Multi-objective multi-item solid transportation problem in fuzzy environment |
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Authors: | Pradip Kundu Samarjit Kar Manoranjan Maiti |
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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 |
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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. |
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Keywords: | Solid transportation problem Fuzzy sets Expected value Minimum of fuzzy number Fuzzy programming technique Global criteria method |
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