Stability analysis and control parameter optimization of an inventory system with order variation limits

This paper considers an one-item inventory system subject to random order lead times and random demand. The key parameter of the control policy is the objective inventory level. In each period, the order to be placed brings the inventory position as close as possible to the objective inventory level, and the variation of the quantity to be ordered from one period to the next one is kept bounded by some given upper and lower variation limits. We show that the inventory level remains finite along the time provided that the variation limits are positive. The average inventory cost is shown to be a convex function of the objective inventory level. A simulation-based approach is proposed for the determination of the optimal objective inventory. A method of dichotomy with derivative is then used to determine the optimal objective inventory level. Thanks to the particular structure of the problem, the average costs and the derivatives needed in various iterations of this method are estimated using a single sample path with respect to a given objective inventory.