A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem

Authors:
Alberto Ceselli;Giovanni Righini
Affiliations:
Dipartimento di Tecnologie dell'Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema, Italy;Dipartimento di Tecnologie dell'Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema, Italy
Venue:
Operations Research
Year:
2006

Citing 6
Cited 1

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Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

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A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems

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Abstract

The multilevel generalized assignment problem (MGAP) is a variation of the generalized assignment problem, in which agents can execute tasks at different efficiency levels with different costs. We present a branch-and-price algorithm that is the first exact algorithm for the MGAP. It is based on a decomposition into a master problem with set-partitioning constraints and a pricing subproblem that is a multiple-choice knapsack problem. We report on our computational experience with randomly generated instances with different numbers of agents, tasks, and levels; and with different correlations between cost and resource consumption for each agent-task-level assignment. Experimental results show that our algorithm is able to solve instances larger than those of the maximum size considered in the literature to proven optimality.