A Production: Inventory Model for Defective Items with Shortages Incorporating Inflation and Time Value of Money

This paper develops a production-inventory model of a single product with imperfect production process in which inflation and time value of money are considered under shortages. Demand rate has been considered to be a function of quadratic decreasing and exponential decreasing of selling price. The selling price of a unit is determined by a mark-up over the production cost. Unit production cost is considered incorporating several features like energy and labour cost, raw material cost, replenishment rate and other factors of the manufacturing system. The defective items which is a certain fraction of the total production or a random number are either reworked or refunded if those reach to the customer. Two scenarios have been considered in which defective items are refunded from the customer with penalty in scenario (a) and the defective items are repaired and sold to the customer as good items in scenario (b). Based on these two scenarios, three models have been developed in which defective items are certain fraction of the produced quantity in Model-I, a random number in Model-II, and are dependent in reliability parameter and time in Model-III. Considering all these phenomena optimum production of the product has been evaluated to have maximum profit. Finally, numerical examples are given to illustrate the results along with graphical analysis. Sensitivity analysis has also been carried out for different values of the parameter.

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