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Mean and CV reduction methods on Gaussian type-2 fuzzy set and its application to a multilevel profit transportation problem in a two-stage supply chain network

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Abstract

The transportation problem (TP) is an important supply chain optimization problem in the traffic engineering. This paper maximizes the total profit over a three-tiered distribution system consisting of plants, distribution centers (DCs) and customers. Plants produce multiple products that are shipped to DCs. If a DC is used, then a fixed cost (FC) is charged. The customers are supplied by a single DC. To characterize the uncertainty in the practical decision environment, this paper considers the unit cost of TP, FC, the supply capacities and demands as Gaussian type-2 fuzzy variables. To give a modeling framework for optimization problems with multifold uncertainty, different reduction methods were proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method and CV reduction method. Then, the TP was reformulated as a chance-constrained programming model enlightened by the credibility optimization methods. The deterministic models are then solved using two different soft computing techniques—generalized reduced gradient and modified particle swarm optimization, where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrated the application and effectiveness of the proposed approaches.

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Acknowledgments

Authors thank the anonymous referees for their valuable comments and suggestions that helped to improve this paper.

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Authors and Affiliations

  1. Department of Applied Science, Haldia Institute of Technology, Haldia, Purba Midnapur, West Bengal, 721657, India

    Dipak Kumar Jana

  2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721 102, India

    Sutapa Pramanik & Manoranjan Maiti

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  1. Dipak Kumar Jana
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  2. Sutapa Pramanik
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Correspondence to Dipak Kumar Jana.

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Jana, D.K., Pramanik, S. & Maiti, M. Mean and CV reduction methods on Gaussian type-2 fuzzy set and its application to a multilevel profit transportation problem in a two-stage supply chain network. Neural Comput & Applic 28, 2703–2726 (2017). https://doi.org/10.1007/s00521-016-2202-2

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