A multi-item transportation problem with fuzzy tolerance |
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Authors: | Anupam Ojha Barun Das Shyamal Kumar Mondal Manoranjan Maiti |
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Affiliation: | 1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India;2. Department of Mathematics, Jhargram Raj College, Midnapore 721507, India |
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Abstract: | This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermann's method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermann's methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters. |
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Keywords: | Fuzzy transportation models Multi-items Genetic Algorithm Solid transportation Modified subgradient method Fuzzy tolerance |
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