Incorporating demand uncertainty and forecast error in supply chain planning models

Abstract

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.

Keywords:

• lot sizing
• forecasting
• service levels
• demand uncertainty
• value of forecasting
• supply chain

This paper represents part of a long-standing research collaboration between Robert Fildes and Brian Kingsman who sadly died before it could be completed. A preliminary version of aspects of this research has been available since 1997 discussing some of the same issues. Valuable comment on this new material has been received from July Jeunet and Alan Mercer but any remaining confusion remains Robert Fildes’ responsibility.

A referee queries why an ARIMA (0,1,1) model has not been considered. The focus of this already long paper is methodological and the proposals carry over to this important case; however, further research into more general demand processes is desirable.

This paper represents part of a long-standing research collaboration between Robert Fildes and Brian Kingsman who sadly died before it could be completed. A preliminary version of aspects of this research has been available since 1997 discussing some of the same issues. Valuable comment on this new material has been received from July Jeunet and Alan Mercer but any remaining confusion remains Robert Fildes’ responsibility.

A referee queries why an ARIMA (0,1,1) model has not been considered. The focus of this already long paper is methodological and the proposals carry over to this important case; however, further research into more general demand processes is desirable.