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Uncertain Solid Transportation Problem with Product Blending

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Abstract

In order to satisfy the required quality of demand points in a practical transportation system of chemical products such as petroleum and gasoline, blending of products should be considered. In this paper, we have considered a solid transportation problem with product blending in an uncertain environment, in which the fixed charges of vehicles and the unit transportation costs of products are assumed to be uncertain variables. Using different criteria to rank uncertain variables, we have constructed uncertain models for this problem, namely expected cost minimization model (ECMM) and chance-constrained uncertain model (CCUM). Within the framework of uncertainty theory, we prove that both of ECMM and CCUM can be transformed into the corresponding deterministic forms. Numerical examples are presented to illustrate the models, and the results are obtained by using the standard optimization solver Gurobi.

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (Nos. 71401008, 71401007 and 71571018), the Fundamental Research Funds for the Central Universities (No. 2014RC038), the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2016ZZ001), Beijing Jiaotong University.

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Authors and Affiliations

  1. State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, China

    Yuan Gao

  2. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, 713209, India

    Samarjit Kar

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  1. Yuan Gao
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  2. Samarjit Kar
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Correspondence to Samarjit Kar.

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Gao, Y., Kar, S. Uncertain Solid Transportation Problem with Product Blending. Int. J. Fuzzy Syst. 19, 1916–1926 (2017). https://doi.org/10.1007/s40815-016-0282-x

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  • DOI: https://doi.org/10.1007/s40815-016-0282-x

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