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A new approach for solving dual-hesitant fuzzy transportation problem with restrictions

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Abstract

This paper addresses a study on the transportation problem based on dual-hesitant fuzzy environment. The dual-hesitant fuzzy set accommodates imprecise, uncertain or incomplete information and knowledge situations in real-life operational research problems that are not possible or difficult to tackle by existing fuzzy uncertainties. Here, we present the concept of uncertainty in a transportation problem using dual-hesitant fuzzy numbers. In most of the research works, fuzzy uncertainty has been considered in transportation parameters. However, we consider the dual-hesitant fuzzy numbers to formulate a mathematical model by considering the capacity of delivering the goods by a decision maker. A special emphasis of this paper is to derive an optimal solution of transportation problem with some restrictions under uncertainty by the traditional approach (cf. Vogel’s approximation method—VAM) without using any mathematical aids. In this regard, an algorithm is developed to find the optimal solution for the dual-hesitant fuzzy transportation problem including some restrictions. Thereafter, the proposed method is illustrated by giving a numerical example for showing the effectiveness. Finally, conclusions are given with the lines of future studies based on this paper.

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Acknowledgements

Gurupada Maity is very thankful to the University Grants Commission of India for providing financial support to continue this research work under JRF(UGC) scheme: Sanction letter number [F.17-130/1998(SA-I)] dated 26/06/2014. The research of Sankar Kumar Roy is partially supported by the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), through the CIDMA–Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal, within the project UID/MAT/04106/2019. The research of Gerhard-Wilhelm Weber is partially supported by the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), through the CIDMA–Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal. The authors are very much thankful to the Corresponding Editor and anonymous reviewers for their precious comments that helped them very much to rigorously improve the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Gurupada Maity & Sankar Kumar Roy

  2. Department of Mathematics, Sai Sadhana College of Basic Sciences, Mayurbhanj, 757041, India

    Dharmadas Mardanya

  3. Department of Engineering Management, Poznan University of Technology, Poznan, Poland

    Gerhard-Wilhelm Weber

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  1. Gurupada Maity
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  2. Dharmadas Mardanya
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  3. Sankar Kumar Roy
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  4. Gerhard-Wilhelm Weber
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Correspondence to Sankar Kumar Roy.

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Maity, G., Mardanya, D., Roy, S.K. et al. A new approach for solving dual-hesitant fuzzy transportation problem with restrictions. Sādhanā 44, 75 (2019). https://doi.org/10.1007/s12046-018-1045-1

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