In “An artificial-free simplex-type algorithm for general LP models” [Math. Comput. Model., 25 (1997), pp. 107–123] and “Initialization of the simplex algorithm: An artificial-free approach” [SIAM Rev., 39 (1997), pp. 736–744], Arsham presents a new Phase 1 algorithm for the simplex method of linear programming, which allegedly obviates the use of artificial variables. He claims in [SIAM Rev., ...

We introduce an algorithm that solves the maximum ow problem without generating ows explicitly. The algorithm solves directly a problem we call the maximum s-excess problem. That problem is equivalent to the minimum cut problem, and is a direct extension of the maximum closure problem. The concepts used also lead to a new parametric analysis algorithm generating all breakpoints in the amount of...

The maximum flow problem (MFP) is a fundamental model in operations research. The network simplex algorithm is one of the most efficient solution methods for MFP in practice. The theoretical properties of established pivot algorithms for MFP is less understood. Variants of the primal simplex and dual simplex methods for MFP have been proven strongly polynomial, but no similar result exists for ...

Abstract. We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cu...

We introduce an algorithm that solves the maximum ow problem without generating ows explicitly The algorithm solves di rectly a problem we call the maximum s excess problem That problem is equivalent to the minimum cut problem and is a direct extension of the maximum closure problem The concepts used also lead to a new parametric analysis algorithm generating all breakpoints in the amount of ti...

Akgiil, M., A genuinely polynomial primal simplex algorithm for the assignment problem, Discrete Applied Mathematics 45 (1993) 93-l 15. We present a primal simplex algorithm that solves the assignment problem in :n(n+3)-4 pivots. Starting with a problem of size 1, we sequentially solve problems of size 2,3,4,. ..,lt. The algorithm utilizes degeneracy by working with strongly feasible trees and ...

In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur in the network simplex algorithm associated with the maximum flow problem.

DYLP is a full implementation of the dynamic simplex algorithm for linear programming. Dynamic simplex attempts to maintain a reduced active constraint system by regularly purging loose constraints and variables with unfavourable reduced costs, and adding violated constraints and variables with favourable reduced costs. In abstract, the code alternates between primal and dual simplex algorithms...

For the problem of cloud service selection, this paper gives a hybrid algorithm. The hybrid algorithm is composed mainly by Simplex Method and Genetic Algorithm. In this algorithm, a tree traversal sequence encoding scheme and some Simplex Method operations are proposed. The design of the tree traversal sequence encoding can support various types of service combinations. In addition, the hybrid...