Algorithms for Separable Nonlinear Resource Allocation Problems - Kodialam, Muralidharan S; Luss, Hanan (Operations research, 1998)
A simple resource allocation problem with a single resource constraint is considered. The objective function is composed of several separable, convex performance functions, 1 for each activity. Likewise, the constraint has separable, convex resource-usage functions, 1 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. Several algorithms are presented to solve the problem. These algorithms extend approaches developed for the linearly constrained problem. They can readily solve large problems magnifying the optimal solution in a number of iterations that does not exceed the number of variables. Several examples are provided for illustration purposes, occupational result are presented, and the similarities and differences among the algorithms are highlighted.