Optimized crisp and fuzzy inventory system of deteriorating items with partial backlogging under the effect of inflation

Abstract

In the present era of financial instability which is a haunting situation for the economy, the inflationary effect cannot be ignored which is prevalent in every inventory system. The incredible increase in the prices of commodities has resulted in monetary depreciation. As the inventory constitutes the substantial capital investment for any type of organization thus it would be completely unethical if the consequence of inflation along with time value of money is not taken into consideration. Also, there is a significant effect of deterioration in any inventory system. There is a vital role played by the shortage of commodities in flawless functioning of the inventories. These may be partially backlogged and even partially lost due to the delay in the replenishment of the orders under consideration. For the conversion of the lost sales into sales the retailer provides a type of incentive to the customers by charging the price from them which is equivalent to that at the time when the order is placed rather than the current price of the commodity due to the effect of inflation. All these conditions have been properly considered in this paper and a system of inventory has been established under these conditions in crisp along with the fuzzy system. The elementary aim of the study is to resolve and compare the cost in total for both crisp along with fuzzy environments. A suitable numerical example is included for illustrating both the models.