Ch. 18: Forecasting
Forecasts underlie almost every management decision: budgets, sales plans, supplier and process selection, capacity, purchasing, scheduling and inventory. Consider the purpose first:
- Strategic forecasts: medium and long term, for aggregate demand and decisions on strategy, capacity, process design, location and sourcing.
- Tactical forecasts: short term (weeks or months), for day-to-day decisions such as replenishing inventory or scheduling production.
Forecasts are needed especially at decoupling points, where inventory separates parts of the supply chain; the closer to the customer, the faster the service but the higher the inventory investment. A perfect forecast is impossible, so continual review and combining two or three methods with common sense is recommended.
Types of forecasting and components of demand
Four basic types: qualitative, time series analysis (past demand predicts future demand), causal relationships (demand depends on underlying factors) and simulation. Demand has six components: average demand, trend, seasonal element, cyclical elements (elections, war, economy), random variation (what is left unexplained) and autocorrelation (a value is correlated with its own past values). Common trend shapes: linear, S-curve (product life cycle), asymptotic and exponential.
Choice of model depends on time horizon, data availability, accuracy required, forecasting budget and qualified personnel. Short term is under 3 months, medium term 3 months to 2 years, long term more than 2 years.
| Forecasting technique | Forecast horizon | Data pattern handled | Data required |
|---|---|---|---|
| Simple moving average | Short | Stationary only | 6 to 12 months |
| Weighted moving average, simple exponential smoothing | Short | Stationary only | 5 to 10 observations |
| Exponential smoothing with trend | Short | Stationary plus trend | 5 to 10 observations |
| Linear regression | Short to medium | Stationary, trend, seasonality | 10 to 20 observations |
| Trend and seasonal models | Short to medium | Stationary, trend, seasonality | 2 to 3 observations per season |
Moving averages
Simple moving average: F(t) = (A(t-1) + A(t-2) + ... + A(t-n)) / n.
Weighted moving average: F(t) = w(1)A(t-1) + w(2)A(t-2) + ... + w(n)A(t-n), with the weights summing to 1.
A moving average removes random fluctuation when demand has no trend or seasonality. Fewer periods follow changes more closely but fluctuate more; more periods give a smoother forecast that lags the trend. Drawback: all data must be stored. A weighted average usually gives the most recent period the highest weight (for example 0.4, 0.3, 0.2, 0.1), but with seasonal data the same season last year may deserve more weight.
Exponential smoothing
F(t) = F(t-1) + α(A(t-1) - F(t-1)): new forecast = old forecast + a fraction α of the last error.
Example: F(t-1) = 1,050, A(t-1) = 1,000, α = 0.05: F(t) = 1,050 + 0.05(1,000 - 1,050) = 1,047.5.
It is the most used technique because it is accurate, easy to formulate and understand, needs little computation and storage (only the last forecast, the last actual and α), and accuracy is easy to test. Stable demand calls for a low α (0.05 to 0.10), growth for a higher α (0.15 to 0.30). To mimic an n-period moving average, α is about 2 / (n + 1). Single smoothing lags a trend and overshoots when the direction changes.
F(t) = FIT(t-1) + α(A(t-1) - FIT(t-1))
T(t) = T(t-1) + δ(F(t) - FIT(t-1))
FIT(t) = F(t) + T(t)
Example 18.1: FIT = 110, T = 10, α = 0.2, δ = 0.3, actual 115: F = 110 + 0.2(5) = 111; T = 10 + 0.3(111 - 110) = 10.3; FIT = 121.3.
Linear regression and decomposition
Linear regression fits Y = a + bt by least squares (minimizing the sum of squared vertical distances). It suits long-term forecasts of aggregate demand (product families) when data are roughly linear; it is used both for time series (t = time) and for causal forecasting. In Example 18.2 (12 quarters of sales) a = 441.67 and b = 359.6, so the forecast for quarter 13 is 441.67 + 359.6 x 13 = about 5,116. The standard error of estimate measures how well the line fits.
Decomposition separates a time series into components. With additive seasonal variation the seasonal amount is constant; with multiplicative variation (the usual case) the trend is multiplied by seasonal factors, so swings grow with the trend.
Seasonal factor = average demand in the season / average demand over all seasons. Forecast = (expected total / number of seasons) x seasonal factor, or trend value x seasonal index.
Example 18.3: 1,000 units per year, seasons 200/350/300/150 give factors 0.8, 1.4, 1.2, 0.6. For 1,100 units next year: 275 x factor = 220, 385, 330, 165.
Forecast errors
Forecast error = actual - forecast. Bias errors come from consistent mistakes (wrong variables or relationships, wrong trend line, shifted seasonality); random errors cannot be explained by the model. Actual errors tend to exceed those the model predicts.
MAD = Σ|A(t) - F(t)| / n. With normal errors, σ is about 1.25 x MAD (and MAD about 0.8 σ).
MAPE = (Σ|A(t) - F(t)| / A(t)) / n x 100 percent.
Tracking signal TS = RSFE / MAD, where RSFE is the running sum of forecast errors (with sign).
MAPE allows comparison between products with very different demand levels. A tracking signal far from zero indicates bias: a positive TS means actual demand keeps exceeding the forecast (forecast too low). In Exhibit 18.12 a constant forecast of 1,000 had MAD 66.7 and TS 3.3, suggesting a bad forecast. In solved problem 4 the errors 40, -80, 30, -45, -60, 60 give MAD 52.5 and TS -1.05, no reason to reject the model.
Causal relationship forecasting
Uses independent variables other than time; they must be leading indicators (known before demand occurs). In Example 18.5, carpet sales Y = 6,698.49 + 344.22 X with X = housing permits; 25 permits give about 15,304 square yards. Multiple regression uses several variables (marriages, housing starts, income, trend) but requires much external data.
Qualitative techniques
Useful for new products or regions with little data: market research (surveys, interviews), panel consensus (open meetings; lower levels may be intimidated), executive judgment (higher-level decisions), historical analogy (use a similar product's history, such as toasters for coffeepots) and the Delphi method: anonymous experts answer questionnaires, results are summarized and fed back with new questions, usually for about three rounds, so everyone has equal weight.
CPFR
Collaborative planning, forecasting and replenishment is a web-based tool to coordinate forecasting, production, purchasing and replenishment among supply chain partners, with the retail-level forecast as the ideal point of collaboration. Five steps: (1) front-end partnership agreement (objectives, resources, confidentiality), (2) joint business planning, (3) development of demand forecasts (often simple moving averages plus promotional knowledge, using POS data), (4) sharing forecasts with exception notices when differences exceed a margin, (5) inventory replenishment. The main barrier is lack of trust and fear of data misuse or loss of control.