An optimal ordering policy for deteriorating items with partial backlogging and time varying selling price and purchasing cost under inflation

In the last several years, most countries have suffered from large-scale inflation and sharp decline in the purchasing power of money. Due to high inflation rate, the time value of money goes down and the future worth of saving decreases. As a result, large capital to purchase item is needed, the selling price and purchasing cost is also affected. Consequently, it will highly affect the return on investment. Therefore, to consider both the inflationary effect and fluctuated selling price and purchasing cost simultaneously is important. Thus, I develop the inventory lot-size model as introduced in Yang (2012) and further take the effect of inflation into account. The proposed model also allows for: 1) time-varying demand; 2) time-varying partial backlogging rate; 3) time-varying selling price and purchasing cost which changed from one replenishment cycle to another. Based on profit maximisation, the optimal replenishment schedule which maximises the total profit exists uniquely. Sensitivity analysis for managerial policymaking is also performed. From the sensitivity analysis, we know that the total profit is relatively influenced by considering the effect of inflation as the selling price and purchasing cost is fluctuated at the replenishment time.