Multi-objective chance constrained transportation problem with fuzzy parameters

Author's Name: Surapati Pramanik, Durga Banerjee and Bibhas C. Giri
Subject Area: Science and Engineering
Subject Mathematics
Section Research Paper


Transportation Problems, Fuzzy Numbers, a-cut, Chance Constrained Programming, Fuzzy Goal Programming, Membership Function, Distribution Function.


This paper deals with multi-objective chance constrained transportation problems. The coefficients of each objective function are considered as fuzzy numbers. The inequality constraints describing supplies and demands are stochastically defined. In the model formulation, objective functions are converted into the functions with crisp coefficients by using a-cut method (Lee and Li, 1993). Supplies and demands related chance constraints are transformed into equivalent deterministic constraints with the help of known distribution function. Then the membership functions are formulated by considering individual best solution. In the solution process, two fuzzy goal programming models are proposed. Lastly, Euclidean distance function is considered to identify the best compromise solution based on the solutions obtained from two fuzzy goal programming models. The efficiency of proposed approach is demonstrated by solving a numerical example.

Download Full Paper