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Combinatorial optimisation problems of the assignment type and a partitioning approach

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  • Klose, Andreas
  • Drexl, Andreas

Abstract

Assignment type problems consist in optimally assigning or allocating a given set of "activities" to a given set of "resources". Optimisation problems of the assignment type have numerous applications in production planning and logistics. A popular approach to solve such problems or to compute lower bounds on the optimal solution value (in case of a minimisation problem) is to employ column generation. By means of considering subsets of "activities" which can feasibly be assigned to a single resource, the problem is reformulated as some kind of set-partitioning problem. Column generation is then used in order to solve the linear relaxation of the reformulation. The lower bound obtainable from this approach may, however, be improved by partitioning the set of resources into subsets and by considering subsets of activities which can feasibly be assigned to subsets of resources. This paper outlines the application of this partitioning method to a number of important combinatorial optimisation problems of the assignment type.

Suggested Citation

  • Klose, Andreas & Drexl, Andreas, 2001. "Combinatorial optimisation problems of the assignment type and a partitioning approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 545, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:545
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    1. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    2. Current, John & Weber, Charles, 1994. "Application of facility location modeling constructs to vendor selection problems," European Journal of Operational Research, Elsevier, vol. 76(3), pages 387-392, August.
    3. Klose, Andreas & Drexl, Andreas, 2001. "Lower bounds for the capacitated facility location problem based on column generation," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 544, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Charles S. Revelle & Gilbert Laporte, 1996. "The Plant Location Problem: New Models and Research Prospects," Operations Research, INFORMS, vol. 44(6), pages 864-874, December.
    5. POCHET, Yves & WOLSEY, Laurence A., 1988. "Lot-size models with backlogging: strong reformulations and cutting planes," LIDAM Reprints CORE 791, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Gelders, Ludo F. & Pintelon, Liliane M. & Van Wassenhove, Luk N., 1987. "A location-allocation problem in a large Belgian brewery," European Journal of Operational Research, Elsevier, vol. 28(2), pages 196-206, February.
    7. Hultberg, Tim H. & Cardoso, Domingos M., 1997. "The teacher assignment problem: A special case of the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 101(3), pages 463-473, September.
    8. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
    9. Monique Guignard & Moshe B. Rosenwein, 1989. "Technical Note—An Improved Dual Based Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 37(4), pages 658-663, August.
    10. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    11. Domschke, Wolfgang & Krispin, Gabriela, 1997. "Location and layout planning: a survey," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 8164, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Beasley, J. E., 1988. "An algorithm for solving large capacitated warehouse location problems," European Journal of Operational Research, Elsevier, vol. 33(3), pages 314-325, February.
    13. Pirkul, Hasan, 1986. "An integer programming model for the allocation of databases in a distributed computer system," European Journal of Operational Research, Elsevier, vol. 26(3), pages 401-411, September.
    14. Jacobsen, Soren Kruse, 1983. "Heuristics for the capacitated plant location model," European Journal of Operational Research, Elsevier, vol. 12(3), pages 253-261, March.
    15. A. Victor Cabot & S. Selcuk Erenguc, 1986. "Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation," Management Science, INFORMS, vol. 32(7), pages 856-869, July.
    16. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    17. Cornuejols, G. & Sridharan, R. & Thizy, J. M., 1991. "A comparison of heuristics and relaxations for the capacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 50(3), pages 280-297, February.
    18. Cattrysse, Dirk & Degraeve, Zeger & Tistaert, Jurgen, 1998. "Solving the generalised assignment problem using polyhedral results," European Journal of Operational Research, Elsevier, vol. 108(3), pages 618-628, August.
    19. Christofides, N. & Beasley, J. E., 1983. "Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem," European Journal of Operational Research, Elsevier, vol. 12(1), pages 19-28, January.
    20. E. William Moore & Janice M. Warmke & Lonny R. Gorban, 1991. "The Indispensable Role of Management Science in Centralizing Freight Operations at Reynolds Metals Company," Interfaces, INFORMS, vol. 21(1), pages 107-129, February.
    21. V. Balachandran, 1976. "An Integer Generalized Transportation Model for Optimal Job Assignment in Computer Networks," Operations Research, INFORMS, vol. 24(4), pages 742-759, August.
    22. Wright, Don D. & von Lanzenauer, Christoph Haehling, 1989. "Solving the fixed charge problem with Lagrangian relaxation and cost allocation heuristics," European Journal of Operational Research, Elsevier, vol. 42(3), pages 305-312, October.
    23. Karen Aardal & Yves Pochet & Laurence A. Wolsey, 1995. "Capacitated Facility Location: Valid Inequalities and Facets," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 562-582, August.
    24. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    25. Aardal, K. & Pochet, Y. & Wolsey, L. A., 1995. "Capacitated facility location: valid inequalities and facets," LIDAM Reprints CORE 1295, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Cattrysse, Dirk. G. & Salomon, Marc & Van Wassenhove, Luk N., 1994. "A set partitioning heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 72(1), pages 167-174, January.
    27. Aikens, C. H., 1985. "Facility location models for distribution planning," European Journal of Operational Research, Elsevier, vol. 22(3), pages 263-279, December.
    28. George Kontoravdis & Jonathan F. Bard, 1995. "A GRASP for the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 10-23, February.
    29. Jeff Kennington & Ed Unger, 1976. "A New Branch-and-Bound Algorithm for the Fixed-Charge Transportation Problem," Management Science, INFORMS, vol. 22(10), pages 1116-1126, June.
    30. Cattrysse, Dirk G. & Van Wassenhove, Luk N., 1992. "A survey of algorithms for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 60(3), pages 260-272, August.
    31. Marshall L. Fisher & R. Jaikumar & Luk N. Van Wassenhove, 1986. "A Multiplier Adjustment Method for the Generalized Assignment Problem," Management Science, INFORMS, vol. 32(9), pages 1095-1103, September.
    32. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
    33. Y. T. Herer & M. J. Rosenblatt & I. Hefter, 1996. "Fast Algorithms for Single-Sink Fixed Charge Transportation Problems with Applications to Manufacturing and Transportation," Transportation Science, INFORMS, vol. 30(4), pages 276-290, November.
    34. Udatta S. Palekar & Mark H. Karwan & Stanley Zionts, 1990. "A Branch-and-Bound Method for the Fixed Charge Transportation Problem," Management Science, INFORMS, vol. 36(9), pages 1092-1105, September.
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