A Dynamic Inventory Model with Periodic Auditing

Abstract

Consider a single-item, periodic review, stationary inventory model with stochastic demands, proportional ordering costs, and convex holding and shortage costs, where shortages are backordered and Veinott's well known terminal condition holds. Orders can be scheduled for any period, but the actual inventory level is determined every T periods through an audit. This leads to a dynamic programming model where stage n contains periods (n − 1)T + 1 through nT. For both discounted and averaging criteria, a simple rule optimally describes the orders for the T periods of a stage as a function of the state (beginning inventory level) and the cumulative T-period order. The latter is optimally determined by a base stock policy with two base stock levels: one for the final stage, another for the rest. (The horizon may be finite or infinite.) Methods are presented for computing optimal policies, together with bounds on the costs of (suboptimal) myopic policies. Models with proportional costs and continuous demands are studied in detail. Computational experiments indicate that myopic policies perform quite well for such models. The selection of a best review period T is covered briefly. Applications of our model include just in time settings where audit decisions play a negligible role.