Quadratic resource allocation with generalized upper bounds

Authors:
Kurt M. Bretthauer;Bala Shetty
Affiliations:
Department of Business Analysis and Research, Texas A&M University, Ciollege Station, TX 77843, USA;Department of Business Analysis and Research, Texas A&M University, Ciollege Station, TX 77843, USA
Venue:
Operations Research Letters
Year:
1997

Citing 10
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Abstract

In this paper we present an algorithm for solving a quadratic resource allocation problem that includes a set of generalized upper bound (GUB) constraints. The problem involves minimizing a quadratic function over one linear constraint, a set of GUB constraints, and bounded variables. GUB constraints, when added to a standard resource allocation problem, can be used to set upper limits on the amount of a resource consumed by one or more subsets of the activities. To solve the problem, we present an efficient algorithm that solves a series of quadratic knapsack subproblems and box constrained quadratic subproblems. Computational results are reported for large-scale problems with as many as 100 000 variables and 1000 constraints. The computational results indicate that our algorithm is up to 4000 times faster than the general purpose nonlinear programming software LSGRG.