Abstract
In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult — at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are alsoNP-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.
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References
Balas E (1975) Facets of the knapsack polytope. Mathematical Programming 8:146–164
Ferreira CE, Martin A, Weismantel R (1993) Facets for the multiple knapsack problem. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Preprint SC 93-4
Gottlieb ES, Rao MR (1990) The generalized assignment problem: Valid inequalities and facets. Mathematical Programming 46:31–52
Gottlieb ES, Rao MR (1990) (1,k)-configuration facets for the generalized assignment problem. Mathematical Programming 46:53–60
Hammer PL, Johnson EL, Peled UN (1975) Facets of regular 0–1 polytopes. Mathematical Programming 8:179–206
Martello S, Toth P (1991) Knapsack problems — Algorithms and computer implementations. John Wiley and Sons, New York
Padberg MW (1980) (1,k)-configurations and facets for packing problems. Mathematical Programming 18:94–99
Wolsey LA (1975) Faces of linear inequalities in 0–1 variables. Mathematical Programming 8:165–178
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On leave from University of São Paulo, Brazil.
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Ferreira, C.E., Grötschel, M., Martin, A. et al. Some integer programs arising in the design of main frame computers. ZOR Zeitschrift für Operations Research Methods and Models of Operations Research 38, 77–100 (1993). https://doi.org/10.1007/BF01416008
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DOI: https://doi.org/10.1007/BF01416008