article

The Nonlinear Resource Allocation Problem

Operations Research, Volume 43, Issue 4

Pages 670 - 683

https://doi.org/10.1287/opre.43.4.670

Published: 01 August 1995 Publication History

Abstract

<P>In this paper we study the nonlinear resource allocation problem, defined as the minimization of a convex function over one convex constraint and bounded integer variables. This problem is encountered in a variety of applications, including capacity planning in manufacturing and computer networks, production planning, capital budgeting, and stratified sampling. Despite its importance to these and other applications, the nonlinear resource allocation problem has received little attention in the literature. Therefore, we develop a branch-and-bound algorithm to solve this class of problems. First we present a general framework for solving the continuous-variable problem. Then we use this framework as the basis for our branch-and-bound method. We also develop reoptimization procedures and a heuristic that significantly improve the performance of the branch-and-bound algorithm. In addition, we show how the algorithm can be modified to solve nonconvex problems so that a concave objective function can be handled. The general algorithm is specialized for the applications mentioned above and computational results are reported for problems with up to 200 integer variables. A computational comparison with a 0, 1 linearization approach is also provided.</P>

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Published In

cover image Operations Research

Operations Research Volume 43, Issue 4

August 1995

178 pages

ISSN:0030-364X

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 August 1995

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Cited By

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https://dl.acm.org/doi/10.1007/s10957-024-02503-5
Wang Q(2021)Knowledge-based approach for dimensionality reduction solving repetitive combinatorial optimization problemsExpert Systems with Applications: An International Journal10.1016/j.eswa.2021.115502184:COnline publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1016/j.eswa.2021.115502
Hatamlou AGhaniyarlou E(2017)Solving knapsack problems using heart algorithmInternational Journal of Artificial Intelligence and Soft Computing10.1504/IJAISC.2016.0813475:4(285-293)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1504/IJAISC.2016.081347
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Li DSun XWang JMckinnon K(2009)Convergent Lagrangian and domain cut method for nonlinear knapsack problemsComputational Optimization and Applications10.1007/s10589-007-9113-142:1(67-104)Online publication date: 1-Jan-2009
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