CHAPTER 13 FORECASTING. Outline Forecasting and Choice of a Forecasting Methods Methods for Stationary Series: Simple and Weighted Moving Average Exponential smoothing TrendBased Methods Regression Double Exponential Smoothing: Holt’s Method A Method for Seasonality and Trend.
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CHAPTER 13FORECASTING
Outline
Forecasting
Production
Aggregate planning, inventory control, scheduling
Marketing
New product introduction, salesforce allocation, promotions
Finance
Plant/equipment investment, budgetary planning
Personnel
Workforce planning, hiring, layoff
Decisions Based on Forecasts
Forecasts are always wrong; so consider both expected value and a measure of forecast error
Longterm forecasts are less accurate than shortterm forecasts
Aggregate forecasts are more accurate than disaggregate forecasts
Forecasting
Components of Demand
Components of Demand
Qantity
Time
(a) Average: Data cluster about a horizontal line.
Components of Demand
Quantity
Time
(b) Linear trend: Data consistently increase or decrease.
Components of Demand
Year 1
Quantity

JFMAMJJASOND
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Components of Demand
Year 1
Quantity
Year 2

JFMAMJJASOND
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Components of Demand
Components of Demand
Quantity

123456
Years
(c) Cyclical movements: Gradual changes over extended periods of time.
Components of Demand
Components of Demand
Trend
Demand
Random
movement
Time
Demand
Trend with
seasonal pattern
Time
Snow Skiing
Seasonal
Long term growth trend
Demand for skiing products increased sharply after the Nagano Olympics
Measures of Forecast Error
Et = At  Ft
RSFE = Et
MAD =
MSE =
MAPE =
= MSE
Et 
n
Et2
n
[Et  (100)]/At
n
Choosing a MethodForecast Error
Absolute
Error AbsolutePercent
Month,Demand,Forecast,Error,Squared,Error,Error,
tAtFtEt Et2 Et(Et/At)(100)
1200225
2240220
3300285
4270290
5230250
6260240
7210250
8275240

Total
Choosing a MethodForecast Error
MSE = =
MAD = =
MAPE = =
Choosing a MethodForecast Error
Measures of Error
RSFE =
Running SumMean Absolute
of Forecast ErrorsDeviation
Method(RSFE  bias)(MAD)
Simple moving average
Threeweek (n = 3)23.117.1
Sixweek (n = 6)69.815.5
Weighted moving average
0.70, 0.20, 0.1014.018.4
Exponential smoothing
= 0.165.614.8
= 0.241.015.3
Choosing a MethodForecast Error
RSFE
MAD
Tracking signal =
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
 0.5 —
 1.0 —
 1.5 —
Control limit
Tracking signal
Control limit

0510152025
Observation number
Choosing a MethodTracking Signals
RSFE
MAD
Tracking signal =
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
 0.5 —
 1.0 —
 1.5 —
Out of control
Control limit
Tracking signal
Control limit

0510152025
Observation number
Choosing a MethodTracking Signals
Choosing a MethodTracking Signals
Problem 132: Historical demand for a product is:
MonthJanFebMarAprMayJun
Demand121115121615
a. Using a weighted moving average with weights of 0.60, 0.30, and 0.10, find the July forecast.
b. Using a simple threemonth moving average, find the July forecast.
c. Using single exponential smoothing with =0.20 and a June forecast =13, find the July forecast.
d. Using simple regression analysis, calculate the regression equation for the preceding demand data
e. Using regression equation in d, calculate the forecast in July
Problem 1315: In this problem, you are to test the validity of your forecasting model. Here are the forecasts for a model you have been using and the actual demands that occurred:
Week123456
Forecast8008509509501,000975
Actual9001,0001,0509009001,100
Compute MAD and tracking signal. Then decide whether the forecasting model you have been using is giving reasonable results.
Methods for Stationary Series
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Actual patient
arrivals

051015202530
Time Series MethodsSimple Moving Averages
Week
Time Series MethodsSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
WeekArrivals
1400
2380
3411
Patient arrivals
Actual patient
arrivals

051015202530
Week
Time Series MethodsSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
WeekArrivals
1400
2380
3411
Patient arrivals
F4 =
Actual patient
arrivals

051015202530
Week
Time Series MethodsSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
WeekArrivals
2380
3411
4415
Patient arrivals
F5 =
Actual patient
arrivals

051015202530
Week
450 —
430 —
410 —
390 —
370 —
3week MA
forecast
Patient arrivals
Actual patient
arrivals

051015202530
Week
Time Series MethodsSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
6week MA
forecast
3week MA
forecast
Patient arrivals
Actual patient
arrivals

051015202530
Time Series MethodsSimple Moving Averages
Week
Taco Bell determined that the demand for each 15minute interval
can be estimated from a 6week simple moving average of sales.
The forecast was used to determine the number of employees needed.
Assigned weights
t10.70
t20.20
t30.10
Time Series MethodsWeighted Moving Average
450 —
430 —
410 —
390 —
370 —
3week MA
forecast
Weighted Moving Average
Patient arrivals
F4 =
Actual patient
arrivals

051015202530
Week
Assigned weights
t10.70
t20.20
t30.10
Time Series MethodsWeighted Moving Average
450 —
430 —
410 —
390 —
370 —
3week MA
forecast
Weighted Moving Average
Patient arrivals
F5 =
Actual patient
arrivals

051015202530
Week
Time Series MethodsExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
Patient arrivals

051015202530
Week
Time Series MethodsExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
F3 = (400 + 380)/2=390
A3 = 411
Patient arrivals

051015202530
Week
Time Series MethodsExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
F3 = (400 + 380)/2=390
A3 = 411
Patient arrivals
F4 =

051015202530
Week
Time Series MethodsExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At + (1  )Ft  1
F4 =
A4 = 415
Patient arrivals
F5 =

051015202530
Week
450 —
430 —
410 —
390 —
370 —
Patient arrivals

051015202530
Week
Time Series MethodsExponential Smoothing
Comparison of Exponential Smoothing and Simple Moving Average
Problem 1320: Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize:
Month1 2 3 4 5 6 7 8 9 10 11 12
Actual demand 62 65 67 68 71 73 76 78 78 80 84 85
a. Calculate the threemonth SMA forecast for periods 412
b. Calculate the weighted threemonth MA using weights of 0.50, 0.30, and 0.20 for periods 412.
c. Calculate the single exponential smoothing forecast for periods 212 using an initial forecast, F1=61 and =0.30
d. Calculate the exponential smoothing with trend component forecast for periods 212 using T1=1.8,F1=60,=0.30,=0.30
e. Calculate MAD for the forecasts made by each technique in periods 412. Which forecasting method do you prefer?
TrendBased Methods
Turkeys have a longterm trend for increasing demand with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
Y
Dependent variable
X
Independent variable
Linear Regression
Regression
equation:
Y = a + bX
Y
Dependent variable
X
Independent variable
Linear Regression
Regression
equation:
Y = a + bX
Y
Actual
value
of Y
Dependent variable
Value of X used
to estimate Y
X
Independent variable
Linear Regression
Regression
equation:
Y = a + bX
Y
Estimate of
Y from
regression
equation
Actual
value
of Y
Dependent variable
Value of X used
to estimate Y
X
Independent variable
Linear Regression
Deviation,
or error
Regression
equation:
Y = a + bX
Y
Estimate of
Y from
regression
equation
{
Actual
value
of Y
Dependent variable
Value of X used
to estimate Y
X
Independent variable
Linear Regression
SalesAdvertising
Month(000 units)(000 $)
12642.5
21161.3
31651.4
41011.0
52092.0
Linear Regression
Sales, yAdvertising, x
Month(000 units)(000 $)
12642.5
21161.3
31651.4
41011.0
52092.0
xy  nxy
x2  n(x)2
a = y  bx
b =
Linear Regression
Sales, yAdvertising, x
Month(000 units)(000 $)xyx 2
12642.5
21161.3
31651.4
41011.0
52092.0
Total
y= x =
xy  nxy
x 2  nx 2
a = y  bx
b =
Linear Regression
300 —
250 —
200 —
150 —
100 —
50
Sales (000s)

1.01.52.02.5
b = 109.229
Y =
Sales, yAdvertising, x
Month(000 units)(000 $)xyx 2y 2
12642.5660.06.25
21161.3150.81.69
31651.4231.01.96
41011.0101.01.00
52092.0418.04.00
Total8558.21560.814.90
y = 171x = 1.64
nxy  x y
[nx 2 (x) 2][ny 2  (y) 2]
r =
Linear Regression
Sales, yAdvertising, x
Month(000 units)(000 $)xyx 2y 2
12642.5660.06.2569,696
21161.3150.81.6913,456
31651.4231.01.9627,225
41011.0101.01.0010,201
52092.0418.04.0043,681
Total8558.21560.814.90164,259
y= 171x = 1.64
r = 0.98 r 2 = 0.96
Linear Regression
Linear Regression
Forecast for Month 6:
Advertising expenditure = $1750
Y =
Time Series MethodsLinear Regression Analysis
80 —
70 —
60 —
50 —
40 —
30 —
Yn = a + bXn
where
Xn = Weekn
Patient arrivals

0123456789101112131415
Week
Time Series MethodsLinear Regression Analysis
80 —
70 —
60 —
50 —
40 —
30 —
Yn = a + bXn
where
Xn = Weekn
Patient arrivals

0123456789101112131415
Week
Time Series MethodsLinear Regression Analysis
Time Series MethodsLinear Regression Analysis
Time Series MethodsDouble Exponential Smoothing
A Comparison of Methods
90
85
Actual
3Mo MA
80
3Mo WMA
Demand
75
Exp Sm
70
Double Exp Sm
65
60
0
5
10
15
Months
Methods for Seasonal Series
QuarterYear 1Year 2Year 3Year 4
14570100100
2335370585725
35205908301160
4100170285215
Total1000120018002200
Average250300450550
Time Series MethodsSeasonal Influences
QuarterYear 1Year 2Year 3Year 4
14570100100
2335370585725
35205908301160
4100170285215
Total1000120018002200
Average250300450550
Actual Demand
Average Demand
Seasonal Index =
Time Series MethodsSeasonal Influences
QuarterYear 1Year 2Year 3Year 4
14570100100
2335370585725
35205908301160
4100170285215
Total1000120018002200
Average250300450550
Seasonal Index = =
Time Series MethodsSeasonal Influences
QuarterYear 1Year 2Year 3Year 4
145/250 = 70100100
2335370585725
35205908301160
4100170285215
Total1000120018002200
Average250300450550
Seasonal Index = =
Time Series MethodsSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18
2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32
3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11
4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39
Time Series MethodsSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18
2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32
3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11
4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39
QuarterAverage Seasonal Index
1(0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20
2
3
4
Time Series MethodsSeasonal Influences
Projected Annual Demand = 2600
Average Quarterly Demand = 2600/4 = 650
QuarterAverage Seasonal IndexForecast
1(0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20
2
3
4
Time Series MethodsSeasonal Influences
(a) Multiplicative influence
Demand

0245810121416
Period
Seasonal Influences
(b) Additive influence
Demand

0245810121416
Period
Seasonal Influences
Time Series MethodsSeasonal Influences with Trend
Step 1: Determine seasonal factors
Step 2: Deseasonalize the original data
Step 3: Develop a regression line on deaseasonalized data
Time Series MethodsSeasonal Influences with Trend
Step 4: Make projection using regression line
Step 5: Reseasonalize projection using seasonal factors
Problem 1321: Use regression analysis on deseasonalized demand to forecast demand in summer 2006, given the following historical demand data:
YearSeasonActual Demand
2004Spring205
Summer140
Fall375
Winter575
2005Spring475
Summer275
Fall685
Winter965
Reading and Exercises