The goal of railway rolling stock maintenance and replacement approaches is to reduce overall cost while increasing reliability which is multi objective optimization problem and a proper predictive maintenance scheduling table should be adequately designed. We propose Breeding Particle Swarm Optimization (BPSO) model based on the concepts of Breeding Swarm and Genetic Algorithm (GA) operators to design this table. The practical experiment shows that our model reduces cost while increasing reliability compared to other models previously utilized.

In this paper the rough interval multiobjective transportation problem (RIMOTP) is presented and its solution procedure is introduced. The concept of solving the interval multiobjective transportation problem is applied for solving RIMOTP. So, The rough interval in the objective function and the constrains, is represented by three different models and such models are solved by using fuzzy programming technique based on the right limit, the center and the half-width of each rough interval using possibly region. Numerical examples are provided to illustrate the solution procedure of three possible types of the original problem.

This paper presents modified Vogel’s method that solves the fixed charge transportation problems, the relaxed transportation problem proposed by Balinski in 1961 to find an approximate solution for the fixed charge transportation problem (FCTP). This approximate solution is considered as a lower limit for the optimal solution of FCTP. This paper developed the modified Vogel’s method to find an approximate solution used as a lower limit for the FCTP. This is better than Balinski’s method in 1961. My approach relies on applying Vogel’s approximation method to the relaxed transportation problem. In addition, an illustrative numerical example is used to prove my hypothesis.