Minimizing the discounted average cost under continuous compounding in the EOQ models with a regular product and a perishable product

Abstract

We consider the EOQ model with an opportunity cost of capital, i.e. an amount x invested now will yield (1+i)x at the beginning of the next period. Here i is the interest rate. Given a cost stream i.e. a stream of costs incurred over time, the Net Present Value (NPV) is used to decide the total cost of the cost stream. This total cost takes into account the opportunity cost of capital. The Discounted Average Cost changes the NPV, which is a total, into a cost rate per unit time. The discounted average cost is a cost rate. If we incur this cost rate for the entire period of time under consideration, it will lead to the same NPV as the actual NPV of the cost stream. The discounted average cost under continuous compounding is thus an alternative objective to the standard objective of average cost, which is also a cost rate. We minimize the discounted average cost under continuous compounding for two EOQ models, one with a regular product and the other with a perishable product. Perishable products include food, medicines, certain chemicals and blood in blood banks. In the EOQ model with a perishable product, inventory decays at a constant rate over time. We find the optimal order quantity for the two models while minimizing discounted average cost under continuous compounding.