1. Chapter 17 Forecasting Demand for Services
Learning Objectives
Demand characteristics
Overview of forecasting models
Common demand pattern for services
Linear regression to account for trend
Seasonality indices for seasonal demand
Combination of trend and seasonality
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2. Demand Characteristics
Time
(a) Trend
(d) Trend with seasonal pattern
(c) Seasonal pattern
(b) Cycle
Demand
Random movement

3. Forecasting Models Subjective Models Delphi Methods
Causal Models Regression Models
Time Series Models Moving Averages Exponential Smoothing
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4. Using Linear Regression to account for trend
b =
a = y - b x
where
n = number of periods
x = = mean of the x values
y = = mean of the y values
xy - nxy
x2 - nx2
x n
y
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for demand for period x

5. Least Squares Example x(PERIOD) y(DEMAND) xy x2 1 37 37 1 2 40 80 4

6. Least Squares Example (cont.)
y = = 46.42
b = = =1.72
a = y - bx
= (1.72)(6.5) = 35.2
(12)(6.5)(46.42)
(6.5)2
xy - nxy
x2 - nx2 78 12
557

7. Linear trend line y = 35.2 + 1.72x Forecast for period 13
= units
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Demand
Period

8. Seasonal Adjustments Repetitive increase/ decrease in demand
Use seasonal factor to adjust forecast
Si = seasonality index of period i
Ai(j) = demand in season i (in year j)
Note: The method used here is different from the book
Seasonal factor = Si =
 Ai
  Aij

9. Seasonal Adjustment (cont.)
Total
DEMAND (1000’S PER QUARTER)
YEAR Total
S1 = = = 0.28
 A1
  Aij
42.0
148.7
S2 = = = 0.20
 A2
29.5
S4 = = = 0.37
 A4
55.3
S3 = = = 0.15
 A3
21.9

10. Forecast to account for both Trend and Seasonality
Step 1: Calculate the seasonal index for each season.
Step 2: Use linear regression to forecast the total demand for the following year to account for trend. (In the previous slide example, use the year as dependent variable, and yearly demand as independent variable)
a = 40.97, b = (Note: 2005/6/7 are years 1/2/3)
F(2008) = (4) = 58.17
Step 3: Use the forecast total demand (obtained in Step 2) and multiply by the seasonal index to determine the forecast seasonal demand.
SF1 = (S1) (F2008) = (0.28)(58.17) = 16.28
SF2 = (S2) (F2008) = (0.20)(58.17) = 11.63
SF3 = (S3) (F2008) = (0.15)(58.17) = 8.73
SF4 = (S4) (F2008) = (0.37)(58.17) = 21.53