Base-Stock Policies with Constant Lead Time: Closed-Form Solutions and Applications

We study stationary base-stock policies for multiperiod dynamic inventory systems with a constant lead time and independently and identically distributed (iid) demands. When ambiguities in the underlying demand distribution arise, we derive the robust optimal base-stock level in closed forms using only the mean and variance of the iid demands. This simple solution performs exceptionally well in numerical experiments, and has important applications for several classes of problems in Operations Management. More important, we propose a new distribution-free method to derive robust solutions for multiperiod dynamic inventory systems. We formulate a zero-sum game in which the firm chooses a base-stock level to minimize its cost while Nature (which is the firm’s opponent) chooses an iid two-point distribution to maximize the firm’s time-average cost in the steady state. By characterizing the steady-state equilibrium, we demonstrate how lead time can affect the firm’s equilibrium strategy (i.e., the firm’s robust base-stock level), Nature’s equilibrium strategy (i.e., the firm’s most unfavorable distribution), and the value of the zero-sum game (i.e., the firm’s optimized worst-case time-average cost). With either backorders or lost sales, our numerical study shows that superior performance can be obtained using our robust base-stock policies, which mitigate the consequence of distribution mis-specification.