Abstract
We consider a sequence of master (zero-one integer programming) problems arising from the application of Benders decomposition to mixed integer programming models. This sequence of related problems was solved by reoptimization using implicit enumeration based algorithms for postoptimizing zero-one programs. Both computational experience and results are reported.
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References
E. Balas, "An Additive Algorithm for Solving Linear Programs with Zero-One Variables", Operations Research, Vol. 13, pp. 517–546 (1965).
J.F. Benders, "Partioning Procedures for Solving Mixed Variables Programming Problems", Numerische Mathematik, Vol. 4, pp. 238–252 (1962).
A.M. Geoffrion, "Generalized Benders Decomposition", Journal of Optimization Theory and its Applications, Vol. 10, pp. 237–260 (1972).
—, "Integer Programming by Implicit Enumeration and Balas Method", SIAM Review, Vol. 9, pp. 178–190 (1967).
—, "An Improved Implicit Enumeration Approach for Integer Programming", Operations Research, Vol. 17, pp. 437–454 (1969).
A.M. Geoffrion & G.W. Graves, "Multicommodity Distribution System Design by Benders Decomposition", Management Science, Vol. 20, pp. 822–844 (1974).
A.M. Geoffrion & R. Nauss, "Parametric and Postoptimality Analysis in Integer Linear Programming", Management Science, Vol. 23, pp. 453–466 (1977).
F. Glover, "Surrogate Constraints", Operations Research, Vol. 16, pp. 741–749 (1968).
F. Glover, "A Multiphase Dual Algorithm for the Zero-One Integer Programming Problem", Operations Research, Vol. 13, pp. 879–919 (1965).
Hoang Hai Hoc, "Network Improvements via Mathematical Programming", Paper presented at the IX th International Symposium on Mathematical Programming, Budapest August 23–27, 1976.
F. Noonan & R.J. Giglio, "Planning Electric Power Generation: A Nonlinear Mixed Integer Programming Model Employing Benders Decomposition", Management Science, Vol. 23, pp. 946–956 (1977).
C.J. Piper & A.A. Zoltners, "Implicit Enumeration Based Algorithms for Postoptimizing Zero-One Programs", Naval Research Logistics Quarterly, Vol. 22, pp. 791–809 (1975).
C.J. Piper & A.A. Zoltners, "Some Easy Postoptimality Analysis for Zero-One Programming", Management Science, Vol. 22, pp. 759–765 (1976).
G.M. Roodman, "Postoptimality Analysis in Zero-One Programming by Implicit Enumeration", Naval Research Logistics Quarterly, Vol. 19, pp. 435–447 (1972).
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© 1978 Springer-Verlag
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Hoc, H.H. (1978). Solving an integer programming problem. In: Stoer, J. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006525
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DOI: https://doi.org/10.1007/BFb0006525
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