A Single Product Cycling Problem Under Brownian Motion Demand

This paper treats a continuous review, single product stochastic cycling problem with demand modelled as a Brownian motion process. A broad class of production policies is admitted: they may be nonstationary, non-Markovian, or, in fact, almost arbitrary. Control theory is used to show that, within this wide class of policies, a simple, stationary, two-number policy is optimal for the average cost minimization problem. This policy switches production on when it is currently off and net inventory reaches a low critical level, or switches it off when it is on and net inventory reaches a high critical level. Simple methods are developed for obtaining the optimal critical levels numerically. Examples are developed comparing the results with those given by Graves and Keilson for a different demand process having the same mean and variance per unit time.