Abstract
The computational tractability of an integer programming problem is heavily dependent on its formulation. There is thus a permanent need for investigations of alternative formulations of a given integer programming problem; some of the results hitherto obtained have certainly proven their usefulness in practice but much more research lies ahead.
In this paper we study the relations between some linear programming 1elaxations of a given integer program on one side and one of its alternative formulations on the other. An estimate is provided for the maximal possible difference between the optimal values for the integer program and the corresponding linear LP-relaxations. In particular, we consider transformations of different linear nad nonlinear location problem. It is also shown how the dynamic programming procedure of the rotation of an integer constraint can reduce the duality gap. In conclusion, we demonstrate how the resultes of the above analyses can be implemented in algorithms for solving integer programs.
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References
Beale E.M.L., Tomlin J.A.: An Integer Programming Approach to Class of Combinatorial Problem. Mathematical Programming, 3, (1972) 339–344.
Bradley G.H., Hammer P.L., Wolsey L.: Coefficient Reduction for Inequalities in 0–1 Variables. Mathematical Programming, 7, (1974) 263–282.
Geoffrion A.M.: Lagrangean Relaxation for Integer Programming. Math. Programming Study, 2, (1974) 82–114.
Greenberg H.J., Pierskalla W.P.: Surrogate Mathematical Programming. Operations Research, 18, (1970) 924–936.
Kaliszewski I., Walukiewicz S.: Tighter Equivalent Formulations of Integer Programming Problems. Proceedings of the IX International Symposium on Mathematical Programming, Budapest, August 1976.
Kaliszewski I., Walukiewicz S.: A Computationally Efficient Transformation of Integer Programming Problems. Mimeo, Systems Research Institute, Warsaw, December 1978.
Karwan M.H., Rardin R.L.: Some Relationships between Lagrangian and Surrogate Duality in Integer Programming. Mathematical Programming, 17, (1979) 320–334.
Kianfar F.: Stronger Inequalities for 0.1 Integer Programming. Operations Research, 19, (1971) 1373–1392.
Kolokolow A.A.: An Upper Bound for Cutting Planes Number in the Method of Integer Forms, (in Russian), Metody Modelirowanija i Obrabotki Informacji, Novosibirsk, Nauka (1976) 106–116.
Krarup J., Pruzan P.M.: Selected Families of Discrete Location Problem. Part III: The Plant Location Family, Working Paper No WP-12-77, University of Calgary, August 1977.
Salkin H.M., Breining P.: Integer Points on the Gomory Fractional Cut. Dept. of Operations Research, Case Western Reserve University, 1971.
Walukiewicz S.: Almost linear integer problems. (in Polish), Prace IOK, Zeszyt nr 23, 1975.
Williams H.P.: Experiments in the Formulation of Integer Programming Problems. Math. Prog. Studies 2, (1974) 180–197.
Williams H.P.: The Reformulation of Two Mixed Integer Programming Problems. Research Report 75-11. University of Sussex, October 1975.
Zemel E.: Lifting the facets of 0–1 Polytopes. Management Sciences Research Report No 354, Carnegie-Mellon University, December 1974.
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© 1980 Springer-Verlag
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Krarup, J., Walukiewicz, S. (1980). Relations among integer programs. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006605
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DOI: https://doi.org/10.1007/BFb0006605
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