Minimax resource allocation problems: Optimization and parametric analysis

We consider a linear minimax resource allocation problem with single-variable terms in the objective function and multiple knapsack-type resource constraints. All variables are continuous and nonnegative. Efficient algorithms for such large-scale problems have been developed by Luss and Smith and by Tang. This paper describes an enhanced algorithm that provides a more efficient search for the optimal solution. Further, we develop post-optimization schemes and parametric analysis that are employed once an optimal solution for the original minimax problem is obtained. Post-optimization provides a perturbed optimal solution under a specified change in the data, whereas parametric analysis provides a continuum of optimal solutions when some data elements are changed over a given interval.