1. The nesting board can be used for forward management.
The starting point for this use is a copy of the most aggregated table of the tree in question, based on the model of this one:
| A | B | C | ||
|---|---|---|---|---|
| Child 1 | Child 2 | Parent | ||
| 1 | Direct investment | 100 | 200 | 450 |
| 2 | Turnover | 500 | 400 | 900 |
| 3 | Direct costs | 300 | 240 | {540 |
| 4 | Direct margin | 200 | 160 | {360 |
| 5 | Direct profitability R | 200% | 80% | 20% |
| 6 | Direct productivity P | 5 | 2 | {3 |
| 7 | Direct profitability P' | 40% | 40% | {40% |
| 8 | Common costs | 340 | ||
| 9 | Direct margin (C4 – C8) | 20 | ||
| If the parent enterprise is the legal-entity enterprise: | ||||
| 10 | Return on capital R (C9/315) | 6,35 % |
2. In forecasting, the table is filled in from bottom to top.
The following are successively introduced:
3. When the margin plus common costs is distributed in proportion to the direct investments of the children, the direct rates of return of the latter are equal.
The direct profitability objectives of the children are then inversely proportional to the corresponding productivity:
| A | B | C | ||
|---|---|---|---|---|
| Child 1 | Child 2 | Parent | ||
| 1 | Direct investment | 100 | 200 | 450 |
| 2 | Turnover | |||
| 3 | Direct costs | 300 | 240 | {540 |
| 4 | Direct margin | 200 | 160 | {360 |
| 5 | Direct profitability R | 200% | 80% | 20% |
| 6 | Direct productivity P | 5 | 2 | {3 |
| 7 | Direct profitability P' | 40% | 40% | {40% |
| 8 | Common costs | 340 | ||
| 9 | Direct margin (C4 – C8) | 20 | ||
| If the parent enterprise is the legal-entity enterprise: | ||||
| 10 | Return on capital R (C9/315) | 6,35 % |
4. Reducing the dispersion of direct rates of return of the same ownership improves competitiveness.
As a result of this reduction, profitability is lowered and raised the more Productivite productivity is higher or lower than its average (row 6, column C). What competition tends to establish is better anticipated. Supply is more competitive because the best-selling products are at prices that subsidize less, or not at all, the least-selling products.
5. The reduction in the dispersion of direct return on capital of the same systemic level makes the final profitability less dependent on changes in the sales structure.
In other words, a legal-entity-enterprise whose sales prices are constantly adjusted in such a way that there is as little inequality as possible in the direct return on capital of the same systemic level. So for the profitability of this enterprise, it becomes irrelevant if the sales structure changes. There are no longer any sales in this enterprise that massively subsidize others. The selling prices are as fair as those of two enterprises that each sell only one supply and whose profitability is equal to each other and to what is nationally necessary to restore or maintain full employment.
6. The distribution of a margin, or even only common costs, in proportion to direct investment is useless when the productivity of sister P is equal.
In such a case, the profitability R and the profitability P' of the same ownership are all in the same ratio, since by definition R = P x P'. So, distributing direct investments in proportion to the same as doing it in proportion to direct costs. In the long term, the evolution of productivity P of the same affiliation is nevertheless to be monitored, as it is always likely to be affected by changes in the structure of sales, increasing where sales are concentrated and remaining stable or decreasing on the rest of the supply. Knowledge of direct investments, even "ladleful", is essential to the exercise of this surveillance, otherwise the productivity of the same membership is invaluable.
7. Some sales have direct profitability but no direct investments and therefore no direct profitability and productivity.
For example, consider how certain sales are made in the trade in medicines and spare parts, as well as in general the subscription of insurance policies. They are part of transactions carried out without tying up a direct investment by the seller, because either the seller passes on a buyer's order to another supplier, who therefore does not tie up any stock, or the nature of the service sold makes it so. Direct profitability from these transactions exists in the form of gross margin rates or commissions, these rates being applied to the amounts sold. But these profitability P' are not matched to profitability R or productivity P, until their aggregation does not reveal the immobilization of at least one investment and a relationship RPP'.
8. The distribution of the number of replenishments per item is made economically optimal by the application of a theorem.
This application optimizes the value of the average stock, and thus the productivity (of stock turnover) of an assortment: for any other distribution of the total number of restocks between items, the average stock is higher and its turnover is a little to much lower. Let be, in fact, a series of fractions N (numerator) over D (denominator). The numerators N are positive numbers and these numbers are known. In contrast, for the denominators D, only their sum S, which is also positive, is known, and each element of this sum must itself be positive. The problem is to determine each denominator D that makes the sum of the N/D fractions minimal. This is the case when only the sum S is distributed among the Ds in proportion to the ratio between the square root of each N and the sum of the square roots of the N (note: the sum of the square roots of the N and not the square root of the sum of the N). This theorem is proved by double derivatives, but a spreadsheet makes it possible to empirically establish by means of arbitrary numerical series that there is indeed an optimal distribution law.
9. The optimal distribution of a total number of orders among the items in the same assortment is an application of the theorem indicated above.
The number of fractions is equal to the number of items. For each item, the numerator N is the product of its quantity sold (or consumed) by the unit cost (the purchase price). S is the total number of orders. The ratio of the square root of N to the sum of the square roots of the N is the distribution key of S, article by article92.
10. To calculate, on the basis of a margin objective, unit prices that tend to equalize the direct rates of return of these items, it is sufficient to use the ratio between the square root of N and the sum of the square roots of N.
For each item, the absolute margin to be assigned to it is equal to this ratio applied to the total margin, also in absolute value. Thus, the items with the highest turnover (productivity) are those to which the lowest sales margin rates (profitability) are assigned and, conversely, the items with the lowest turnover are those to which the highest sales margin rates are assigned. It can then be verified experimentally that the prices calculated in this way are those that competition tends to form. In other words, we verify experimentally that these prices are those that tend to equalize profitability (productivity times profitability) item by item.
11. Instead of using the square root of each N, the product of the quantity sold (or consumed) by the unit cost (the purchase price), we can also use the power of 0.5 of this amount, which is mathematically equivalent.
By making this power an exponent e (with e = 1), the profitability, i.e. in this case the margin rates on the selling price, are identical while the competition tends to disperse them – with, as already noted, the smallest profitability for items with the largest stock turnover, as a general rule. With e = 0.1, on the contrary, we obtain profitability that is considerably more dispersed than the competition tends to make them. It is most often with e between 0.6 and 0.8 that we obtain the price line closest to that which competition tends to prevail. And it is also, more often than not, with e = 0.5 that we obtain the price line that best anticipates future price decreases on the best-selling items. This would not exist if competition did not tend to equalize the direct profitability of the same membership93.
12. The "pure and perfect competition" of neoclassical theory is unachievable.
Strengthening the trend towards equalization of direct rates of return of the same membership is achievable.