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.03.1998; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; allocation of one resource; Applied sciences; Budget allocation; Capital costs; Exact sciences and technology; Flows in networks. Combinatorial problems; Lagrange multipliers; Marketing; Mathematical programming; Minimax; Minimization of cost; nonlinear; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Operations research; Optimal solutions; Production costs; Programming; Resource allocation; resource allocation algorithms; Run time; Studies; Theory; Lagrange multiplier; Combinatorial problem; Algorithm; Resource allocation; Marketing; Mathematical programming
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.46.2.272

We consider a simple resource allocation problem with a single resource constraint. The objective function is composed of separable, convex performance functions, one for each activity. Likewise, the constraint has separable, convex resource-usage functions, one for each activity. The objective is to minimize the sum of the performance functions, subject to satisfying the resource constraint and nonnegativity constraints. This problem extends the well-studied problem in which the resource constraint is linear. We present several algorithms to solve the problem. These algorithms extend approaches developed for the linearly constrained problem. They can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables. We provide several examples for illustration purposes, present computational results, and highlight the similarities and differences among the algorithms.