We study a generalised order-up-to policy that has highly desirable properties in terms of order and inventory variance and customer service. We quantify exactly the variance amplification in replenishment orders, i.e. the bullwhip effect, and the variance of inventory levels over time, for i.i.d., Auto Regressive (AR), Moving Average (MA) and the weakly stationary Auto Regressive Moving Average (ARMA) demand process. We demonstrate that high customer service as measured by fill rate, and smooth replenishments are not mutually exclusive. We observe that in many instances of the ARMA demand pattern this comes at the expense of a relatively small increase in safety stock, while in other instances inventory levels can actually be reduced.Studies; Policy; Bullwhip effect; Inventory; Time; Demand;
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