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Usually in stock control studies demand data are considered as an input to the model, without explicitly considering that they are the results of a demand forecasting system. Stock control system is examined independently of the demand forecasting system, and it is assumed that demand data (or forecast errors) have been properly modelled. However, the interactions that may exist between demand forecasting methods and stock control systems, in terms of their effects on global system performances, are not considered. In the paper an approach for evaluating these interactions, based on a comparative simulation test of global system costs using historical data, is presented. The approach is explained through a real case: the replenishment, from different suppliers, of a central depot of tinned food, which supplies more than 700 items to warehouses at the lower echelon. Results of the simulation study show that traditional measures of forecast errors cannot be taken as sole indicators for the choice among different demand forecasting methods. These methods, on the contrary, have to be evaluated on the basis of total costs and service level of the global inventory control system.

Demand forecasting and stock control are two topics that have been widely studied in the literature. Traditionally, these two phases of inventory control systems are considered in sequence, assuming that there are no interactions between them. Regarding demand forecasting, the classic approach is to calculate measures of forecast errors (like the mean absolute deviation (MAD) or the mean absolute percentage error (MAPE)) and to consider the minimisation of such indicators as the best practice in order to minimise the part of total costs associated with the forecasting method. In many stock control studies, the parameters values that lead to total costs minimisation are found on the basis of demand data, which are modelled in a probabilistic way (stationary or non-stationary). Utilising such demand data as inputs to the stock control problem means not to consider that, in practice, a clean distinction between effective demand and forecasted demand does exist, and that in many real cases it is through forecasted demand data that values for stock control parameters have to be assigned. The main limit of traditional approaches is ignoring the possible effects that utilisation of different forecasting methods may have on stock control policies. The aim of this work is to explore the effects of overcoming this limit, and in particular to point out that the most common procedure for evaluating a demand forecasting method (DFM), that is to compare per period forecast errors (usually measured by the MAD, the MSE or the MAPE), is not always appropriate. And that, on the contrary, a better way to do this is to analyse the DFM effect on stock control parameters, and to compare resulting system total costs and service level. To this purpose, a simulation model of a real case, the replenishment of the central depot of a distribution company, has been developed. Features of the case studied are multiple items, highly variable demand patterns (due to seasonality), coordinated replenishment issues (the same supplier furnishes multiple items) and considerable transportation costs. A literature review on studies dealing with these issues is reported in Section 2. The model development, described in detail in Section 3, includes the implementation of two different DFMs. By using historical demand data, forecasted demand data are obtained from both methods. Then, different stock control and replenishment policies, whose parameters are calculated on the basis of forecasted demand data, are simulated on new effective demand data. The details of the experiment are reported in Section 4. The results obtained (see Section 5) allow to compare total system performances of different “forecasting method/replenishment policy” combinations, and to study the interactions between the two components of the inventory control system.

In the paper, an approach for the joint evaluation of DFMs and stock control policies has been proposed. The approach has been tested on a real case, dealing with multiple suppliers, multiple items and with time-varying demands due to seasonality; results show that when choosing among different forecasting methods, the choice based on a comparative simulation test of global system costs and service level may lead to different results with respect to the choice based on traditional measures of forecast errors. In the case studied, the forecasting method based on a CMA demonstrates higher accuracy than the method based on the CMV. The simulation test, based on historical data, has shown, however, that when CMA-forecasted demands are used as inputs for the stock control system, the stock control parameter set of values, for which suitable solutions are achieved in terms of trade-off between total costs and service level, is quite limited. On the contrary, when data coming from the CMV method, though less accurate, are used, many solutions with equal total costs but with higher service level are obtained. The accuracy of CMV and CMA has been evaluated through measures that compare per period forecast errors, namely MAD, MAPE, BIAS and TS (see Table 1). These are surely among the most utilised accuracy measures in scientific literature dealing with DFMs. It is possible, however, that a different accuracy measure, leading to opposite conclusions, exists; that is, a measure indicating that the CMV method is more accurate than the CMA method. In general, one may think to develop ‘ad hoc’ accuracy measures for DFMs so that, when choosing among different DFMs, the choice based on these measures (that utilise only effective and forecasted demand data) and the choice based on the comparison between overall system performances (including the stock control part) bring about the same results. But two main problems arise following this approach. First, the number of different types (and variants) of stock control policies implies the same number of ‘ad hoc’ measures. Secondly, it is very difficult to build measures able to consider the interactions with all the parameters that characterize the stock control system. For these reasons, to know beforehand which measure is exactly the most appropriate for a particular case seems to be very complicated. On the contrary, the approach presented herein suggests that it is better to evaluate and study directly the whole ‘package’, consisting of a DFM and a stock control policy, because to evaluate separately these two components may easily lead to poorer overall performances. Furthermore, through the study of the interactions of the two components, the approach allows to include other interesting considerations about the evaluation of a DFM. By analysing interactions between demand forecasting and stock control, it is possible to notice that there are stronger interactions between the more accurate forecasting method (CMA) and the stock control parameters. The weaker interactions between the CMV method and the other stock control parameters allow achieving good solutions without the need of a very precise tuning of the stock control system. This point is closely related to what can be defined as the property of robustness: the choice of a particular DFM should be based also on an insensitivity to the data quality, missing observations and so forth, and the property for which, even in case of little shifts from the optimal values of stock control parameters, the solution is still acceptable, falls in this same concept. This “insensitivity” has to be measured on the global performances of the inventory control system, and not only on the accuracy of the forecasting method.