A fuzzy production inventory control model using granular differentiability approach
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METHODOLOGIES AND APPLICATION
A fuzzy production inventory control model using granular differentiability approach D. Khatua1,2 · K. Maity3 · S. Kar2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we have created a single-period fuzzy production inventory control model on the finite time horizon. A new nonlinear demand function has been introduced, which depends on the stock, selling price and product quality. The realistic reasons come from logistical function and entry into the initial demand for the product and the reliance on uncertain advertising rates, uncertain stock rates, uncertain selling prices and uncertain product quality. In order to control and test the stability, the model needs to be defuzzified. The concept of granular differentiability has been applied to defuzzification. Granular differentiability is the new definition of fuzzy derivatives based on the function of horizontal membership. For the first time in this paper, we have used the granular differentiation method in production inventory systems. We analyzed vaguely optimized controls in terms of granular differentiation analytically and numerically. Keywords Production inventory control model · Fuzzy exponential demand function · Fuzzy product innovation · Nonlinear fuzzy dynamical system · Granular differentiability
1 Introduction In the organizational management, one of the most important problems is in the area of production inventory control model. The related tasks that have come with the problems are mathematical model development and define the optimal inventory control strategy. Inventory control model includes many different features and limitations for different types of company or firm. The inventory models constructed on the assumption of the key variables such as stock rate, demand
Communicated by V. Loia.
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S. Kar [email protected] D. Khatua [email protected] K. Maity [email protected]
1
Department of Basic Science and Humanities, Global Institute of Science and Technology, Haldia, West Bengal, India
2
Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India
3
Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupati Nagar, West Bengal, India
rate and production rate. The premises of these variables always may not suit to the physical environment. There is a heavy heap of uncertainty and variability. Sometimes, just about sites are enhanced when the interval of the selling season of items is brusque. After ending the season, the excess stocks cannot be satisfied with the demand of the next season. Then, in that case, a single period is needed. Obtaining realistic input values for the mathematical inventory model parameters is a tough job. Essentially, all the models and methods for finding the decision-making variables in the existing theory of inventory management usually focus on deterministic. That is why the target does not meet the broad demands of the material environment. In such instances, an important p
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