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A result in surrogate duality for certain integer programming problems

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Abstract

We consider linear programming problems with some equality constraints. For such problems, surrogate relaxation formulations relaxing equality constraints existwith zero primal-dual gap both when all variables are restricted to be integers and when no variable is required to be integer. However, for such surrogate formulations, when the variables are mixed-integer, the primal-dual gap may not be zero. We establish this latter result by a counterexample.

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References

  1. G.H. Bradley “Transformation of integer programs to knapsack problems,”Discrete Mathematics 1 (1971) 29–45.

    Google Scholar 

  2. R.L. Bush “Restructuring and solving zero-one integer and fixed-charge mixed integer programming problems,” Ph.D. Dissertation (Stanford University, 1972).

  3. S.E. Elmaghraby and M.K. Wig, “On the treatment of cutting stock problems as diophantine problems,” Report No. 61, North Carolina University and Corning Glass Research Center (Chapel Hill, North Carolina, 1970).

    Google Scholar 

  4. F. Glover, “New results for reducing integer linear programs to knapsack problems,” Management Science Report Series 72-7 (University of Colorado, Boulder, 1972).

    Google Scholar 

  5. F. Glover and R.F. Woolsey, “Aggregating Diophantine Constraint,”Operations Research 16 (1972) 1–10.

    Google Scholar 

  6. B. Ram, M.H. Karwan and A.J.G. Babu, “Aggregation of constraints in integer programming,” Research Report IE-BR-01, North Carolina A&T State University, Greensboro, North Carolina, (1984), to appear inEuropean Journal of Operations Research.

    Google Scholar 

  7. K.E. Kendall and S. Zionts, “Solving integer programming problems by aggregating constraints,”Operations Research 25 (1977) 346–351.

    Google Scholar 

  8. M.W. Padberg, “Equivalent knapsack-type formulations of bounded integer linear programs: An alternative approach,”Naval Research Logistics Quarterly 19 (1972) 699–708.

    Google Scholar 

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Authors and Affiliations

  1. North Carolina A&T State University, Greensboro, NC, USA

    Balasubramanian Ram

  2. State University of New York at Buffalo, NY, USA

    Mark H. Karwan

Authors
  1. Balasubramanian Ram
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  2. Mark H. Karwan
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Ram, B., Karwan, M.H. A result in surrogate duality for certain integer programming problems. Mathematical Programming 43, 103–106 (1989). https://doi.org/10.1007/BF01582282

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  • DOI: https://doi.org/10.1007/BF01582282

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