A new economic order quantity model for deteriorated items under the joint effects of stock dependent demand and inflation

In the present market scenario, it is seen that commodity is attracted by the stock of the items. Considering this fact in this present work, the demand for the item is considered as stock dependent in an inventory control system, where the items are deteriorating in nature. When the number of items in the stock increases, the number of deteriorations also increases. Also, this is important to know for a retailer that when an order will be placed and when the order will be received from the supplier. So, the lead time has an important role in the inventory control system in this stock-dependent demand inventory model. Also, it is seen that the market price of any item may increase gradually with time. Considering this phenomena, the inflation has been incorporated in this work. Here, the proposed model has been analyzed in a finite time horizon. From our analysis, the optimal profit has been calculated for optimal replenishment period of each cycle. Also, depending on the changes in the parameters such as demand, stock, and deterioration, the changes in optimal profit have been analyzed numerically and graphically in the numerical section and the effects of inflation also has been analyzed in this section. As the parameters associated with the system are not always deterministic, so uncertainty arises in the model. To remove this uncertainty, the model has been extended to a fuzzy model considering the q-fuzzy membership function. The fuzzy model has been defuzzified using the Center of Gravity (COG) method and fuzzy extension principle. Also, the fuzzy model has been analyzed by numerical illustration and some sensitivity analysis have been shown corresponding to different values of q and different membership values of the fuzzy parameters.