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A branch-and-cut algorithm for a generalization of the Uncapacitated Facility Location Problem

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Summary

We introduce a generalization of the well-know Uncapacitated Facility Location Problem, in which clients can be served not only by single facilities but also by sets of facilitities. The problem, calledGaneralized Uncapacitated Facility Lacition Problem (GUFLP), was inspired by the Index Selection Problem in physical database design. We for mulate GUFLP as a Set Packing Problem, showing that our model contains all the clique inequalities (in polynomial number). Moreover, we describe and exact separation procedure for odd-hole inequalities, based on the particular structure of the problem. These results are used within a branch-and-cut algorithm for the exact solution of GUFLP. Computational results on two different classes of test problems are given.

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References

  • Bilde, O. and J. Krarup (1977). “Sharp Lower Bounds and Efficient algorithms for the Simple Plant Location Problem”,Annals of Discrete Mathematics 1, 79–97.

    Article  Google Scholar 

  • Balas, E. and M.W. Padberg (1976). “Set Partitioning: A survey”,SIAM Review 18, 710–760.

    Article  Google Scholar 

  • Caprara, A. and M. Fischetti (1993). “Odd-Cut Sets, Odd Cycles, and 0–1/2 Chvátal-gomory cuts”, working paper, University of Bologna.

  • Caprara, A., M. Fischetti and D. Maio, (1995). “Exact and Approximate Algorithms for the Index Selection Problem in Physical Database Design”,IEEE Transactions on Knowledge and Data Engineering 7, 955–967.

    Article  Google Scholar 

  • Ceria, S. (1994). “Solving Mixed Integer Programs with General Cutting Planes”, talk presented at the workshopSolving Large and Complex Optimization Problems, Giens.

  • Cho, D.C., E.L. Johnson, M.W. Padberg and M.R. Rao, (1983). “On the Uncapacitated Plant Location Problem. I: valid Inequalities and Faces”,Mathematics of Operations Research 8, 579–589.

    Google Scholar 

  • Cho, D.C., M.W. Padberg and M.R. Rao, (1983) “On the Uncapacitated Plant Location Problem. II: Facets and Lifting Theorems”,Mathematics of Operations Research 8, 590–612.

    Google Scholar 

  • Conn, A.R. and G. Cornuejols (1990). “A Projection Method for the Uncapacitated Facility Location Problem”,Mathematical Programming 46, 273–298.

    Article  Google Scholar 

  • Cornuejols, G., G.L. Nemhauser and L.A. Wolsey (1991). “The Uncapacitated Facility Location Problem”, in P.B. Mirchandani, R.L. Francis.Discrete Location Theory, John Wiley.

  • Conuejols, G. and J.M. Thizy, (1982). “Some Facets of the Simple Plant Location Polytope”,Mathematical Programming 23, 50–74.

    Article  Google Scholar 

  • Cornuejols, G. and J.M. Thizy (1982). “A Primal Approach to the Simple Plant Location Problem”,SIAM Journal on Algebraic and Discrete Methods 3, 504–510.

    Google Scholar 

  • Erlenkotter, D. (1978). “A Dual-Based Procedure for Uncapacitated Facility Location”.Operations Research 26, 992–1009.

    Article  Google Scholar 

  • Finkelstein, S., M. Schkolnick and P. Tiberio (1988). “Physical Database Design for Relational Databases”,ACM Transactions on Database Systems 13, 91–128.

    Article  Google Scholar 

  • Grötschel, M., L. Lovász and A. Schrijver (1988).Geometric Algorithms and Combinatorial Optimization, Springer-Verlag.

  • Guignard, M. (1980). “Fractional Vertices, Cuts and Facets of the Simple Plant Location Problem”,Mathematical Programming Study 12, 150–162.

    Google Scholar 

  • Krarup, J. and P.M. Pruzan (1983). “The Simple Plant Location Problem: Survey and Synthesis”,European Journal of Operational Research 12, 36–81.

    Article  Google Scholar 

  • Morris, J.G. (1978). “On the Extent to Which Certain Fixed-Charge Depot Location. Problems Can Be Solved by LP”,Journal of the Operational Research Society 29, 71–76.

    Article  Google Scholar 

  • Nemhauser, G.L. and G. Sigismondi (1992). “A Strong Cutting Plane/Branch-and-Bound Algorithm for Node Packing”,Journal of Operational Research Society 43, 443–457.

    Article  Google Scholar 

  • Padberg, M.W. (1973). “On the Facial Structure of Set Packing Problems”,Mathematical Programming 5, 199–215.

    Article  Google Scholar 

  • Padberg, M.W. and G. Rinaldi (1991). “A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems”,SIAM Review 33, 60–100.

    Article  Google Scholar 

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Authors and Affiliations

  1. DEIS, University of Bologna, Italy

    A. Caprara

  2. DEIOC, University of La Laguna, Spain

    J. J. Salazar González

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  1. A. Caprara
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  2. J. J. Salazar González
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Caprara, A., González, J.J.S. A branch-and-cut algorithm for a generalization of the Uncapacitated Facility Location Problem. Top 4, 135–163 (1996). https://doi.org/10.1007/BF02568608

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  • DOI: https://doi.org/10.1007/BF02568608

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