Abstract
We consider generalized assignment problems with different objective functions: min-sum, max-sum, min-max, max-min. We review transformations, bounds, approximation algorithms and exact algorithms. The results of extensive computational experiments are given.
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G. Carpaneto, S. Martello, P. Toth (1988). Algorithms and codes for the assignment problem. In B. Simeone, P. Toth, G. Gallo, F. Maffioli, S. Pallottino (eds.). Fortran Codes For Network Optimization, Annals of Operations Research 13, 193–223.
A. De Maio, C. Roveda (1971). An all zero-one algorithm for a certain class of transportation problems. Operations Research 19, 1406–1418.
M.L. Fisher (1981). The Lagrangian relaxation method for solving integer programming problems. Management Science 27, 1–18.
M.L. Fisher, R. Jaikumar, L.N. VanWassenhove (1986). A multiplier adjustment method for the generalized assignment problem. Management Science 32, 1095–1103.
E.S. Gottlieb, M.R. Rao (1990a). The generalized assignment problem: valid inequalities and facets. Mathematical Programming 46, 31–52.
E.S. Gottlieb, M.R. Rao (1990b). (1,k)-configuration facets for the generalized assignment problem. Mathematical Programming 46, 53–60.
M.M. Guignard, S. Kim (1987). Lagrangean decomposition: A model yielding stronger Lagrangean bounds. Mathematical Programming 39, 215–228.
M.M. Guignard, M.B. Rosenwein (1989). An improved dual based algorithm for the generalized assignment problem. Operations Research 37, 658–663.
T.D. Klastorin (1979). An effective subgradient algorithm for the generalized assignment problem. Computers and Operations Research 6, 155–164.
N.W. Kuhn (1955). The hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97.
E.L. Lawler (1976). Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York.
K. Jörnsten, M. NÄsberg (1986). A new Lagrangian relaxation approach to the generalized assignment problem. European Journal of Operational Research 27, 313–323.
S. Martello, P. Toth (1980). Solution of the zero-one multiple knapsack problem. European Journal of Operational Research 4, 276–283.
S. Martello, P. Toth (1981). An algorithm for the generalized assignment problem. In J.P. Brans (ed.), Operational Research'81, North-Holland, Amsterdam, 589–603.
S. Martello, P. Toth (1990). Knapsack Problems: Algorithms and Computer Implementations, Wiley, Chichester.
S. Martello, P. Toth (1991).The bottleneck generalized assignment problem. Research report DEIS OR/5/91, University of Bologna.
J.B. Mazzola (1989). Generalized assignment with nonlinear capacity interaction. Management Science 35, 923–941.
J.B. Mazzola, A.W. Neebe (1988). Bottleneck generalized assignment problems. Engineering Costs and Production Economics 14, 61–65.
G.T. Ross, R.M. Soland (1975). A branch and bound algorithm for the generalized assignment problem. Mathematical Programming 8, 91–103.
V. Srinivasan, G.L. Thompson (1973). An algorithm for assigning uses to sources in a special class of transportation problems. Operations Research 21, 284–295.
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© 1992 Springer-Verlag Berlin Heidelberg
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Martello, S., Toth, P. (1992). Generalized assignment problems. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_88
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DOI: https://doi.org/10.1007/3-540-56279-6_88
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