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A novel reduction method for type-2 uncertain normal critical values and its applications on 4D profit transportation problem involving damageable and substitute items

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Abstract

In this paper, we developed and investigated some four-dimensional profit maximization transportation problems considering damageablity and substitutability, where the parameters are of a type-2 normal uncertain variable in nature. Here, unit transportation cost, distances of the paths, fixed charges, rate of breakability, availability, demands, capacities of conveyances, the unit selling price, unit purchasing cost, unit procurement cost are regarded as type-2 normal uncertain variables. Two models are formulated based on two separate criteria of the substitution items. We use a critical value-based reduction method to reduce type-2 normal uncertain variables into type-1 normal uncertain variables and then apply some properties of uncertainty theory to convert the profit transportation parameters into deterministic form. The two deterministic models are solved using the optimization software named LINGO -18.0. A real-life numerical example and optimal results are presented here to show the application of the proposed model and the proposed reduction method.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, West Bengal, 713209, India

    Palash Sahoo & Goutam Panigrahi

  2. School of Applied Sciences & Humanities, Haldia Institute of Technology, Haldia, Purba Midnapur, West Bengal, 721657, India

    Dipak Kumar Jana

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

    Sutapa Pramanik

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  1. Palash Sahoo
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  2. Dipak Kumar Jana
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Correspondence to Dipak Kumar Jana.

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Sahoo, P., Jana, D.K., Pramanik, S. et al. A novel reduction method for type-2 uncertain normal critical values and its applications on 4D profit transportation problem involving damageable and substitute items. Int. J. Appl. Comput. Math 7, 123 (2021). https://doi.org/10.1007/s40819-021-01062-x

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