A pegging algorithm for the nonlinear resource allocation problem

Abstract

In this paper we present a new algorithm for solving the nonlinear resource allocation problem. The nonlinear resource allocation problem is defined as the minimization of a convex function over a single convex constraint and bounded integer variables. We first present a pegging algorithm for solving the continuous variable problem, and then incorporate the pegging method in a branch and bound algorithm for solving the integer variable problem. We compare the computational performance of the pegging branch and bound algorithm with three other methods: a multiplier search branch and bound algorithm, dynamic programming, and a 0,1 linearization method. The computational results demonstrate that the pegging branch and bound algorithm advances the state of the art in methods for solving the nonlinear resource allocation problem. Scope and purpose The nonlinear resource allocation problem (i.e., a knapsack problem where both the objective function and single constraint may be nonlinear) is encountered in a variety of applications, including financial modeling, sampling, production and inventory management, and queueing network models of manufacturing and computer systems. Despite its importance to these and other applications, the nonlinear resource allocation problem has received limited attention in the literature. Therefore, we develop methods for solving continuous and integer variable versions of the problem and report extensive computational testing of the algorithms.