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Analyzing a Two-Staged multi-objective Transportation Problem Under Quantity Dependent Credit Period Policy Using q-fuzzy Number

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International Journal of Applied and Computational Mathematics 2020年第5期6卷 1-33页

作者： Bera, Raj Kumar Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 W.B. India

Recently, the inclusion of a credit period policy becomes a beneficial strategy to improve a transportation business from the point of views of source and destination. In this regard, this study addresses a two-staged multi-objective transportation problem to transport the products from a production house to some retailers through some distributors by minimizing total transportation cost of retailers and by maximizing total profit of distributors simultaneously. Here, distributors offer a quantity dependent credit period policy to the retailers to induce them to procure the items from that distributors. Under this policy, those retailers who collect the materials more than a threshold value, would get this facility. Ideally, to assign a value of the credit period, there is no specific rule. It is totally the own strategy of the distributors with uncertainty. So, it takes different amounts at different times depending on the market situations. In that sense, it has been considered as q-fuzzy number, which is a combination of linear and non-linear memberships. To simplify the model, some arithmetic operations on q-fuzzy number and its defuzzification procedure have been introduced. Finally, two examples have been considered to examine the feasibility for both the cases (crisp and fuzzy) of the model and a non-elitist multi-objective genetic algorithm has been used to find the optimal solution. © 2020, Springer Nature India Private Limited.

关键词： multi-objective transportation problem non-elitist multi-objective genetic algorithm q-fuzzy number Quantity dependent credit period

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