Parametric approach and genetic algorithm for multi objective linear programming with imprecise parameters

Many real world decision making problems are multi objective in nature. However, in some cases the model parameters are imprecise in nature. Such type of problems cannot be solved using classical techniques. These modelling complications can be handled with the help of the concept developed in the theory of fuzzy sets. For the imprecise parameters the model users are normally able to give realistic intervals. Using parametric approach the fuzzy multi objective model may be reduced to multi objective linear programming with crisp parameters. Genetic Algorithm is a powerful technique to solve multi objective decision making problems. A set of non-dominated pareto optimal solutions may be obtained with this approach. In this paper the multi objective linear programming with imprecise parameter has been considered and solved using parametric approach and Genetic Algorithm. To illustrate the procedure a numerical example has been solved. A case study has been done for the allocation of coal and its by-products from a mine establishment to different consumption sites. The transportation cost, availability and the demands are defined by a realistic interval. The problem is solved by GA approach and efficient numerical solution has been found.