Pink Future PLC · Sales planning

How many injectoplactors will we sell next year?

Injectoplactors are small devices that emit happiness when tickled. We know two years of monthly sales. We don't know next year's growth, so we simulate many possible sales paths and combine them into one forecast.

growth in history ΔY(T) = Y(T) / Y(T−1) − 1 one path G_i(T) = G_i(T−1) + G_i(T−1)·W(μ,σ) start G_i(1) = last known sales forecast F(T) = Σ G_i(T) / n

1What history tells us about growth

Each number gives its own two years of sales and its own type of history. The same number always gives the same data.

History type

Each bar counts past months with that growth rate ΔY. From them we read the typical growth μ (median) and how much it varies σ.

Past months Shape of W we simulate

From history: μ (median)

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From history: σ (deviation)

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μ used in model

σ used in model

2Choose the shape of W

3Simulate n possible sales paths, then combine them

Actual sales Y(T) Simulated paths G_i(T) Average F(T) 70% of paths 90% 95%

Where the paths end

Compare shapes of W (final month)

Shape of W	n	Average	Median	90% range

Run each shape once to fill the table. Changing the history, μ, σ or months ahead clears it.

Paths simulated (n)–

Forecast F(T)–units in the final month, average of all paths

Median path–half the paths end above, half below

Ranges for the final month

70%–90%–95%–

Chance sales fall below today–today = – units

What to try

Press n = 1 several times. One path is one possible future, and each press gives a different one.
Go through 10, 100, 1,000, 10,000. Watch the forecast F(T) change less and less.
Switch between Average and Median. Why does the average end a little higher?
Run all six shapes of W with n = 10,000 and compare them in the table. Which shapes change the 95% range most?
Switch to the Volatile history. What happens to the bands and to the chance of falling below today?
Switch to the Seasonal history and press n = 1. Do the simulated paths have seasons? What does this model miss?