the most costly operation in the oil exploration is the well network drilling. one of the most effectiveways to reduce the cost of drilling networks is decreasing the number of the required wells byselecting the optimum situation of the rig placement. in this paper, balas algorithm is used as a modelfor optimizing the cost function in oil well network, where the vertical and directional drillin...

We propose a cutting plane algorithm for mixed 0-1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point. This cut is found through the solution of a linear program that has about twice the size of the usual LP relaxation. A lifting step is used to re...

Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.

The vertex separator problem (VSP) in an undirected connected graph G = (V,E) asks for a partition of V into nonempty subsets A, B, C such that |C| is minimized subject to there is no edge between A and B, and max{|A|, |B|} ≤ β(n) with β(n) integer such as 1 ≤ β(n) ≤ n. We investigate the (VSP) in a polyhedral way, starting from the formulation given by E. Balas and C. De Souza [1]. We introduc...

Since the 1970s, several authors have studied the structure of the set partitioning polytope and proposed adaptations of the simplex algorithm that find an optimal solution via a sequence of basic integer solutions. Balas and Padberg in 1972 proved the existence of such a sequence with nonincreasing costs, but degeneracy makes it difficult to find the terms of the sequence. This paper uses idea...

Intersection cuts were introduced by Balas and the corner polyhedron by Gomory. Balas showed that intersection cuts are valid for the corner polyhedron. In this paper we show that, conversely, every nontrivial facet-defining inequality for the corner polyhedron is an intersection cut.