پیش بینی خطاها و عملکرد موجودی تحت اشتراک اطلاعات پیش بینی

Previous research has shown that the forecast accuracy is to be distinguished from the performance of the forecasts when utility measures are employed. This is particularly true in an inventory management context, where the interactions between forecasting and stock control are not yet fully understood. In this paper, the relationship between the forecasting performance and inventory implications is explored under an ARIMA representation of the demand process. Two distinct scenarios are incorporated in our analysis: Forecast Information Sharing (FIS) and No Information Sharing (NIS) in a two-stage supply chain. We approach the problem analytically and by means of simulation. The validity of the theoretical results is assessed on a real sales dataset from a major European superstore. The results indicate that the gain in accuracy from Forecast Information Sharing depends on the demand process. The translation to inventory savings then depends on the magnitude of the forecast accuracy improvement, regardless of the demand process. Insights into pertinent managerial issues are also offered, and our paper concludes with an agenda for further research in this area.

Previous research has shown that forecast accuracy is to be distinguished from forecast utility (e.g. Syntetos, Nikolopoulos, & Boylan, 2010, and Timmermann & Granger, 2004). Goodwin (2009, p. 10) argued that forecast accuracy metrics often provide a poor indication of the costs and benefits resulting from forecasts. He recommended ‘…that we should never see forecasting as an isolated task, carried out for its own sake’, and called for more theoretical contributions exploring the relationship between forecast accuracy and empirical utility. The relationship between accuracy and utility is particularly complex in an inventory management setting. In the context of this application, replenishment requirements are calculated according to an anticipated probability distribution of demand, obtained from the results of a forecasting procedure. However, parametric stock control theory has been developed based on the assumption of known distribution parameters. The interactions between forecasting and stock control are not yet fully understood. Nevertheless, many researchers have shown that the performance of a stock control system is not always directly related to the forecasting accuracy, as calculated by standard measures (see, for example, Eaves & Kingsman, 2004, Flores, Olson, & Pearce, 1993, Gardner, 1990, Mahmoud & Pegels, 1989, Sani & Kingsman, 1997, and Syntetos & Boylan, 2006). These papers argue that improvements in forecast accuracy must be distinguished from improvements in inventory performance, i.e. a more accurate forecast does not necessarily imply reduced inventory costs and/or an increased service level, which is what matters from a practitioner’s perspective (see also Boylan & Syntetos, 2006). In this paper, we explore, in a two-stage supply chain, the relationship between forecast accuracy and inventories, and the factors upon which this relationship depends. We analyse a supply chain with one member at each stage (say, a retailer and a manufacturer). We do so by assuming an underlying ARIMA demand process at the retailer. In particular, we focus on three stationary processes, namely AR(1), MA(1), and ARMA(1, 1). Such processes are prevalent in industrial sales data, and, as is discussed in Section 5.1, they also collectively represent more than half of the data series available for the purposes of our research. Two distinct scenarios are incorporated in our analysis: Forecast Information Sharing (FIS) and No Information Sharing (NIS) between the retailer and the manufacturer. In the NIS scenario, the retailer does not share any information with the manufacturer, and therefore the latter organisation forecasts on the basis of the orders received from the former. Conversely, in the FIS scenario, the retailer shares its forecasts with the manufacturer. The orders placed with its supplier by the latter organisation are then based on these shared forecasts. The two approaches are compared here by calculating the forecast accuracy, inventory holdings and inventory costs. The literature abounds in discussions of the benefits of sharing information in supply chains, and metrics such as the forecast accuracy and inventory costs have been employed to measure such benefits. However, the linkage between these metrics has never been explored systematically in the academic literature, and this constitutes the main contribution of our work. We start by assuming an AR(1) demand process at the retailer, and mathematically analyse the association between the Mean Squared Error (MSE) and inventory holdings. Owing to the mathematical complexity of extending this association to inventory costs, we continue by employing simulations on theoretically generated data. This helps us to establish the relationship between the MSE and inventory costs and to explore the effects of the autoregressive parameter on this relationship. It also enables us to assess the accuracy of approximate mathematical relationships. We repeat this exercise for the MA(1) and ARMA(1, 1) processes. The results indicate that information sharing leads to considerable reductions in MSE, particularly for an AR(1) process at the retailer, confirming previous findings by Lee, So, and Tang (2000). However, the MSE reductions for MA(1) processes are found to be more modest. The analysis of ARMA(1, 1) shows reductions in MSE between those achieved for the AR(1) and MA(1) processes. The findings relating to the MA(1) and ARMA(1, 1) processes constitute new results in the academic literature. The analytical findings show that the translation of the MSE improvements into inventory savings is independent of the underlying demand process. Greater reductions in MSE imply greater reductions in inventory holdings and costs. The validity of the theoretical/simulation results is assessed using a real dataset from a major European superstore. The remainder of our paper is structured as follows: in Section 2 we review the literature on the relationship between forecast accuracy and inventory performance, and we also consider previous studies that refer to the value of information sharing in supply chain management. The supply chain model used for the purposes of our research is discussed in Section 3, where approximate theoretical results on the relationship between the mean squared error and the inventory holdings are presented. This is followed by a simulation experiment, developed in Section 4, that is used to extend our analysis to inventory costs. Section 5 describes the empirical study carried out for the purposes of our research and its results. Managerial insights are offered in Section 6, along with the conclusions of our work and some natural avenues for further research.

The performance of a forecasting system is generally measured via various forecast error measures such as the Mean Absolute Percentage Error (MAPE) and Mean Squared Error (MSE). A major factor which an organisation must consider when attempting to improve its forecasting system is the use of measurable and meaningful forecast accuracy measures that can be linked with costs. In this paper, we consider the scale of inventory savings according to the degree of improvement in forecasting accuracy. The effect of the latter on the former is a very important issue, and our work constitutes an initial attempt to analyse the relationship under consideration systematically. In this paper, we establish a relationship between forecast accuracy and inventory holdings/costs for three demand processes: AR(1), MA(1) and ARMA(1, 1). From an inventory management perspective, it is important to consider what savings in inventory costs could be caused by a given percentage reduction in forecast error. Organisations may simulate a representative sample of SKUs and establish the relationship between the forecast accuracy and inventory costs for their supply chain model. As we have found out that the relationship is independent of the demand process, the results of the SKU sample could then begeneralised for the rest of the SKUs. These results could then be used to evaluate the cost implications of the improved forecast method/system. In addition, this paper has shown that Forecast Information Sharing has a great potential to improve the forecasting accuracy (for a two-level supply chain, e.g. retailer and manufacturer); however, this improvement depends on both the demand process and the demand parameters at the retailer. The translation to inventory savings has been analysed for three common demand processes and the theoretical results have been confirmed by an empirical analysis. The restriction of our analysis to only three processes may be perceived as a limitation of our study. However, the majority of the demand series in our empirical data were represented by these three demand processes. A further research avenue could be to analyse other demand processes, such as an ARIMA(0, 1, 1) process. Moreover, the empirical analysis conducted in our study was based on data from a major European grocery supermarket. Further empirical evidence may provide insights into the phenomenon we consider, and the study could be enhanced by analysing empirical data from other industries. In addition, our analysis has been constrained by the lack of availability of real cost and lead time information. Additional empirical research that relies upon actual cost figures and lead times would also appear to be merited. It is important to note that, for mathematical simplicity, in our work lead times have been assumed to be the same for both links in the supply chain. Although the supply chain model discussed in this paper is flexible enough to incorporate unequal lead times, this is left as a subject for further research. In this work we have considered only one forecast error measure: the MSE. In order to have insights into the factors that affect the association between forecast accuracy and inventory costs, it is imperative to analyse more forecast error measures. Finally, the demand variability has been considered without incorporating the forecast bias. This is an important issue (see for example Lee, Cooper, & Adam, 1993; Sanders & Graman, 2009), and an interesting avenue for further research would be to model the effects of forecast bias on the three performance metrics (MSE, inventory holdings and inventory costs) considered in this paper.