A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem
Alberto Ceselli, Giovanni Righini
Operations Research · 2006 · Volume 54 · Issue 6
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.
Keywords
integer programming: branch-and-price, production-scheduling: generalized assignment
Enable JavaScript for citation tools and additional paper interactions.