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A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem
Alberto Ceselli and Giovanni Righini
Vol. 54, No. 6 (Nov. - Dec., 2006), pp. 1172-1184
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/25147045
Page Count: 13
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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.
Operations Research © 2006 INFORMS