Heuristics for the multi‐resource generalized assignment problem

Abstract

Abstract:The well-known generalized assignment problem (GAP) involves the identification of a minimum-cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi-resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three-phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near-optimal solutions.

Integrative Dynamic Reconfiguration in a Parallel Stream Processing Engine

“…The minimization problem is NP-hard, because it is an instance of the Multi-Resource Generalized Assignment Problem [28]. To derive a solution, we model the minimization problem as a Mixed-Integer Linear Program as follows.…”

A patient assignment algorithm for home care services

“…Finding a feasible solution to an MRGAP is an NP-hard problem since, as shown in Martello and Toth (1990), it is already NP-hard with one resource constraint. Heuristic solution methods have been developed to solve the MRGAP with a linear objective function (eg Gavish and Pirkul (1991), Mazzola and Wilcox (2001) and Yagiura et al (2004)). …”

Bicriteria multiresource generalized assignment problem

“…Dell'Amico and Martello [5], and Cattrysse and Van Wassenhove [3] give extensive surveys for the solution approaches of the AP and GAP, respectively. The solution approaches for the MRGAP are addressed in [10,21,22,33]. Gavish and Pirkul [10] study different Lagrangean relaxations of the model and develop heuristic procedures and a B&B algorithm based on these relaxations.…”