Probabilistic Inventory Model with Expiration Date and All-Units Discount

Abstract

Inventory is a substantial factor for company to ensure the continuity of its production process. In the inventory management, products usually have expiration date that should be considered in the inventory model, especially in chemical or food industry. Another factor that has an influence to the inventory model is discount factor offered by the supplier. A retailer can accept this offer in order to reduce its total inventory cost. Although buying in a large quantity can decrease purchase cost per unit and set up cost, but it can increase holding cost and expiration cost which all directly has an impact in the total inventory cost. Inventory model with expiration date and all-units discount for probabilistic demand is the focus of this paper. From the mathematical model, an optimal order quantity that minimize the total cost of inventory can be obtained. In building the mathematical model, we assume that lead time is constant and the lead time demand follows Gamma distribution. Numerical examples are given to illustrate our model and algorithm to find the optimal solution. Sensitivity analysis for parameters used in the model is also performed in order to see the impact on the optimal order quantity and total inventory cost.