Net present value analysis of the economic production quantity

Using Laplace transforms we extend the economic production quantity (EPQ) model by analysing cash flows from a net present value (NPV) viewpoint. We obtain an exact expression for the present value of the cash flows in the EPQ problem. From this, we are able to derive the optimal batch size. We obtain insights into the monotonicity and convexity of the present value of each of the cash flows, and show that there is a unique minimum in the present value of the sum of the cash flows in the extended EPQ model. We also obtain exact point solutions at several values in the parameter space. We compare the exact solution to a Maclaurin series expansion and show that serious errors exist with the first-order approximation when the production rate is close to the demand rate. Finally, we consider an alternative formulation of the EPQ model when the opportunity cost of the inventory investment is made explicit.