Minimum variance allocation among constrained intervals
We propose a weighted minimum variance allocation model, denoted by WMVA, which distributes an amount of a divisible resource as fairly as possible while satisfying all demand intervals. We show that the problem WMVA has a unique optimal solution and it can be characterized by the uniform distribution property (UDP in short). Based on the UDP property, we develop an efficient algorithm. Theoretically, our algorithm has a worst-case \(O(n^2)\) complexity, but we prove that, subject to slight conditions, the worst case cannot happen on a 64-bit computer when the problem dimension is greater than 129. We provide extensive simulation results to support the argument and it explains why, in practice, our algorithm runs significantly faster than most existing algorithms, including many O(n) algorithms.
KeywordsSingly constrained quadratic program Separable convex programming Quadratic knapsack problem Resource distribution
Mathematics Subject Classification90C20 90C30 90C47 90C60
The authors thank the reviewers for reading this article and for making suggestions. Thanks also to Professor Silva for providing the source codes for experiment.