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Sashi Bhusan, D., Bagaban, B., Tripathy, J.P.. (1388). Some Results on facets for linear inequality in 0-1 variables. نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 4(1), 292-303.
D. Sashi Bhusan; B. Bagaban; J.P. Tripathy. "Some Results on facets for linear inequality in 0-1 variables". نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 4, 1, 1388, 292-303.
Sashi Bhusan, D., Bagaban, B., Tripathy, J.P.. (1388). 'Some Results on facets for linear inequality in 0-1 variables', نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 4(1), pp. 292-303.
Sashi Bhusan, D., Bagaban, B., Tripathy, J.P.. Some Results on facets for linear inequality in 0-1 variables. نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 1388; 4(1): 292-303.

Some Results on facets for linear inequality in 0-1 variables

Iranian Journal of Optimization
مقاله 3، دوره 4، شماره 1، فروردین 2012، صفحه 292-303    اصل مقاله (334.16 K)
نوع مقاله: Research Paper
نویسندگان
D. Sashi Bhusan1؛ B. Bagaban2؛ J.P. Tripathy* 3
1Department of Mathematics, Balasore College of Engg . & Technology Teach. Sergarh, Balasore , Orissa , India
2Ms.student of Mathematics, F. M. Autonomous College, Balasore, Orissa, India
3Department of Mathematics Gurukul Institute of Technology Bhubaneswar, Orissa, India
چکیده
The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first part of the present paper. Generating family of valid cutting planes that satisfy inequality with 0-1 variables through algorithms are the attraction of this paper.
کلیدواژه‌ها
Convex- hull؛ set-covering؛ set-partitioning؛ Matrodial-intersection؛ vertex-packing؛ cutting-planes
مراجع
[1] Balas E., An Additive Algorithm for solving for linear program with 0-1 variable, operation research, Vol. 13, 517 -545, 1965.

[2] Balas E., Facets of the Knapsack Polytope, Mathematical programming, Vol. 8, 146-164, 1975.

[3] Balas E., and Jeroslow R., Canonical Cuts, on the unit Hypercube, SIAM Journal of Applied Mathematics Vol. 23, 61-69, 1972. 

[4] Balas E., Mazzola J.B., Non linear Zero – one programming | I, Linearisation Technique mathematical programming, Vol. 30, 1-21, 1984a.

[5] Wolfe P., The simplex Algorithm for Quadratic Programming.  Econometrical, Vol. 27, 382-398, 1959.

[6] Walsey LA., Facets for a linear inequality in zero- one variable mathematical programming, Vol. 8, 165 – 178, 1975.

[7] Walsey L.A., A resource decomposition algorithm for general mathematical programming study Vol. 14, 244 -257, 1981.

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