A Mathematical Model for Inventory and Price-Dependent Demand with All-Units Discount

Inventory becomes one of the factors a company especially a retailer must consider. A good inventory management will guarantee a retailer in running the business. However, inventory management is a difficult task since it is affected by many factors such as the demand fluctuation, deterioration, discount, sales price, uncertain delivery from the supplier and any other factors. Some factors that affect the consumers demand behavior is the quantity of displayed (available) goods and the sales price. When the customers see that there are still a lot of goods available, there is a perception that the goods available is new and fresh, therefore this will induce demand compared to the least available goods on display. On the other aspect, discount offered by the supplier can be exercised to minimize the total inventory cost by ordering more goods. This paper deals with inventory model where demand depends on the inventory level and sales price and also considering all-unit discount from the supplier. From the model, we will find the optimum order quantity and sales price per unit that minimize the total inventory cost.