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

The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.

[1]  Monique Guignard-Spielberg,et al.  Technical Note - An Improved Dual Based Algorithm for the Generalized Assignment Problem , 1989, Oper. Res..

[2]  L. V. Wassenhove,et al.  A survey of algorithms for the generalized assignment problem , 1992 .

[3]  Martin W. P. Savelsbergh,et al.  MINTO, a mixed INTeger optimizer , 1994, Oper. Res. Lett..

[4]  S. Thomas McCormick,et al.  Integer Programming and Combinatorial Optimization , 1996, Lecture Notes in Computer Science.

[5]  Ellis Horowitz,et al.  Computing Partitions with Applications to the Knapsack Problem , 1974, JACM.

[6]  George L. Nemhauser,et al.  Solving binary cutting stock problems by column generation and branch-and-bound , 1994, Comput. Optim. Appl..

[7]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[8]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[9]  George L. Nemhauser,et al.  The Set-Partitioning Problem: Set Covering with Equality Constraints , 1969, Oper. Res..

[10]  M. Fisher,et al.  A multiplier adjustment method for the generalized assignment problem , 1986 .

[11]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[12]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[13]  K. Jörnsten,et al.  A new Lagrangian relaxation approach to the generalized assignment problem , 1986 .

[14]  M. Trick.  A Linear Relaxation Heuristic for the Generalized Assignment Problem , 1992 .

[15]  Martin Desrochers,et al.  A Column Generation Approach to the Urban Transit Crew Scheduling Problem , 1987, Transp. Sci..

[16]  Dirk Cattrysse,et al.  A set partitioning heuristic for the generalized assignment problem , 1994 .