A generalized cost model for stochastic clearing systems

A stochastic clearing system is a stochastic input-output system in which the output occurs periodically in the form of clearing operations that instantaneously clear the total content of the system. In this paper a generalized cost model for the system is assumed in which the cost of clearing the system is C1+C2q, where q is the quantity cleared, and C1 and C2 are positive constants. An equation is derived whose unique solution yields the optimal clearing level, and the resulting solutions are demonstrated using three example systems with renewal, compound Poisson and gamma input processes. The minimum long-run average cost of the stochastic clearing system is shown to be less than the optimal cost of an approximating EOQ deterministic system. Finally, the system is analyzed using a Brownian motion input process with positive drift under this cost model and an equation for the optimal clearing level is derived.