Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differenti
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Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach A. De1 · D. Khatua2 · S. Kar1 Received: 22 April 2020 / Revised: 7 September 2020 / Accepted: 17 September 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
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. Keywords Fuzzy dynamical system (FDS) · Granular differentiability (gr-differentiability) · Fuzzy preservation technology · Fuzzy optimal control · Assortment items Mathematics Subject Classification 34A07; 93-10; 90-08
1 Introduction Optimal control theory is one of the earliest and important techniques of modern optimization. It has useful applications in various disciplines that can be found since the end of the 1630s.
Communicated by Rosana Sueli da Motta Jafelice.
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S. Kar [email protected] D. Khatua [email protected]
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Department of Mathematics, National Institute of Technology, Durgapur, India
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Department of Basic Science and Humanities, Global Institute of Science & Technology, Haldia, India 0123456789().: V,-vol
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Bellman’s method of dynamic programming, Pontryagin’s maximum principle and Kalman’s filtering are the important contributions for the study of optimal control theory. In recent developments, the application of optimal control theory can be found in different fields of space technology (Biswas et al. 2011), economics (Derakhshan 2015), medicine (Thomas et al. 2019), management (Biswas and Ali 2016; Khatua et al. 2017), and other branches of science and technology. The classical control system is generally defined by a deterministic differential equation. The stochastic differential equation defines a stochastic control system which is introduced to characterize the random behavior of the control system. Hamilton– Jacobi Bellman equation is one of the most important results in the stochastic control system. Besides probability theory, fuzzy set th
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