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Multi-objective multi-item solid transportation problem in fuzzy environment
Authors:Pradip Kundu  Samarjit Kar  Manoranjan Maiti
Institution:1. Department of Mathematics, National Institute of Technology, Durgapur 713209, India;2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapur 721102, India
Abstract:A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of “minimum of fuzzy number” is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.
Keywords:Solid transportation problem  Fuzzy sets  Expected value  Minimum of fuzzy number  Fuzzy programming technique  Global criteria method
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