On incorporating business risk into continuous review inventory models

Abstract

This paper analyzes the effect of risk on the lot size and reorder point decisions of a firm, when both these decisions are considered simultaneously. It considers the ( Q, r) inventory model with setup, inventory, and backorder costs with the objective of minimizing the present value of total cost. The capital asset pricing model is used to value the uncertain cash flows from inventory decisions. Optimality conditions for the lot size and the reorder point are derived. Numerical analysis suggest several conclusions. First, an increase in demand riskiness, measured by the covariance of demand with the market return, leads to lower reorder point and lower lot size when the replenishment lead time is small. When the replenishment lead time is large an increase in demand riskiness decreases the reorder point, but may result in a larger lot size. Second, the average inventory in either case is a strictly decreasing function of demand riskiness. Third, comparison with the cost minimization model which uses a fixed opportunity cost of capital shows that large penalties in cost can result if the opportunity cost of capital is not adjusted for the risk of the cash flows from inventory decisions.