When solving families of related linear programming (LP) problems and many classes of single LP problems, the simplex method is the preferred computational technique. Hitherto there has been no efficient parallel implementation of the simplex method that gives good speed-up on general, large sparse LP problems. This paper presents a variant of the dual simplex method and a prototype parallelisa...

The problem of determining a maximum-weight marking in a marked graph is mathematically dual to the transshipment problem of operations research. The special structure of the transshipment problem facilitates efficient implementation of the simplex method of linear programming, for solving such problems. In this paper, we first show that the maximum-weight marking problem possesses as much stru...

The railway crew scheduling problem is to determine an optimal crew assignment to minimize the number of crews required to cover all of railway assignment satisfying several crew working constraints. The problem can be formulated as a huge set covering problem. Column generation method is commonly used to solve the railway crew scheduling problem. Conventional column generation method has a sho...

An improved dual simplex algorithm for the solution of the discrete linear Lj approximation problem is described. In this algorithm certain intermediate iterations are skipped. This method is comparable with an improved simplex method due to Barrodale and Roberts, in both speed and number of iterations. It also has the advantage that in case of ill-conditioned problems, the basis matrix can len...

This paper gives a general method for the stable evaluation of multivariate simplex splines, based on the well-known recurrence relation of Micchelli [12]. This paper deals with two problems which arise in the implementation of the recurrence relation. First, the coefficients in the recurrence are shown to be efficiently computable via the dual simplex method of linear programminig. Secondly, t...

Kitahara and Mizuno (2011a) obtained an upper bound for the number of different solutions generated by the primal simplex method with Dantzig’s (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The bound is applied to special linear programming problems. We also g...

This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and Existing Method Solving Interval problems are used linear programming Furthermore, illustration, some numerical examples one real problem to demonstrate correctness usefulness proposed method. The algorithm is flexible, easy, reas...

The Minimum Cost Network Flow Problem (MCNFP) constitutes a wide category of network flow problems. A Dual Network Exterior Point Simplex Algorithm (DNEPSA) for the MCNFP is presented here, together with some computational results. Similarly to the classical Dual Network Simplex Algorithm (DNSA), the new algorithm starts with a dual feasible tree-solution and, after a number of iterations, it p...

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...