The bullwhip effect under count time series: The case of first order integer auto-regressive demand processes

The impact of fast moving items, modeled by auto-regressive moving average (ARMA) type processes, on the bullwhip effect is well known. However, slow moving items that can be modeled using integer ARMA processes have received little attention. Herein, we measure the impact of bullwhip effect under a first order integer auto-regressive, INAR(1), demand process. We consider a simple two-stage supply chain consisting of a retailer and a manufacturer. We assume that the retailer employs a base stock inventory policy when the demand is forecasted using a minimum mean squared error method. We investigate the impact of the INAR(1) demand process parameter, ,  and the replenishment lead time, L, on the bullwhip effect generated by the order-up-to replenishment policy. We show that the bullwhip effect is increasing with the lead-time L.