The Cost of Allocation Errors

Summary

Forecast error leads to misallocation of inventory across demand channels, driving lost sales. For example, for a product with 100 units of demand split across two channels, we find that relying on a single prior sales cycle to guide allocation leads to a loss of roughly 3% of potential sales. In general, we find that misallocation losses scale as fraction of sales lost∝# of channels / total demand​​ In practice, this means misallocation matters most for lower-volume products and for assortments spread across many locations. Combining our worked example with this scaling law provides a quick way to estimate misallocation losses for general products. While these losses can be meaningful, they fall sharply with improved forecasting, for example via data pooling across related products. Misallocation and Avoidable Loss The mathematics of allocation applies whenever a fixed supply must be divided across independent demand channels. Two common applications include the distribution of units across retail locations and the setting of size breaks for a garment. The goal in allocation is to avoid scenarios where some channels are systematically over-resourced – and so unlikely to sell through their units, while others are systematically under-resourced – and so likely to stock out early, resulting in missed sales. In a situation like this, shifting units around to improve balance will lift expected net sales. In fact, we showed in a prior post that to maximize net unit sales, we must allocate units so that each channel has the same probability of stocking out. To implement this optimal strategy, we must first be able to accurately forecast the demand distribution of each channel (i.e., how likely it is that demand will come in at each possible value for that channel). If our forecasts are inaccurate, supply will again be imbalanced. In the appendix to this post, we work out the following approximation for the misallocation loss that then results, Fraction of sales lost due t...