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.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
CHAPTER 13FORECASTING
Outline
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
Characteristics of ForecastsForecasting and a measure of forecast error
Components of Demand and a measure of forecast error
Components of Demand and a measure of forecast error
Qantity
Time
(a) Average: Data cluster about a horizontal line.
Components of Demand and a measure of forecast error
Quantity
Time
(b) Linear trend: Data consistently increase or decrease.
Components of Demand and a measure of forecast error
Year 1
Quantity
           
J F M A M J J A S O N D
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Components of Demand and a measure of forecast error
Year 1
Quantity
Year 2
           
J F M A M J J A S O N D
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Components of Demand and a measure of forecast error
Components of Demand and a measure of forecast error
Quantity
     
1 2 3 4 5 6
Years
(c) Cyclical movements: Gradual changes over extended periods of time.
Components of Demand and a measure of forecast error
Components of Demand and a measure of forecast error
Trend
Demand
Random
movement
Time
Demand
Trend with
seasonal pattern
Time
Snow Skiing and a measure of forecast error
Seasonal
Long term growth trend
Demand for skiing products increased sharply after the Nagano Olympics
Measures of Forecast Error and a measure of forecast error
Et = At  Ft
RSFE = Et
MAD =
MSE =
MAPE =
= MSE
Et 
n
Et2
n
[Et  (100)]/At
n
Absolute and a measure of forecast error
Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error,
tAtFtEt Et2 Et (Et/At)(100)
1 200 225
2 240 220
3 300 285
4 270 290
5 230 250
6 260 240
7 210 250
8 275 240

Total
MSE = = and a measure of forecast error
MAD = =
MAPE = =
Measures of Error
RSFE =
Running Sum Mean Absolute and a measure of forecast error
of Forecast Errors Deviation
Method (RSFE  bias) (MAD)
Simple moving average
Threeweek (n = 3) 23.1 17.1
Sixweek (n = 6) 69.8 15.5
Weighted moving average
0.70, 0.20, 0.10 14.0 18.4
Exponential smoothing
= 0.1 65.6 14.8
= 0.2 41.0 15.3
RSFE and a measure of forecast error
MAD
Tracking signal =
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
 0.5 —
 1.0 —
 1.5 —
Control limit
Tracking signal
Control limit
    
0 5 10 15 20 25
Observation number
RSFE and a measure of forecast error
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
    
0 5 10 15 20 25
Observation number
Choosing a Method and a measure of forecast errorTracking Signals
Problem 132: and a measure of forecast errorHistorical demand for a product is:
Month Jan Feb Mar Apr May Jun
Demand 12 11 15 12 16 15
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: and a measure of forecast errorIn 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:
Week 1 2 3 4 5 6
Forecast 800 850 950 950 1,000 975
Actual 900 1,000 1,050 900 900 1,100
Compute MAD and tracking signal. Then decide whether the forecasting model you have been using is giving reasonable results.
Methods for Stationary Series and a measure of forecast error
450 — and a measure of forecast error
430 —
410 —
390 —
370 —
Patient arrivals
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
1 400
2 380
3 411
Patient arrivals
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
1 400
2 380
3 411
Patient arrivals
F4 =
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
2 380
3 411
4 415
Patient arrivals
F5 =
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 — and a measure of forecast error
430 —
410 —
390 —
370 —
3week MA
forecast
Patient arrivals
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 — and a measure of forecast error
430 —
410 —
390 —
370 —
6week MA
forecast
3week MA
forecast
Patient arrivals
Actual patient
arrivals
     
0 5 10 15 20 25 30
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 interval
t1 0.70
t2 0.20
t3 0.10
450 —
430 —
410 —
390 —
370 —
3week MA
forecast
Weighted Moving Average
Patient arrivals
F4 =
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
Assigned weights interval
t1 0.70
t2 0.20
t3 0.10
450 —
430 —
410 —
390 —
370 —
3week MA
forecast
Weighted Moving Average
Patient arrivals
F5 =
Actual patient
arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
Patient arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
F3 = (400 + 380)/2=390
A3 = 411
Patient arrivals
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At1 + (1  )Ft  1
F3 = (400 + 380)/2=390
A3 = 411
Patient arrivals
F4 =
     
0 5 10 15 20 25 30
Week
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
= 0.10
Ft = At + (1  )Ft  1
F4 =
A4 = 415
Patient arrivals
F5 =
     
0 5 10 15 20 25 30
Week
450 — interval
430 —
410 —
390 —
370 —
Patient arrivals
     
0 5 10 15 20 25 30
Week
Comparison of Exponential Smoothing and Simple Moving Average
Problem 1320: AverageYour 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:
Month 1 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?
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 with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
Dependent variable
X
Independent variable
Regression with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
equation:
Y = a + bX
Y
Dependent variable
X
Independent variable
Regression with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
equation:
Y = a + bX
Y
Actual
value
of Y
Dependent variable
Value of X used
to estimate Y
X
Independent variable
Regression with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
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
Deviation, with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
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
Sales Advertising with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
Month (000 units) (000 $)
1 264 2.5
2 116 1.3
3 165 1.4
4 101 1.0
5 209 2.0
Sales, y Advertising, x with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
Month (000 units) (000 $)
1 264 2.5
2 116 1.3
3 165 1.4
4 101 1.0
5 209 2.0
xy  nxy
x2  n(x)2
a = y  bx
b =
Sales, with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. y Advertising, x
Month (000 units) (000 $) xyx 2
1 264 2.5
2 116 1.3
3 165 1.4
4 101 1.0
5 209 2.0
Total
y= x =
xy  nxy
x 2  nx 2
a = y  bx
b =
300 — with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
250 —
200 —
150 —
100 —
50
Sales (000s)
   
1.0 1.5 2.0 2.5
b = 109.229
Y =
Sales, with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. y Advertising, x
Month (000 units) (000 $) xyx 2y 2
1 264 2.5 660.0 6.25
2 116 1.3 150.8 1.69
3 165 1.4 231.0 1.96
4 101 1.0 101.0 1.00
5 209 2.0 418.0 4.00
Total 855 8.2 1560.8 14.90
y = 171 x = 1.64
nxy  x y
[nx 2 (x) 2][ny 2  (y) 2]
r =
Sales, with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. y Advertising, x
Month (000 units) (000 $) xyx 2y 2
1 264 2.5 660.0 6.25 69,696
2 116 1.3 150.8 1.69 13,456
3 165 1.4 231.0 1.96 27,225
4 101 1.0 101.0 1.00 10,201
5 209 2.0 418.0 4.00 43,681
Total 855 8.2 1560.8 14.90 164,259
y= 171 x = 1.64
r = 0.98 r 2 = 0.96
Linear Regression
Forecast for Month 6:
Advertising expenditure = $1750
Y =
80 —
70 —
60 —
50 —
40 —
30 —
Yn = a + bXn
where
Xn = Weekn
Patient arrivals
              
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Week
80 —
70 —
60 —
50 —
40 —
30 —
Yn = a + bXn
where
Xn = Weekn
Patient arrivals
              
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Week
Time Series Methods with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. Linear Regression Analysis
Time Series Methods with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. Linear Regression Analysis
Time Series Methods with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January. Double Exponential Smoothing
A Comparison of Methods with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
90
85
Actual
3Mo MA
80
3Mo WMA
Demand
75
Exp Sm
70
Double Exp Sm
65
60
0
5
10
15
Months
Quarter Year 1 Year 2 Year 3 Year 4 with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
1 45 70 100 100
2 335 370 585 725
3 520 590 830 1160
4 100 170 285 215
Total 1000 1200 1800 2200
Average 250 300 450 550
Quarter Year 1 Year 2 Year 3 Year 4 with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
1 45 70 100 100
2 335 370 585 725
3 520 590 830 1160
4 100 170 285 215
Total 1000 1200 1800 2200
Average 250 300 450 550
Actual Demand
Average Demand
Seasonal Index =
Quarter Year 1 Year 2 Year 3 Year 4 with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
1 45 70 100 100
2 335 370 585 725
3 520 590 830 1160
4 100 170 285 215
Total 1000 1200 1800 2200
Average 250 300 450 550
Seasonal Index = =
Quarter Year 1 Year 2 Year 3 Year 4 with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.
1 45/250 = 70 100 100
2 335 370 585 725
3 520 590 830 1160
4 100 170 285 215
Total 1000 1200 1800 2200
Average 250 300 450 550
Seasonal Index = =
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18
2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32
3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11
4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18
2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32
3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11
4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20
2
3
4
Projected Annual Demand = 2600 Year 3 Year 4
Average Quarterly Demand = 2600/4 = 650
Quarter Average Seasonal Index Forecast
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20
2
3
4
(a) Multiplicative influence Year 3 Year 4
Demand
               
0 2 4 5 8 10 12 14 16
Period
(b) Additive influence Year 3 Year 4
Demand
               
0 2 4 5 8 10 12 14 16
Period
Time Series Methods Year 3 Year 4Seasonal 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 Methods Year 3 Year 4Seasonal Influences with Trend
Step 4: Make projection using regression line
Step 5: Reseasonalize projection using seasonal factors
Problem 1321: Year 3 Year 4 Use regression analysis on deseasonalized demand to forecast demand in summer 2006, given the following historical demand data:
Year Season Actual Demand
2004 Spring 205
Summer 140
Fall 375
Winter 575
2005 Spring 475
Summer 275
Fall 685
Winter 965
Reading and Exercises Year 3 Year 4