A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems

One of the most interesting models of the linear programming is the flexible linear programming problem. It is shown that by using a suitable membership function for their constraints, we can obtain an equivalent Fuzzy Variable Linear Programming (FVLP) problem. Some methods have been developed for solving these problems by introducing and solving a certain auxiliary problem. Here, we first propose a fuzzy primal simplex algorithm for solving the flexible linear programming problem and then suggest the fuzzy primal simplex method to solve the flexible linear programming problems directly without solving any auxiliary problem. This method will also be especially useful for sensitivity analysis using the primal simplex tableaus. Thereafter, we shall illustrate our method with some examples. [Received 05 April 2008; Revised 05 October 2008; Revised 14 September 2009; Accepted 15 September 2009]