A pegging algorithm for the nonlinear resource allocation problem
Computers and Operations Research
Exact Algorithm for Concave Knapsack Problems: Linear Underestimation and Partition Method
Journal of Global Optimization
Convergent Lagrangian and domain cut method for nonlinear knapsack problems
Computational Optimization and Applications
The design of optimum component test plans for system reliability
Computational Statistics & Data Analysis
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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.