Start with something familiar
Arriving five minutes early one day and five minutes late the next gives average signed timing error zero. Yet neither arrival was exactly on time. Forecast errors can cancel the same way. A useful scorecard separates how large misses are from which direction they take. It also keeps the original appointment time: changing the target afterward would make the record look better without showing whether the initial plan was useful.
Words to know: Bias, MAE, WAPE.
Declare the sign
Here error equals actual demand minus forecast. Positive means underforecasting; negative means overforecasting. Other businesses may reverse the sign, so publish the formula. Mean error describes signed bias over the selected rows. Near-zero bias does not imply small misses, and a short window does not prove long-run systematic behavior.
For actuals 40,60,0,20 and forecasts 50,50,10,10, errors are -10,10,-10,10. Their mean is zero, while mean absolute error is ten bottles. Both are correct. Inspect signed row errors and magnitude together rather than treating one balanced total as evidence that the planning process needs no improvement.
Make denominators visible
RMSE is the square root of mean squared error and penalizes large misses more heavily. WAPE here is summed absolute error divided by summed actual demand. The example gives 40/120, or 33.33%. Ordinary MAPE divides each row by its actual and is undefined at the zero-demand row; silently dropping that row changes the evaluation.
WAPE is undefined when total actual demand is zero. Use absolute errors and explain the missing denominator. Portfolio WAPE emphasizes high-volume demand and can hide weak performance on small critical items. Show selected product metrics as well as the aggregate, and state whether you pool units or average item-level percentages.
Score the decision fairly
Compare methods on identical targets, origins, and horizons. A forecast updated one day before shipment has more information than one frozen four weeks earlier. Preserve both versions if both matter, but do not confuse the information advantage with model quality. Use demand actuals consistent with the target, not shipments capped by capacity.
Business costs can be asymmetric: a shortage may cost more than an excess unit. Keep cost scenarios separate from statistical error metrics and state the rates used. Preserve baseline and adjusted forecasts to test whether judgment helped. A favorable business result does not retroactively make an incorrect forecast correct.
- Define target
- Check evidence
- Calculate
- Challenge assumptions
- Record decision
Measure magnitude and direction — worked case
All inputs below describe fictional Northstar bottles. Keep the stated units and timing when reproducing the calculation.
| Week | Actual | Forecast | Error |
|---|---|---|---|
| 1 | 40 | 50 | -10 |
| 2 | 60 | 50 | 10 |
| 3 | 0 | 10 | -10 |
| 4 | 20 | 10 | 10 |
- 1. Bias = (-10+10-10+10)/4 = 0.
- 2. MAE = 40/4 = 10.
- 3. RMSE = sqrt(400/4) = 10.
- 4. WAPE = 40/120 = 33.33%; MAPE undefined.
Zero bias coexists with ten-unit MAE and RMSE.
Assumptions
- Periods and quantities use the definitions stated in this example.
- Only explicitly supplied events or adjustments are included.
Where this can fail: The arithmetic checks the stated assumptions; it does not establish that uncertain future events will occur.
Build, test and explain a plan
Eight actuals [40,60,0,20,50,70,10,30]. Baseline [50,50,10,10,55,55,15,15]. Adjusted [45,55,5,15,50,65,10,25]. All frozen one week ahead. Separate inactive SKU actuals [0,0,0,0], forecasts [2,2,2,2]. All units are bottles unless stated otherwise. Use a spreadsheet or ruled paper. Eight hours includes construction, comparison, writing, and teach-back; this is a planning estimate, not an experimentally validated completion time.
Use paper or a spreadsheet. The estimates below include the study and worked example already on this page.
| Estimated hours | Activity |
|---|---|
| 0.5 | Study the lesson and write a data dictionary defining every field, time bucket, unit, and cutoff. Separate observed facts from assumptions. Identify two ways a colleague could misread the target and rewrite its definition to prevent those errors. |
| 0.5 | Reproduce the worked example independently, showing formulas and intermediate values. Compare against the answer and keep a correction log explaining each difference. Check one result a second way using a total, balance, or direct manual calculation. |
| 3 | Build row errors, absolute and squared errors, cumulative signed error, bias, MAE, RMSE, WAPE. Show inactive SKU separately and combined portfolio WAPE. Chart signed misses. Keep inputs separate from formulas, label every origin and target, and add independent row and total checks. Produce an annotated chart with at least two observations tied to specific rows; include a brief explanation of why each check matters. |
| 2 | Use under/over costs five/one per unit, then one/five. Compare ranking with MAE. Demonstrate the misleading result of taking an absolute value only after signed errors have been averaged. Preserve each variant separately. Create an output comparison table and explain which changed assumption caused each movement. Identify a scenario that affects timing differently from totals and state what the planner should do with that distinction. |
| 1 | Write a 400-word decision memo using your own numerical outputs. State the proposed action, evidence, two limitations, an owner for the next check, and a measurable condition that would change your recommendation. Attach the model so a reader can audit every cited value. |
| 1 | Prepare a five-minute teach-back using one worked row and one scenario comparison. Explain it aloud to a colleague or recording. Write three skeptical questions, answer them with evidence, and revise the memo or model where your explanation exposes an unsupported assumption. |
Your deliverables
- Auditable input and formula model with checks
- Scenario comparison and annotated chart
- Decision memo, correction log, and teach-back notes
Check your practice work
- Baseline errors [-10,10,-10,10,-5,15,-5,15]: bias 2.5, MAE ten, RMSE sqrt(112.5)=10.6066.
- Adjusted errors [-5,5,-5,5,0,5,0,5]: bias 1.25, MAE 3.75, RMSE sqrt(18.75)=4.3301.
- Actual total 280; baseline WAPE 28.5714%, adjusted 10.7143%.
- Inactive SKU MAE two, bias -2, WAPE undefined. Combined baseline WAPE 88/280=31.4286%.
- Under/over costs 5/1: baseline 280, adjusted 110. Costs 1/5: baseline 200, adjusted 70.
Keep these three ideas
- Calculate MAE, RMSE, WAPE, and signed bias without hiding zero-demand failures.
- Keep original evidence distinct from modeled values and assumptions.
- A precise output remains conditional on definitions and timing.
Common mistakes
- Overwriting the original evidence after a revision.
- Reporting a number without its unit, period, cutoff, and assumptions.
Optional video study
Calculate MAE, RMSE, WAPE, and signed bias without hiding zero-demand failures.
- Declare the sign
- Make denominators visible
- Score the decision fairly
One half of the module narration, with a distinct Northstar calculation and a bridge to the paired lesson.
Open the module media & quizPut this idea to use
Carry your assumptions into a practical tool, then compare your result with a short guide.
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