COORDINATING DEMAND FORECASTING AND OPERATIONAL DECISION-MAKING WITH ASYMMETRIC COSTS: THE TREND CASE

This article presents two methods for coordinating demand forecasting and operational decisionmaking when time series data display a trend and the unit costs of under-forecasting (cu) and over-forecasting (co) may differ. The first method, called ordinary least squares with adjustment (OLSA), makes a simple additive adjustment to the forecasts generated by OLS regression. The second method generates forecasts by fitting a weighted least absolute value (WLAV) regression line through the data, where the weights correspond to the unit underage and overage costs. Using simulation, both methods are tested against OLS regression forecasts made in the presence of one of four types of error distributions, and numerous combinations of cu and co. The performance measure used for evaluation is the mean opportunity loss (MOL) over the postsample periods. Simulation results show that the benefits of both approaches increase rapidly as cu and co diverge, regardless of the error distribution. In particular, when the ratio of costs is 3:1, OLSA can reduce post-sample MOL of OLS by 19-23%. Even when the ratio of costs is closer to 2:1, OLSA can still reduce post-sample MOL by 6-7%. In a few scenarios, WLAV outperforms OLSA, but generally is not as robust as OLSA. I. INTRODUCTION Traditionally, articles and texts concerned with demand forecasting tend to ignore the related decision-making aspects of the situation. Similarly, those concerned with operational decisionmaking tend to ignore how the relevant demand forecasts were developed. Many assume that a manager somehow already possesses a demand forecast, or that demand can be represented by some specific probability distribution (Brown, 1982). In reality, demand forecasting and decisionmaking should not be activities performed in isolation from one another. A few articles bridge this gap and show how these two activities interact, especially in the context of inventory control. For example, Gardner (1990) demonstrated how the choice of forecasting model plays a key role in determining the amount of investment needed to support a desired customer service level in a large physical distribution system. Eppen and Martin (1988) showed how various stationary demand distributions and lead time length affect forecasting error and, thus, error in the proper amount of safety stock required to meet a given service level. Watson (1987) studied how lumpy demand patterns can lead to large fluctuations in forecasts, which, in turn, increase ordering and holding costs as well as distort the actual level of service provided. Importantly, positive and negative forecasting errors often have asymmetric impacts on operations and, therefore, may be viewed differently by the manager who actually uses the forecasts to make a decision. Symmetric performance measures (e.g., MAD, MSE, MAPE) may be misleading if the cost of over-forecasting is substantially different from that of underforecasting. Consequently, the methods presented here are evaluated from the viewpoint of a decision-maker who adopts mean opportunity loss (MOL) as the best measure of forecasting performance. Unfortunately, articles and texts that use symmetric measures of forecasting performance and do not consider the role played by forecasts within the larger decision-making context dominate the forecasting literature. One exception is the situation described by Lee and Adam (1986), who report that some MRP systems can reduce total production costs if demand for final product is over-forecast by 10-30%. Conversely, class schedulers at a large university (SFSU) prefer to under-forecast enrollment in multi-section courses, finding it easier to add a section at the last minute if demand turns out to be higher than expected, rather than cancel an under-filled section if demand is lower than expected. Another common situation in which the costs of overforecasting (co) and under-forecasting (cu) may be quite different is in the classical single-period