Encyclopedia of Optimization

2001 Edition
| Editors: Christodoulos A. Floudas, Panos M. Pardalos

Set Covering, Packing and Partitioning Problems

  • Karla Hoffman
  • Manfred Padberg
Reference work entry
DOI: https://doi.org/10.1007/0-306-48332-7_459
How to cite
We consider the class of problems having the following structure:
90C10 90C11 90C27 90C57 
integer programming combinatorial optimization enumeration polyhedral methods disjunctive programming lift-and-project 
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References

  1. [1]
    Aourid, M., and Kaminska, B.: ‘Neural networks for the set covering problem: An application to the test vector compaction’, IEEE Internat. Conf. Neural Networks: Conf. Proc.7 (1994), 4645–4649.Google Scholar
  2. [2]
    Balas, E., and Carrera, M.C.: ‘A dynamic subgradient-based branch-and-bound procedure for set covering’, Oper. Res.44 (1996), 875–890.MathSciNetMATHGoogle Scholar
  3. [3]
    Balas, E., and Ho, A.: ‘Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study’, Math. Program.12 (1980), 37–60.MathSciNetMATHGoogle Scholar
  4. [4]
    Balas, E., and Padberg, M.W.: ‘Set partitioning: A survey’, SIAM Rev.18 (1976), 710–760.MathSciNetMATHGoogle Scholar
  5. [5]
    Barnhart, C., Johnson, E.D., Nemhauser, G.L., Savelsbergh, M.W.P., and Vance, P.H.: ‘Branch and price column generation for solving hugh integer programs’, Oper. Res.46 (1998), 316–329.MathSciNetMATHGoogle Scholar
  6. [6]
    Beasley, J.E.: ‘A Lagrangian heuristic for set-covering problems’, Naval Res. Logist.37 (1990), 151–164.MathSciNetMATHGoogle Scholar
  7. [7]
    Bramel, J., and Simchi-Levi, D.: ‘On the effectiveness of set covering formulations for the vehicle routing problem with time windows’, Techn. Report Dept. Industr. Engin. and Management Sci. Northwestern Univ. (1998).Google Scholar
  8. [8]
    Chan, L.M.A., Muriel, A., and Simchi-Levi, D.: ‘Parallel machine scheduling, linear programming, and parameter list scheduling heuristics’, Techn. Report Dept. Industr. Engin. and Management Sci. Northwestern Univ. (1998).Google Scholar
  9. [9]
    Chan, L.M.A., Simchi-Levi, D., and Bramel, J.: ‘Worst-case analysis, linear programming and the bin-packing problem’, Techn. Report Dept. Industr. Engin. and Management Sci. Northwestern Univ. (1998).Google Scholar
  10. [10]
    Cornuejols, G., and Sassano, A.: ‘On the 0–1 facets of the set covering polytope’, Math. Program.43 (1989), 45–56.MathSciNetMATHGoogle Scholar
  11. [11]
    Desrochers, M., and Soumis, F.: ‘A column generation approach to the urban transit crew scheduling problem’, Transport. Sci.23 (1989), 1–13.MATHGoogle Scholar
  12. [12]
    Etcheberry, J.: ‘The set covering problem: A new implicit enumeration algorithm’, Oper. Res.25 (1977), 760–772.MathSciNetMATHGoogle Scholar
  13. [13]
    Feo, A., Mauricio, G.C., and Resende, A.: ‘Probabilistic heuristic for a computationally difficult set covering problem’, Oper. Res. Lett.8 (1989), 67–71.MathSciNetMATHGoogle Scholar
  14. [14]
    Fisher, M., and Wolsey, L.: ‘On the greedy heuristic for covering and packing problems’, SIAM J. Alg. Discrete Meth.3 (1982), 584–591.MathSciNetMATHGoogle Scholar
  15. [15]
    Garfinkel, R.S., and Nemhauser, G.L.: Integer programming, Wiley, 1972, pp. 302–305.Google Scholar
  16. [16]
    Gilmore, P.C., and Gomory, R.E.: ‘A linear programming approach to the cutting stock problem’, Oper. Res.9 (1961), 849–859.MathSciNetMATHGoogle Scholar
  17. [17]
    Goldfarb, D., and Reid, J.K.: ‘A practicable steepest-edge algorithm’, Math. Program.12 (1977), 361–371.MathSciNetMATHGoogle Scholar
  18. [18]
    Hall, N., and Hochbaum, D.: ‘A fast approximation algorithm for the multicovering problem’, Discrete Appl. Math.15 (1989), 35–40.MathSciNetGoogle Scholar
  19. [19]
    Hoffman, K., and Padberg, M.W.: ‘Solving airline crew scheduling problems by branch and cut’, Managem. Sci.39 (1993), 657–682.MATHGoogle Scholar
  20. [20]
    Huang, W.C., Kao, C.Y., and Hong, J.T.: ‘A genetic algorithm for set covering problems’: IEEE Internat. Conf. Genetic Algorithms: Proc., 1994, pp. 569–574.Google Scholar
  21. [21]
    Jacobs, L., and Brusco, M.: ‘Note: A local-search heuristic for large set-covering problems’, Naval Res. Logist.42 (1995), 1129–1140.MathSciNetMATHGoogle Scholar
  22. [22]
    Padberg, M.W.: ‘On the facial structure of set packing polyhedra’, Math. Program.5 (1973), 199–215.MathSciNetMATHGoogle Scholar
  23. [23]
    Padberg, M.W.: ‘Perfect zero-one matrices’, Math. Program.6 (1974), 180–196.MathSciNetMATHGoogle Scholar
  24. [24]
    Padberg, M.W.: ‘On the complexity of the set packing polyhedra’, Ann. Discrete Math.1 (1975), 421–434.MathSciNetGoogle Scholar
  25. [25]
    Padberg, M.W.: ‘Covering, packing and knapsack problems’, Ann. Discrete Math.4 (1979).Google Scholar
  26. [26]
    Padberg, M.W.: ‘Lehman’s forbidden minor characterization of ideal 0–1 matrices’, Discrete Math.111 (1993), 409–410.MathSciNetMATHGoogle Scholar
  27. [27]
    Parker, M., and Ryan, J.: ‘A column generation algorithm for bandwidth packing’, Telecommunication Systems2 (1994), 185–196.Google Scholar
  28. [28]
    Sassano, A.: ‘On the facial structure of the set covering polytope’, Math. Program.44 (1989), 181–202.MathSciNetMATHGoogle Scholar
  29. [29]
    Savelsbergh, M.W.P.: ‘A branch-and-price algorithm for the generalized assignment problem’, Oper. Res.45 (1997), 831–841.MathSciNetMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Karla Hoffman
    • 1
  • Manfred Padberg
    • 2
  1. 1.George Mason UnivMasonUSA
  2. 2.New York Univ.New YorkUSA