On the bullwhip behaviour of a hybrid manufacturing and remanufacturing system under autocorrelated demand and returns

This study explores the bullwhip behaviour of a hybrid manufacturing-remanufacturing system, replenished by the order-up-to policy, under auto-correlated autoregressive and integrated moving average (ARIMA) demand and corrected returns. The phenomena of demand auto-correlation are common in various industries such as automobile, beverage, and fruit and vegetables industries. However, only first-order vector autoregressive (VAR(1)) and independent and identically distributed (i.i.d.) process have been studied in the context of closed loop supply chains (CLSCs) system dynamics. Therefore, by using $z$-transform and discrete-time simulation, we explore bullwhip and inventory variance under i.i.d, AR (1), first-order moving average (MA(1)) and first-order autoregressive and moving average (ARMA(1,1)) demand processes. It is found that, for products that have autoregressive demand characteristics, bullwhip decreases with the autoregressive demand parameter, while autoregressive return parameter has a U-shaped impact on the bullwhip. For those with moving average demand patterns, bullwhip increases with the moving average demand parameter and decreases with the moving average return parameter. Also, system parameters including return rate, inventory proportional controller and forecasting smoothing not only directly impact on bullwhip and inventory variance, but also act as the moderator in influencing the relationship between demand processes and bullwhip/inventory variance. These findings imply important managerial implication to control the bullwhip costs associated with products characterised by both autoregressive and moving average demand processes.