Optimal policies and approximations for a serial multiechelon inventory system with time-correlated demand

Since Clark and Scarf's pioneering work, most advances in multiechelon inventory systems have been based on demand processes that are time independent. This paper revisits the serial multiechelon inventory system of Clark and Scarf and develops three key results. First, we provide a simple lower-bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of Clark and Scarf. Second, we show that the structure of the optimal stocking policy of Clark and Scarf holds under time-correlated demand processes using a Martingale model of forecast evolution. Third, we extend the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times and autocorrelation on the performance of the serial inventory system.