図解された在庫報酬関数
The 在庫報酬関数は、確率的予測を最大限に活用し、サプライチェーンパフォーマンスを向上させるための重要な要素です。在庫報酬は、追加の在庫ユニットを購入または製造する際の投資収益率（ROI）を計算するために使用されます.
The 在庫報酬関数は表現力豊かで、多岐にわたる状況に対応するための小規模なフレームワークのように利用することができます。しかし、一方で、この関数による計算内容を理解するのは必ずしも容易ではありません。以下に、予測に適用されたさまざまな変換を示すグラフの簡単なリストを紹介します.
The first graph - entitled 将来の需要 - represents a probabilistic demand forecast associated with a given SKU. The curve represents a distribution of probabilities, with the total area under the curve equal to one. In the background, this future demand is implicitly associated with a probabilistic リードタイム forecast, also represented as a distribution of probabilities. Such a distribution is typically generated through a 確率的予測エンジン.
The Marginal fill rate graph represents the fraction of extra demand that is captured by each extra unit of stock. In other words, this graph demonstrates what happens to the fill rate as the stock increases. Since we are representing a marginal fill rate here, the total area under the curve remains equal to one. The marginal fill rate distribution can be computed with the fillrate() 関数.
The Demand with backorders graph is identical to the 将来の需要 graph, except that 8 units have been introduced to represent a back order. The バックオーダー represents guaranteed demand since these units have already been bought by clients. As a result, when backordered units are introduced, the probability distribution of demand is shifted to the right as the backordered units being guaranteed demand. The shift operator » is available as part of the algebra of distribution to compute such a transformation over the initial distribution.
The Fill rate with backorders graph is also very similar to the original Marginal fill rate graph, but has also been shifted 8 units to the right. Here, the plotted fill rate is only associated with the uncertain demand, hence the shape of the distribution remains the same.
The Margin graph represents the margin economic reward as computed by the stock reward function taking the Demand with backorders as input. The stock reward can be visualized as a distribution, but this is not a distribution of probabilities: the area under the curve is not equal to one but is instead equal to the total margin which would be captured with unlimited inventory. On the left of the graph, each backordered unit yields the same margin, which is not surprising as there is no uncertainty in capturing the margin given that the units have already been bought.
The 品切れペナルティ represents the second component of the stock reward function. The shape of the distribution might feel a bit unexpected, but this shape merely reflects that, by construction of the stock reward function, the total area under the curve is zero. Intuitively, starting from a stock level of zero, we have the sum of all the ストックアウト penalties as we are missing all the demand. Then, as we move to the right with higher stock levels we are satisfying more and more demand and thus further reducing the stockout penalties; until there is no penalty left because the entire demand has been satisfied. The stock-out penalty of not serving backorders is represented as greater than the penalty of not serving the demand that follows. Here, we are illustrating the assumption that clients who have already backordered typically have greater service expectations than clients who haven’t yet bought any items.
The Carrying costs graph represents the third and last component of the stock reward function. As there is no upper limit for the carrying costs - it’s always possible to keep one more unit in stock thus further increasing the carrying costs - the distribution is divergent: it tends to negative infinity on the right. The total area under the curve is negative infinity, although this is a rather theoretical perspective. On the right, the carrying costs associated with the backordered units are zero: indeed, as those units have already been bought by clients they won’t incur any carrying costs, since those units will be shipped to clients as soon as possible.
The final stock reward - not represented above - would be obtained by summing the three components of the stock reward function. The resulting distribution would be interpreted as the ROI for each extra unit of stock to be acquired. This distribution typically starts with positive values,the first units of stock being profitable, but converge to negative infinity as we move to higher stock levels given the unbounded carrying costs.
The term support (mathematics) classically refers to the demand levels associated with non-zero probabilities. In the graphs above, the term サポート is used loosely to refer to the entire range that needs to processed as non-zero values by Envision. In particular, it’s worth mentioning that there are multiple calculations that require the distribution support to be extended in order to make sure that the final resulting distribution isn’t truncated.
- The shift operation, which happens when backorders are present, requires the support to be increased by the number of backordered units.
- The margin and carrying cost components of the stock reward function have no theoretical limits on the right, and can require arbitrarily large extensions of the support.
- Ordering constraints, such as 最小発注量, may require having inventory levels that are even greater than the ones reached by the shifted distributions. Properly assessing the tail of the distribution is key for estimating whether the MOQ can be profitably satisfied or not.
In practice, the Envision runtime takes care of automatically adjusting the support to make sure that distributions aren’t truncated during the calculations.