A Hybrid Forecasting Technique to Deal with Heteroskedastic Demand in a Supply Chain

Under demand uncertain environment, maintaining a proper safety stock is very important to cope with the stock-out situation. Improper estimation of safety stock quantity leads to an improper estimation of the order and further causes bullwhip effect and net-stock amplification. In practice, demand is heteroskedastic in nature i.e. the variance of the demand varies with time. Therefore, it is important to predict the changing demand variance to update safety stock level in each replenishment cycle. The Autoregressive Integrated Moving Average (ARIMA) model applied to predict the mean demand assuming it is homoscedastic in nature. Whereas, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model deal with heteroskedastic demand and help in projecting the changing demand variance. Hence, a combined approach of ARIMA and GARCH (ARIMA-GARCH) model has been proposed to evaluate the safety stock level and order quantity. The performance of ARIMA and ARIMA-GARCH has been evaluated considering the demand from a cement manufacturing company. The cement demand is seasonal in pattern and highly fluctuate. Using cement demand data, ARIMA (2, 1, 1) (0, 1, 1)12 and GARCH (2, 1) model is identified to forecast 12-months ahead mean and variance of demand to determine the safety stock and order quantity in each replenishment cycle applying the equations proposed by Zhang (2004) and Luong & Phien (2007). Further, bullwhip effect and net-stock amplification ratio are estimated to evaluate the performance of ARIMA-GARCH model against the ARIMA model. From the study, it has found that ARIMA-GARCH model outperforms the ARIMA as it updates the safety stock to calculate order quantity in each replenishment cycle.