Question 5 of 7: New-Toy Sales Forecast and Order Quantities

Question 5: New-Toy Sales Forecast and Order Quantities (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Monthly total sales, Feb–Sep 2019; on October 10, on-hand inventory $=685$ units with no pending orders outstanding.

Find. Order quantities for the remainder of October (Oct 11–31), and for all of November and December.

Approach. The sales history is a classic new-product adoption curve: a rapid rise (Feb–Jul) that has visibly plateaued in the last two data points (Aug $=$ Sep $=1{,}030$). A moving average of the most recent, now-stable months is the appropriate forecasting method — a naive (last-value-only) forecast would ignore two months of confirming plateau data, while a linear-regression trend line fit across the whole Feb–Sep history would incorrectly extrapolate the early ramp-up slope forward and badly over-forecast, since the process is no longer growing linearly. A 3-month moving average, rolled forward using each month's own forecast as the stand-in for its not-yet-observed actual, is used for October, November and December.

1. October forecast (3-month MA of Jul, Aug, Sep). $$F_{\text{Oct}}=\frac{1{,}020+1{,}030+1{,}030}{3}=\boxed{1{,}026.7\ \text{units/month}}.$$
2. November and December forecasts, rolled forward. With Sep the last known actual, each successive month's MA uses the prior two known actuals plus the most recently forecast month: $$F_{\text{Nov}}=\frac{1{,}030+1{,}030+1{,}026.7}{3}=\boxed{1{,}028.9},\qquad F_{\text{Dec}}=\frac{1{,}030+1{,}026.7+1{,}028.9}{3}=\boxed{1{,}028.5}.$$
3. Remainder-of-October demand and order. With 21 selling days left in a 31-day October (Oct 11–31), pro-rate the monthly forecast: $$d_{\text{rem.Oct}}=\frac{1{,}026.7}{31}\times21=\boxed{695.5\ \text{units}}.$$ Against the on-hand $685$ units, the order needed to just cover the remainder of October is $$\text{Order}_{\text{Oct}}=695.5-685=\boxed{10.5\approx11\ \text{units}},$$ leaving zero inventory carried into November.
4. November and December orders. With zero inventory carried forward, each month's order equals its own forecast: $$\text{Order}_{\text{Nov}}=F_{\text{Nov}}=\boxed{1{,}029\ \text{units}},\qquad\text{Order}_{\text{Dec}}=F_{\text{Dec}}=\boxed{1{,}029\ \text{units}}.$$

(b) Choice of Method and Accuracy Discussion

A 3-month moving average was chosen because the last two actual months (August, September) are essentially identical ($1{,}030$ both), signalling the product has left its growth phase and entered a stable plateau; a moving average of the most recent, representative months tracks a stable process well while smoothing out the small month-to-month noise still visible in the data (Jul–Sep only spans $1{,}020$–$1{,}030$). A naive forecast (repeat September's $1{,}030$) would be almost as good here precisely because the series is so flat, but it discards the confirming information in July and August; a full linear-regression trend fit across all eight months would substantially over-forecast, since it would extrapolate the steep Feb–Jun growth slope forward into a period where growth has clearly stopped — regression is the wrong tool whenever the underlying pattern is not actually linear over the fitted range.

The main accuracy risk is the reverse of the usual moving-average lag problem: because the series only just plateaued, a 3-month window still contains a small amount of "memory" of the tail of the growth phase, which is why $F_{\text{Oct}}=1{,}026.7$ came in slightly below the last two actuals rather than exactly matching them — a shorter window (e.g., 2-month) would track the plateau more tightly at the cost of more sensitivity to random monthly noise. The pro-rated remainder-of-October figure also assumes sales are distributed evenly across the month's days, which is a simplifying approximation; if online sales in this category cluster around specific promotional dates, the true remainder-of-month demand curve would not be flat and the $11$-unit top-up order could be off by a similar order of magnitude without materially changing the November/December picture.