Approximation Algorithms for Stochastic Inventory Control Models

We consider stochastic control inventory models in which the goal is to coordinate a sequence of orders of a single commodity, aiming to supply stochastic demands over a discrete finite horizon with minimum expected overall ordering, holding and backlogging costs. In particular, we consider the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem in the case where demands over time are correlated and non-stationary (time-dependent). In these cases, it is usually very hard to compute the optimal policy. We provide what we believe to be the first computationally efficient policies with constant worst-case performance guarantees. More specifically, we provide a general 2-approximation algorithm for the periodic-review stochastic inventory control problem and a 3-approximation algorithm for the stochastic lot-sizing problem. Our approach is based on several novel ideas: we present a new (marginal) cost accounting for stochastic inventory models; we use cost-balancing techniques; and we consider non base-stock (order-up-to) policies that are extremely easy to implement on-line. Our results are valid for all of the currently known approaches in the literature to model correlation and non-stationarity of demands over time.