Algorithms for the Multi-Resource Generalized Assignment Problem

Abstract

The multi-resource generalized assignment problem is encountered when a set of tasks have to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to the availability of a set of multiple resources consumed by that agent. This problem differs from the generalized assignment problem in that an agent consumes not just one but a variety of resources in performing the tasks assigned to him. This paper develops effective solution procedures for the multi-resource generalized assignment problem. Various relaxations of the problem are studied and theoretical relations among these relaxations are pointed out. Rules for reducing problem size are discussed and are shown to be effective through computational experiments. Heuristic solution procedures and an efficient branch and bound procedure are developed. Results of computational experiments testing these procedures are reported.combinatorial optimization, Lagrangian relaxation, subgradient optimization, generalized assignment problem

A Two-stage Model for a Day-ahead Paratransit Planning Problem

“…Gavish and Pirkul 1991;Mazzola and Wilcox 2001). MRGAP is a generalized assignment problem in which agents may use different, limited resources to perform the jobs assigned to them.…”

Heuristics for the multi‐resource generalized assignment problem

“…We next review such a procedure for the MRGAP that is defined in Gavish and Pirkul [16]. We then offer a modification of that approach which reduces the computational burden significantly.…”

“…Gavish and Pirkul [16] define three heuristics for MRGAP. The first of these involves a singlepass heuristic approach in which an assignment is constructed on the basis of regrets calculated from a single selection function.…”

“…Gavish and Pirkul [16] employ such an approach to define a heuristic for MRGAP. We present a modified version of the Gavish and Pirkul heuristic procedure.…”

A Multi-objective Resource-constrained Project-scheduling Problem Using Mean Field Annealing Neural Networks

“…The objectives of the MRCPSP are namely: the minimization of the makespan Cmax, the minimization of the total cost and the maximization of the probability of success The exact methods often adopt mathematical models such as integer programming, Talbot (1982), and dynamic programming, Gavish and Pirkul (1991), or are based on implic enumeration with branch and bound by considering the RCPSP as NP-hard problem. But the exact methods may be computationally infeasible or face combinatorial explosion problem if the practical projects under study are larger or more complicated, Leu and Yang (1999), Chan ,Chua and Kannan (1996)The general heuristic methods adopt priority rules reflecting one or multiple factors such as activity's critical index, duration, and minimum late finish time in generation of schedules, such as the ones used by Boctor (1990), Padilla and Carr (1991), Bell and Han (1991) and Sampson and Weiss (1993)).…”