The inventory ripple effect in just-in-time systems with auto-correlated demand


We investigate a replenishment system with periodic inventory inspections, where at least one batch is completed between inspections, and where orders are placed once every P inspection periods. In this type of system, each ordering occasion will generate P orders for delivery in each of P periods in the future. We can keep the inventory level in each inspection period centered on the inventory norm (the safety stock level), but generating multiple orders at one point in time, with different delivery dates (effectively different lead-times), will cause the inventory variance to change over time. We call this phenomenon the inventory ripple effect. This paper identifies an Order-Up-To policy with minimum mean square error forecasts, under linear holding and backlog costs when demand is a normally distributed first-order autoregressive process. For this we identify a lower bound for the inventory ripple effect. We find that the introduction of positive autocorrelation in demand amplifies the inventory ripple effect in comparison to demand with independent and identically distributed (i.i.d.) error terms, while negatively correlated demand provides an effect smaller than that of i.i.d. demand. A time-varying safety stock setting proves optimal, being significantly more efficient than constant safety stock levels.

Pre-prints of the 18th International Working Seminar of Production Economics, Innsbruck, Austria, 24th-28th Feburary, Vol. 3, 207-217