Abstract
The Generalized Assignment Problem, in the class of NP-hard problems, occurs in a wide range of applications — vehicle packing, computers, and logistics, to name only a few. Previous research has been concentrated on optimization methodologies for the GAP. Because the Generalized Assignment Problem is NP-hard, optimization methods tend to require larger computation times for large-scale problems. This paper presents a new heuristic,Variable-Depth-Search Heuristic (VDSH). We show that on the sets of large test problems, the quality of the solution found by VDSH exceeds that of the leading heuristic by an average of over twenty percent, while maintaining acceptable solution times. On difficult problem instances, VDSH provides solutions having costs 140% less than those found by the leading heuristic. A duality gap analysis of VDSH demonstrates the robustness of our heuristics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Balachandran, An integer generalized trasportation model for optimal job assignment in computer networks, Working Paper 34-72-3, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh (November 1972).
D.O. Casco, B.L. Golden and E.A. Wasil, Vehicle routing with backhauls: Models, algorithms and case studies, in:Vehicle Routing: Methods and Studies, ed. B.L. Golden and A.A. Assad (Elsevier Science, 1988).
G. Clarke and J.W. Wright, Scheduling of vehicles from a central depot to a number of delivery points, Oper. Res. 12(1964)568–581.
M.L. Fisher and R. Jaikumar, A generalized assignment heuristic for vehicle routing, Networks 11(1981)109–124.
M.L. Fisher, R. Jaikumar and L.N. Vanwassenhove, A multiplier adjustment method for the Generalized Assignment Problem, Manag. Sci. 32(1986)1095–1103.
B. Gavish and H. Pirkul, Algorithms for the multi-resource Generalized Assignment Problem, Manag. Sci. 37(1991)695–713.
M.D. Grigoriadis, D.T. Tang and L.S. Woo, Considerations in the optimal synthesis of some communication networks,Joint National Meeting of ORSA/TIMS, Boston, MA (April 1974).
R.W. Hall, Route choice on networks with concave costs and exclusive arcs, Transp. Res. 23b(1989)103–121.
M. Laguna, J. Kelly, J.L. Gonzalez-Velarde and F. Glover, Working Paper, University of Colorado, Boulder (1991).
S. Lin, Computer solutions of the traveling salesman problem, BSTJ 44(1965)2245–2269.
S. Martello and P. Toth,Knapsack Problems: Algorithms and Computer Implementations (Wiley, 1990).
S. Martello and P. Toth, Linear assignment problems, Ann. Discr. Math. 31(1987)259–282.
C.H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, 1982).
M. Racer, Coordinating inbound and outbound vehicle routes within a decentralized decision environment, University Microfilms, International, Ann Arbor, MI (Dissertation, Industrial Engineering and Operations Research Department, University of California at Berkely, Berkeley, CA, December 1990).
G.T. Ross and R.M. Soland, A branch and bound algorithm for the Generalized Assignment Problem, Math. Progr. 8(1975)92–103.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Racer, M., Amini, M.M. A robust heuristic for the Generalized Assignment Problem. Ann Oper Res 50, 487–503 (1994). https://doi.org/10.1007/BF02085655
Issue Date:
DOI: https://doi.org/10.1007/BF02085655