Chapter 17Forecasting Demand for Services

Learning ObjectivesDemand characteristicsOverview of forecasting modelsCommon demand pattern for servicesLinear regression to account for trendSeasonality indices for seasonal demandCombination of trend and seasonality

17-1

Demand Characteristics

TimeTime(a) Trend(a) Trend

TimeTime(d) Trend with seasonal pattern(d) Trend with seasonal pattern

TimeTime(c) Seasonal pattern(c) Seasonal pattern

TimeTime(b) Cycle(b) Cycle

Dem

and

Dem

and

Dem

and

Dem

and

Dem

and

Dem

and

Dem

and

Dem

and

Random Random movemenmovementt

Forecasting Models

Subjective ModelsDelphi Methods

Causal ModelsRegression Models

Time Series ModelsMoving AveragesExponential Smoothing

17-3

yy = = aa + + bxbx

wherewherea a = intercept= interceptb b = slope of the line= slope of the linex x = time period= time periody y = forecast for = forecast for demand for period demand for period xx

Using Linear Regression to account for trend

b =

a = y - b x

wheren = number of periods

x = = mean of the x values

y = = mean of the y values

xy - nxy

x2 - nx2

xn

yn

Least Squares Examplexx(PERIOD)(PERIOD) yy(DEMAND)(DEMAND) xyxy xx22

11 3737 3737 1122 4040 8080 4433 4141 123123 9944 3737 148148 161655 4545 225225 252566 5050 300300 363677 4343 301301 494988 4747 376376 646499 5656 504504 8181

1010 5252 520520 1001001111 5555 605605 1211211212 5454 648648 144144

7878 557557 38673867 650650

x = = 6.5

y = = 46.42

b = = =1.72

a = y - bx= 46.42 - (1.72)(6.5) = 35.2

3867 - (12)(6.5)(46.42)650 - 12(6.5)2

xy - nxyx2 - nx2

781255712

Least Squares Example (cont.)

Linear trend line y = 35.2 + 1.72x

Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units

70 70 –

60 60 –

50 50 –

40 40 –

30 30 –

20 20 –

1010 –

0 0 –

| | | | | | | | | | | | |11 22 33 44 55 66 77 88 99 1010 1111 1212 1313

ActualActual

Dem

and

Dem

and

PeriodPeriod

Linear trend lineLinear trend line

Seasonal Adjustments

Repetitive increase/ decrease in demandRepetitive increase/ decrease in demand Use seasonal factor to adjust forecastUse seasonal factor to adjust forecast SSii = seasonality index of period i = seasonality index of period i

AAi(j)i(j) = demand in season i (in year j) = demand in season i (in year j)

Note: The method used here is different from Note: The method used here is different from the bookthe book

Seasonal factor = Seasonal factor = SSii = = AAii

AAijij

Seasonal Adjustment (cont.)

2005 12.62005 12.6 8.68.6 6.36.3 17.517.5 45.045.0

2006 14.12006 14.1 10.310.3 7.57.5 18.218.2 50.150.1

2007 15.32007 15.3 10.610.6 8.18.1 19.619.6 53.653.6

Total 42.0Total 42.0 29.529.5 21.921.9 55.355.3 148.7148.7

DEMAND (1000’S PER QUARTER)DEMAND (1000’S PER QUARTER)

YEARYEAR 11 22 33 44 TotalTotal

SS11 = = = 0.28 = = = 0.28 AA11

AAijij

42.042.0148.7148.7

SS22 = = = 0.20 = = = 0.20 AA22

AAijij

29.529.5148.7148.7

SS44 = = = 0.37 = = = 0.37 AA44

AAijij

55.355.3148.7148.7

SS33 = = = 0.15 = = = 0.15 AA33

AAijij

21.921.9148.7148.7

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 = 4.30 (Note: 2005/6/7 are years a = 40.97, b = 4.30 (Note: 2005/6/7 are years 1/2/3)1/2/3)

F(2008)F(2008) = 40.97 + 4.30(4) = 58.17= 40.97 + 4.30(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) = 16.28SF1 = (S1) (F2008) = (0.28)(58.17) = 16.28 SF2 = (S2) (F2008) = (0.20)(58.17) = 11.63SF2 = (S2) (F2008) = (0.20)(58.17) = 11.63SF3 = (S3) (F2008) = (0.15)(58.17) = 8.73SF3 = (S3) (F2008) = (0.15)(58.17) = 8.73SF4 = (S4) (F2008) = (0.37)(58.17) = 21.53SF4 = (S4) (F2008) = (0.37)(58.17) = 21.53