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 distributi...

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Veröffentlicht in:Journal of global optimization Jg. 74; H. 1; S. 21 - 44
Hauptverfasser: Sun, Hsin-Min, Sheu, Ruey-Lin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2019
Springer Nature B.V
Schlagworte:
Algorithms
Computer Science
Computer simulation
Intervals
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Separable convex programming
90C20
90C30
90C47
Resource distribution
90C60
Singly constrained quadratic program
Quadratic knapsack problem
ISSN:0925-5001, 1573-2916
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00748-3