Lagrangian heuristic for a class of the generalized assignment problems

Authors:
Igor Litvinchev;Miguel Mata;Socorro Rangel;Jania Saucedo
Affiliations:
Dorodnicyn Computing Center Russian Academy of Sciences, Moscow, Russia;Faculty of Mechanical and Electrical Engineering, UANL - Nuevo Leon State University, Mexico;Department of Computer Science and Statistics, UNESP - Sao Paulo State University, Brazil;Faculty of Mechanical and Electrical Engineering, UANL - Nuevo Leon State University, Mexico
Venue:
Computers & Mathematics with Applications
Year:
2010

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Lagrangian relaxation

Modern heuristic techniques for combinatorial problems
Assignment Problems

Assignment Problems
Benders decomposition, Lagrangean relaxation and metaheuristic design

Journal of Heuristics

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Abstract

A Lagrangian based heuristic is proposed for many-to-many assignment problems taking into account capacity limits for task and agents. A modified Lagrangian bound studied earlier by the authors is presented and a greedy heuristic is then applied to get a feasible Lagrangian-based solution. The latter is also used to speed up the subgradient scheme to solve the modified Lagrangian dual problem. A numerical study is presented to demonstrate the efficiency of the proposed approach.