This paper introduces a new shortest path simplex pivot rule choosing a subset of non-basic arcs to simultaneously enter into the basis. The term multiple pivot for this operation is used. From this concept, a generic shortest path simplex algorithm with multiple pivots is described. In addition, a simplex multiple pivot rule is provided to design a shortest path simplex algorithm requiring O(n...

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007...

in this research, both resource allocation and reactive resource allocation problems in multi-server dynamic pert networks are analytically modeled, where new projects are expected to arrive according to a poisson process, and activity durations are also known as independent random variables with exponential distributions. such system is represented as a queuing network, where multi servers at ...

In this paper, we study the primal and dual simplex algorithms for the maximum flow problem. We show that aVny primal simplex algorithm for the maximum flow problem can be converted into a dual simplex algorithm that performs the same number of pivots and runs in the same time. The converse result is also true though in a somewhat weaker form.