A fuzzy production inventory control model using granular differentiability approach

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.