An Inventory Model with Time-Dependent Demand and Limited Storage Facility under Inflation

The main objective of this paper is to develop a two-warehouse inventory model with partial backordering and Weibull distribution deterioration. We consider inflation and apply the discounted cash flow in problem analysis. The discounted cash flow (DCF) and optimization framework are presented to derive the optimal replenishment policy that minimizes the total present value cost per unit time. When only rented or own warehouse model is considered, the present value of the total relevant cost is higher than the case when two-warehouse is considered. The results have been validated with the help of a numerical example. Sensitivity analysis with respect to various parameters is also performed. From the sensitivity analysis, we show that the total cost of the system is influenced by the deterioration rate, the inflation rate, and the backordering ratio. 1. Introduction Deterioration is the change, damage, decay, spoilage, evaporation, obsolescence, pilferage, and loss of utility or loss of marginal value of a commodity that results in decreasing usefulness from the original one. Most products such as medicine, blood, fish, alcohol, gasoline, vegetables, and radioactive chemicals have finite shelf life and start to deteriorate once they are replenished. In addition, for certain types of commodities, deterioration is usually observed during their normal storage period. In most of the inventory models it is unrealistically assumed that during stockout either all demand is backlogged or all is lost. In reality often some customers are willing to wait until replenishment, especially if the wait will be short, while others are more impatient and go elsewhere. The backlogging rate depends on the time to replenishment the longer customers must wait, the greater the fraction of lost sales. The classical inventory models usually assume that the available warehouse has unlimited capacity. In many practical situations, there exist many factors like temporary price discounts making retailers buy a capacity of goods exceeding their own warehouse (OW). In this case, retailers will either rent other warehouses or rebuild a new warehouse. However, from economical point of views, they usually choose to rent other warehouses. Hence, an additional storage space known as rented warehouse (RW) is often required due to limited capacity of showroom facility. In recent years, various researchers have discussed a two-warehouse inventory system. This kind of system was first proposed by Hartely [1]. In this system, it was assumed that the holding cost in RW is greater than that in