Forecasting methods for demand planning

Why it matters

Every plan in a vehicle plant — how many cars to build each month, how much steel and how many engines to order, how many people to hire — starts from a demand forecast. A forecast that is consistently high fills the yard with unsold cars; one that is consistently low causes stock-outs and lost orders. Forecasting by moving averages, exponential smoothing and regression, and measuring forecast error, are regular GATE numericals.

Key ideas

Components of demand. A demand series is usually viewed as:

• Level (average value), trend (steady rise or fall), seasonal variation (repeating within a year — festive-season car sales, monsoon tyre demand), cyclic variation (multi-year economic cycles), and random variation that cannot be forecast.

Qualitative methods — used when there is little or no history (a new model launch) or when conditions change sharply:

• Executive opinion (jury of executives), sales-force composite, market surveys and the Delphi method (anonymous experts answer rounds of questionnaires, see the summary and revise until views converge).

Quantitative methods.

• Time-series methods assume the future follows the pattern of the past: simple and weighted moving averages, exponential smoothing, trend projection, seasonal indices.
• Causal (associative) methods relate demand to another variable — interest rates, fuel prices, GDP — usually by linear regression.

Moving averages. A simple n-period moving average gives equal weight to the last n demands. Larger n smooths more but reacts more slowly; with a trend, any moving average lags behind. A weighted moving average gives larger weights to recent periods (weights add up to 1).

Simple exponential smoothing (SES). The new forecast is the old forecast plus a fraction α of the last error. Weights on past demands fall geometrically: α, α(1−α), α(1−α)², … so all history is used but recent data counts most. A high α (0.3–0.5) responds quickly but follows noise; a low α (0.05–0.2) is stable but slow. SES, like moving averages, lags a trend; trend-adjusted (Holt's) smoothing adds a smoothed trend term. An SES with α = 2/(n + 1) has about the same average age of data as an n-period moving average.

Linear regression (least squares). Fits D = a + b·x by minimising the sum of squared errors, where x is time (trend projection) or a causal variable. The correlation coefficient r measures how well the line fits.

Seasonality. A seasonal index is the average demand of a season divided by the average over all seasons. Deseasonalise the data (divide by the index), forecast the trend, then multiply back by the index.

Measuring forecast error. Error e_t = D_t − F_t (actual minus forecast). MAD and MSE measure size of error, MAPE gives it in per cent, and the running sum of errors (RSFE) shows bias. The tracking signal RSFE/MAD flags a forecast that has drifted; values beyond about ±4 (limits are set by policy) mean the model should be revised.

Formulas

F_(t+1) = (D_t + D_(t−1) + … + D_(t−n+1)) / n

• Simple moving average forecast for period t+1 (units); D = actual demand (units); n = number of periods.

F_(t+1) = Σ w_i · D_i with Σ w_i = 1

• Weighted moving average; w_i = weight for period i.

F_(t+1) = α · D_t + (1 − α) · F_t = F_t + α · (D_t − F_t)

• Simple exponential smoothing; α = smoothing constant, 0 < α < 1; F_t = forecast that was made for period t.

D = a + b · x, b = (nΣxy − ΣxΣy) / (nΣx² − (Σx)²), a = (Σy − bΣx) / n

• Least-squares line; x = period number or causal variable; y = demand; n = number of data points.

MAD = Σ|e_t| / n, MSE = Σe_t² / n, MAPE = (100/n) · Σ|e_t / D_t|

• Error measures (units, units², %).

TS = RSFE / MAD = Σe_t / MAD

• Tracking signal (dimensionless).

Worked examples

Example 1 (standard) — exponential smoothing and error. Given: initial forecast for month 1 is F₁ = 100 units, α = 0.2; actual demands in months 1–3 are 110, 96 and 120 units. Find forecasts for months 2–4, MAD and the tracking signal after month 3.

1. F₂ = 0.2 × 110 + 0.8 × 100 = 102.0
2. F₃ = 0.2 × 96 + 0.8 × 102 = 100.8
3. F₄ = 0.2 × 120 + 0.8 × 100.8 = 104.64
4. Errors e = D − F: 110 − 100 = 10; 96 − 102 = −6; 120 − 100.8 = 19.2
5. MAD = (10 + 6 + 19.2) / 3 = 11.73 units; RSFE = 10 − 6 + 19.2 = 23.2
6. TS = 23.2 / 11.73 = 1.98

Answer: F₄ ≈ 104.6 units; MAD ≈ 11.7 units; TS ≈ 1.98 (within limits, but the forecast is running low).

Example 2 (GATE level) — trend projection by least squares. Given: monthly sales of a model over five months: 40, 46, 50, 55, 59 (hundreds of units) for x = 1 to 5. Forecast month 6.

1. Σx = 15, Σy = 250, Σxy = 40 + 92 + 150 + 220 + 295 = 797, Σx² = 55, n = 5
2. b = (5 × 797 − 15 × 250) / (5 × 55 − 15²) = (3985 − 3750) / (275 − 225) = 235 / 50 = 4.7
3. a = (250 − 4.7 × 15) / 5 = (250 − 70.5) / 5 = 35.9
4. F₆ = 35.9 + 4.7 × 6 = 64.1

Answer: about 64.1 hundred units (6,410 vehicles) in month 6. A 3-month moving average would give (50 + 55 + 59)/3 = 54.7 — showing how averages lag a trend.

Example 3 — weighted moving average. Given: last three months 100, 120, 130 (oldest first), weights 0.2, 0.3, 0.5 (most recent largest).

1. F = 0.2 × 100 + 0.3 × 120 + 0.5 × 130 = 20 + 36 + 65 = 121

Answer: 121 units, against 116.7 for the simple 3-month average.

Common mistakes

• Using the current period's own demand in the moving average for that same period; the forecast for period t+1 uses data up to t only.
• Putting α on the old forecast instead of the new demand.
• Taking error as F − D; the standard convention is D − F, so a positive RSFE means the forecast is too low.
• Dropping the absolute value in MAD, which lets positive and negative errors cancel.
• Expecting simple smoothing or moving averages to follow a trend; they always lag.
• Forgetting to divide by n in the regression intercept, or mixing up Σx² and (Σx)².

For GATE ME

Expect short numericals on moving averages, weighted averages, exponential smoothing (one or two steps), least-squares trend lines, and MAD or tracking signal. Conceptual one-mark questions ask about the effect of α, the lag of moving averages, and which methods are qualitative. Practise laying out a neat table of D, F and e period by period.

Quick check

1. F_t = 200, D_t = 220, α = 0.25. What is F_(t+1)?
2. Which reacts faster to a sudden change: α = 0.1 or α = 0.5?
3. Errors over four periods are 5, −3, 4, −2. Find MAD and RSFE.
4. Is the Delphi method qualitative or quantitative?
5. For n = 5, Σx = 15, Σy = 100, Σxy = 330, Σx² = 55, find the slope b.

Answers: 1. 205. 2. α = 0.5. 3. MAD = 3.5, RSFE = 4. 4. Qualitative. 5. b = (1650 − 1500)/(275 − 225) = 3.