MA.7:5 - Archetypal Grounding
MA.7:5.1 - Locate the aggregate difference
A constructed material-consumption account planned 100 accepted units, two material units per accepted unit and a price of 3 per material unit. Planned cost was 100 × 2 × 3 = 600.
The actual comparable account has 120 accepted units, 2.5 material units per accepted unit and a price of 4. Actual cost is 120 × 2.5 × 4 = 1,200, a difference of 600.
Using the stated order volume, usage, then price:
| Component | Calculation | Amount |
|---|---|---|
| Volume at planned usage and price | (120 − 100) × 2 × 3 | 120 |
| Usage at actual volume and planned price | 120 × (2.5 − 2) × 3 | 180 |
| Price at actual volume and usage | 120 × 2.5 × (4 − 3) | 300 |
| Total difference | 120 + 180 + 300 | 600 |
The decomposition is complete arithmetically. It does not establish that the extra 0.5 material units were waste. If the actual workload included a different product mix legitimately requiring more material, the comparison needs that distinction. If the mix is unchanged and adequate records identify failed attempts, the process question becomes more specific. A changed measuring convention would instead require repairing the account.
Another valid decomposition order can assign interaction amounts differently. Retain the chosen convention rather than using a component’s exact size as independent evidence of causal responsibility.
MA.7:5.2 - Reconstruct the comparison when product mix changes
Suppose the original 100 units comprised fifty A requiring one material unit each and fifty B requiring three. Their reference requirement was 50 × 1 + 50 × 3 = 200 materials. Actual output is thirty A and ninety B. Under unchanged requirements within each product, those outputs require 30 × 1 + 90 × 3 = 300 materials.
The planned and actual totals are still 600 and 1,200, but the intermediate accounts now expose a different explanation:
| Account | Material quantity | Price | Cost | Difference from preceding account |
|---|---|---|---|---|
| Planned 50 A and 50 B | 200 | 3 | 600 | — |
| Actual volume 120 at original 50:50 mix: 60 A and 60 B | 240 | 3 | 720 | 120 volume |
| Actual mix: 30 A and 90 B, at reference requirements | 300 | 3 | 900 | 180 mix |
| Actual material consumption | 300 | 3 | 900 | 0 within-product usage |
| Actual price | 300 | 4 | 1,200 | 300 price |
Thus 120 + 180 + 0 + 300 = 600. The earlier 180 aggregate usage component is now replaced by 180 mix plus zero within-product usage. Adding a further 180 mix to the old decomposition would double count it. The aggregate average rose from two to 2.5 because the output composition changed; this account supplies no evidence of increased waste.
Now change actual consumption to 324 materials on that same actual mix. At the reference price, consumption costs 972, so usage contributes 972 − 900 = 72. Actual price gives 1,296 and a price component of 324. The total difference is 1,296 − 600 = 696, reconciled as 120 volume + 180 mix + 72 usage + 324 price. Investigate the additional twenty-four materials through the operating records and competing explanations; their arithmetic cost does not establish a defect or assign responsibility.
If evidence supports a persistent move toward product B, MA.5 can update the future composition and its resource consequences. The earlier forecast remains available for learning. A different decomposition order can move interaction amounts between components, while the total and the need for causal evidence remain.