Table gives the average MAPE, again for all SKUs with positive preview demand together (overall) and also per preview demand class. We remark that despite of the large differences in performance, the relatively small number of SKUs implies that almost none of these differences are signi?cant (at the 5% signi?cance level). For this reason, the signi?cantly better methods (which would include most) are not indicated in Table 5, as they were for Table.
The two expert judgment methods provide similar performances, and overall clearly outperform all methods based on preview demand. Surprisingly, their comparative performance is especially good for SKUs with a large preview demand. This is counter-intuitive, as one would expect the statistical accuracy of the methods based on preview demand to increase with the preview demand size. More formally, assume that the scaling-up ratio of total demand (for the entire season) to preview demand has been correctly estimated based on historic sales of comparable SKUs. The inverse of this ratio, r, can be interpreted as the probability that a realized demand will be pre-ordered in the preview period. So, given total demand S, preview demand P follows a Binomial distribution with S repetitions and probability of success r. The associated mean and standard deviation of P are rS and r(1 r)S, respectively. Therefore, the scaled-up preview demand P/r has mean S (and is unbiased), variance (1 r)S/r and squared coef?cient of variation (1 r)/rS. Since the squared coef?cient of variation is decreasing in S, SKUs with larger season demands and larger corresponding preview demands are expected to implymore reliable statistical extrapolations.
However, this is apparently not the case. Possible explanations are that preferences change during the season and that preview buyers, who order at a discount, are mainly price-sensitive customers and therefore only represent a segment of the market. Also, the pre-order catalogue is only distributed amongst loyal customers, who may not be representative of the entire customer base in the ?rst place.