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Index-Matrix Interpretation of a Two-Stage Three-Dimensional Intuitionistic Fuzzy Transportation Problem

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Recent Advances in Computational Optimization (WCO 2021)

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Abstract

The transportation problem (TP) is a special type of linear programming problem where the objective is to minimise the cost of distributing a product from a number of sources or origins to a number of destinations. In classical TP, the values of the transportation costs, availability and demand of the products are clear defined. The pandemic situation caused by Covid-19 and rising inflation determine the unclear and rapidly changing values of TP parameters. Uncertain values can be represented by fuzzy sets (FSs), proposed by Zadeh. But there is a more flexible tool for modeling the vague information environment. These are the intuitionistic fuzzy sets (IFSs) proposed by Atanasov, which, in comparison with the fuzzy sets, also have a degree of hesitancy. In this paper we present an index-matrix approach for modeling and solving a two-stage three-dimensional transportation problem (2-S 3-D IFTP), extending the two-stage two-dimensional problem proposed in Traneva and Tranev (2021), in which the transportation costs, supply and demand values are intuitionistic fuzzy pairs (IFPs), depending on locations, diesel prices, road condition, weather, time and other factors. Additional constraints are included in the problem: limits for the transportation costs. Its main objective is to determine the quantities of delivery from producers and resselers to buyers to maintain the supply and demand requirements at time (location, etc.) at the cheapest intuitionistic fuzzy transportation cost extending 2-S 2-D IFTP from Traneva and Tranev (2021). The solution algorithm is demonstrated by a numerical example.

Work on Sects. 1 and 3.1 is supported by the Asen Zlatarov University through project Ref. No. NIX-440/2020 “Index matrices as a tool for knowledge extraction”. Work on Sects. 2 and 3.2 is supported by the Asen Zlatarov University through project Ref. No. NIX-449/2021 “Modern methods for making management decisions”.

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Authors and Affiliations

  1. Prof. Asen Zlatarov University, Prof. Yakimov Blvd, Bourgas, 8000, Bulgaria

    Velichka Traneva & Stoyan Tranev

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  1. Velichka Traneva
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  2. Stoyan Tranev
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Correspondence to Velichka Traneva .

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  1. Department Parallel Algorithms, Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Traneva, V., Tranev, S. (2022). Index-Matrix Interpretation of a Two-Stage Three-Dimensional Intuitionistic Fuzzy Transportation Problem. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2021. Studies in Computational Intelligence, vol 1044. Springer, Cham. https://doi.org/10.1007/978-3-031-06839-3_10

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