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Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach

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Abstract

This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin’s maximum principle. Here, we have used the Runge–Kutta forward–backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Durgapur, India

    A. De & S. Kar

  2. Department of Basic Science and Humanities, Global Institute of Science & Technology, Haldia, India

    D. Khatua

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  1. A. De
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  2. D. Khatua
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  3. S. Kar
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Correspondence to S. Kar.

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Communicated by Rosana Sueli da Motta Jafelice.

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De, A., Khatua, D. & Kar, S. Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach. Comp. Appl. Math. 39, 285 (2020). https://doi.org/10.1007/s40314-020-01333-1

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  • DOI: https://doi.org/10.1007/s40314-020-01333-1

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