Optimal periodic replenishment policies for spectrally positive Lévy demand processes

Abstract

We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.

27 pages, 3 figures. Forthcoming in SIAM Journal on Control and Optimization