Multi-Objective Fuzzy Linear Programming and Its Application in Transportation Model

[[abstract]]In this study, the solution procedure of Multi-objective Fuzzy Linear Programming Problem (MOFLPP) with mixed constraints and its application in solid transportation problem, is going to be presented. There are two parts in this paper. In the first part, a Multi-objective Linear Programming Problem MOLPP) with fuzzy coefficients occurring in constraints and objective functions and fuzzy constraint goals, has been considered. Here fuzzy constraint goals and coefficients of objective and constraint functions are characterised by Triangular Fuzzy Numbers (TFNs). Using Bellman and Zadeh’s (1970) multicriteria fuzzy decision-making process, the very problem has been converted to a crisp non-linear programming problem. Then it has been solved using fuzzy decisive set method. In other part, a linear multi-objective solid transportation problem with mixed constraint as well as additional restriction in fuzzy environment is considered. In this transportation problem, cost coefficients of objective functions and additional restriction function, the supply, demand and conveyance capacity have been expressed as TFNs. This MOFLPP is solved by fuzzy decisive set method as before. Numerical examples have been provided for two parts to illustrate the solution procedure