forecasting

forecasting - Transcript

Forecasting Forecasting

Forecasting Forecasting
Predicting the Future Qualitative forecast methods


subjective

Quantitative forecast Quantitative methods methods


based on mathematical based formulas formulas

Qualitative Methods
Executive Judgment

Grass Roots

Historical analogy

Qualitative Methods

Market Research

Delphi Method

Panel Consensus

Delphi Method Delphi
l Choose the experts to participate representing a variety of l knowledgeable people in different areas knowledgeable 2 Through a questionnaire or E mail obtain forecasts and 2 any premises or qualifications for the forecasts from all participants participants 3 Summarize the results and redistribute them to the 3 participants along with appropriate new questions 4 Summarize again refining forecasts and conditions and again develop new questions again 5 Repeat Step 4 as necessary and distribute the final results 5 to all participants to

Forecasting and Supply Chain Management
Accurate forecasting determines how much Accurate inventory a company must keep at various points along its supply chain along Continuous replenishment


supplier and customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery quick response JIT just in time VMI vendor managed inventory stockless inventory

Variations of continuous replenishment


Forecasting and TQM
Accurate forecasting customer demand is a key to providing good quality service Continuous replenishment and JIT complement TQM




eliminates the need for buffer inventory which in turn reduces both waste and inventory costs a primary goal of TQM smoothes process flow with no defective items meets expectations about on time delivery which is perceived as good quality service

Types of Forecasting Methods Types
Depend on


time frame demand behavior causes of behavior

Time Series Analysis Time
Time series forecasting models try to Time predict the future based on past data predict You can pick models based on 1 Time horizon to forecast 2 Data availability 3 Accuracy required 4 Size of forecasting budget 5 Availability of qualified personnel 5

Time Frame Time
Indicates how far into the future is Indicates forecast forecast


Short to mid range forecast
typically

encompasses the immediate future daily up to two years


Long range forecast
usually usually

encompasses a period of time longer than two years than

Demand Behavior Demand
Trend


a gradual long term up or down movement of gradual demand demand movements in demand that do not follow a pattern an up and down repetitive movement in demand an up and down repetitive movement in demand an occurring periodically occurring

Random variations


Cycle


Seasonal pattern


Forms of Forecast Movement
Demand Demand Random Random movement movement Time Time a Trend Time b Cycle Time c Seasonal pattern Demand Time d Trend with seasonal pattern

Demand

Forecasting Methods
Qualitative


use management judgment expertise and opinion to use predict future demand predict statistical techniques that use historical demand data statistical to predict future demand to attempt to develop a mathematical relationship attempt between demand and factors that cause its behavior between

Time series


Regression methods


Qualitative Methods Qualitative
Management marketing purchasing and engineering are sources for internal qualitative forecasts Delphi method


involves soliciting forecasts about technological advances from experts

Forecasting Process Forecasting
1 Identify the purpose of forecast 2 Collect historical data 3 Plot data and identify patterns 6 Check forecast accuracy with one or more measures 7 Is accuracy of forecast acceptable 5 Develop compute forecast for period of historical data 4 Select a forecast model that seems appropriate for data

No

8b Select new forecast model or adjust parameters of existing model

Yes
8a Forecast over planning horizon 9 Adjust forecast based on additional qualitative information and insight 10 Monitor results and measure forecast accuracy

Time Series Time
Assume that what has occurred in the past will continue to occur in the future Relate the forecast to only one factor time Include


moving average exponential smoothing linear trend line

Moving Average
Naive forecast Naive forecast


demand of the current period is used as next demand period s forecast period s stable demand with no pronounced stable behavioral patterns behavioral weights are assigned to most recent data

Simple moving average


Weighted moving average


Moving Average Moving Na ve Approach
MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 FORECAST 120 90 100 75 110 50 75 130 110 90

Simple Moving Average
n

i 1 Di

MAn MA
where n Di



n

number of periods number in the moving average average demand in period i demand

3 month Simple Moving Average 3 month
ORDERS MONTH Jan MONTH MONTH Feb Mar Apr May June July PER PER 120 90 100 75 110 50 75 MOVING MOVING AVERAGE AVERAGE 103 3 88 3 95 0 78 3 78 3 85 0 105 0 110 0

i 1



3

Di

MA3

3 90 110 130 3

110 orders for Nov

5 month Simple Moving Average 5 month
ORDERS MONTH Jan MONTH MONTH Feb Mar Apr May June July PER PER 120 90 100 75 110 50 75 MOVING MOVING AVERAGE AVERAGE 99 0 99 0 85 0 82 0 88 0 95 0 91 0

i 1



5

Di

MA5

5

90 110 130 75 50 5 91 orders for Nov

Smoothing Effects Smoothing
150 150 125 125 100 100 Orders 75 75 50 50 25 25 0 Jan Feb Mar Actual Apr May June July Month Aug Sept Oct Nov 3 month 5 month

Weighted Moving Average Weighted
Adjusts Adjusts moving average method to more closely reflect data fluctuations fluctuations
WMAn Wi Di i 1
i 1

where

Wi the weight for period i
between 0 and 100 percent percent

W 1 00 1 00
i

Weighted Moving Average Example Weighted
MONTH MONTH August September October November Forecast WEIGHT 17 17 33 33 50 50 DATA DATA 130 110 90

WMA3 i 1 Wi Di

3

0 50 90 0 33 110 0 17 130 103 4 orders

Exponential Smoothing



Averaging method Averaging Weights most recent data more strongly Reacts more to recent changes Widely used accurate method

Exponential Smoothing cont
Ft 1 Dt 1 Ft
where Ft 1 forecast for next period 1 Dt actual demand for present period Ft previously determined forecast previously for present period for weighting factor smoothing constant

Effect of Smoothing Constant Effect
0 0 1 0 0 0 If 0 20 then Ft 1 0 20 Dt 0 80 Ft If 0 20 If 0 then Ft 1 0 Dt 1 Ft 0 Ft If
Forecast does not reflect recent data Forecast

If 1 then Ft 1 1 Dt 0 Ft Dt If
Forecast based only on most recent data Forecast

Exponential Smoothing 0 30
PERIOD DEMAND 1 2 3 4 5 6 7 MONTH Jan Feb Mar Apr May May Jun Jul Jul 37 40 41 37 45 45 50 43 43 F2 D1 1 F1 0 30 37 0 70 37 37 F3 D2 1 F2 0 30 40 0 70 37 37 9 F13 D12 1 F12 0 30 54 0 70 50 84 51 79

Exponential Smoothing Exponential cont cont
PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 13 MONTH Jan Feb Mar Apr May May Jun Jul Jul Aug Aug Sep Sep Oct Nov Dec Dec Jan DEMAND 37 40 41 37 45 45 50 43 43 47 47 56 56 52 55 54 54 FORECAST Ft 1 0 3 0 5 37 00 37 90 38 83 38 28 40 29 43 20 43 14 44 30 47 81 49 06 50 84 51 79 37 00 38 50 39 75 38 37 41 68 45 84 44 42 45 71 50 85 51 42 53 21 53 61

Exponential Smoothing cont
70 60 60 50 50 40 40 Orders 30 30 20 20 10 0 1 2 3 4 5 6 Month 7 8 9 10 11 12 13 0 30 0 30 Actual 0 50 0 50

Adjusted Exponential Smoothing
AFt 1 Ft 1 Tt 1 AF 1 1 1
where T an exponentially smoothed trend factor Tt 1 Ft 1 Ft 1 Tt 1 1 where Tt the last period trend factor the a smoothing constant for trend smoothing

Adjusted Exponential Smoothing 0 30 Smoothing
PERIOD DEMAND 1 2 3 4 5 6 MONTH Jan Feb Mar Apr May May Jun 37 40 41 37 45 45 50

T3

F3 F2 1 T2 1 0 30 38 5 37 0 0 70 0 0 45

AF3 F3 T3 38 5 0 45 38 5 38 95 T13 F13 F12 1 T12 1 13 0 30 53 61 53 21 0 70 1 77 1 36 AF13 F13 T13 53 61 1 36 54 96 53 61 13

Adjusted Exponential Smoothing Example Example
PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 13 MONTH Jan Feb Mar Apr May May Jun Jul Jul Aug Aug Sep Sep Oct Nov Dec Dec Jan DEMAND 37 40 41 37 45 45 50 43 43 47 47 56 56 52 55 54 54 FORECAST Ft 1 37 00 37 00 38 50 39 75 38 37 38 37 45 84 44 42 45 71 50 85 51 42 53 21 53 61 TREND Tt 1 0 00 0 45 0 69 0 07 0 07 1 97 0 95 1 05 2 28 1 76 1 77 1 36 ADJUSTED FORECAST AFt 1 37 00 38 95 40 44 38 44 38 44 47 82 45 37 46 76 58 13 53 19 54 98 54 96

Adjusted Exponential Smoothing Forecasts Forecasts
70 70 60 60 50 50 40 40 Demand 30 30 20 20 10 0 1 2 3 4 5 6 7 Period 8 9 10 11 12 13 Forecast 0 50 Adjusted forecast 0 30 Actual

Linear Trend Line
y a bx bx
where where a intercept intercept b slope of the line slope x time period time y forecast for demand for period x xy nxy b x2 nx2 a y bx where n number of periods x x mean of the x values n y y n mean of the y values

Least Squares Example Least
x PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 78 y DEMAND 73 40 41 37 45 50 43 47 56 52 55 54 557 xy 37 80 123 148 225 300 301 376 504 520 605 648 3867 x2 1 4 9 16 25 36 49 64 81 100 121 144 650

Least Squares Example Least cont cont
78 6 5 12 557 y 46 42 12 xy nxy 3867 12 6 5 46 42 b 1 72 2 2 2 x nx 650 12 6 5 x a y bx 46 42 1 72 6 5 35 2

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 Actual 50 50 Demand 40 40 30 30 20 20 10 0 1 2 3 4 5 6 7 Period 8 9 10 11 12 13 Linear trend line

Seasonal Adjustments Seasonal
Repetitive increase decrease in demand Use seasonal factor to adjust forecast Di D

Seasonal factor Si Seasonal

Seasonal Adjustment cont Seasonal
YEAR 2002 2003 2004 Total DEMAND 1000 S PER QUARTER 1 2 3 4 Total 12 6 14 1 15 3 42 0 8 6 10 3 10 6 29 5 6 3 7 5 8 1 21 9 17 5 18 2 19 6 55 3 45 0 50 1 53 6 148 7

42 0 S1 0 28 D 148 7 29 5 S2 0 20 D 148 7 D2

D1

S3

D3 D D4



21 9 0 15 148 7

55 3 S4 0 37 D 148 7

Seasonal Adjustment cont Seasonal

For 2005 y 40 97 4 30x 40 97 4 30 4 58 17 40 97 SF1 S1 F5 0 28 58 17 16 28 SF2 S2 F5 0 20 58 17 11 63 SF SF3 S3 F5 0 15 58 17 8 73 SF4 S4 F5 0 37 58 17 21 53

Forecast Accuracy Forecast
Forecast error


difference between forecast and actual demand MAD


mean absolute deviation mean absolute percent deviation



MAPD




Cumulative error Average error or bias

Mean Absolute Deviation MAD MAD
Dt Ft MAD n
where t period number Dt demand in period t demand Ft forecast for period t forecast n total number of periods absolute value absolute

MAD Example MAD
PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 DEMAND Dt DEMAND 37 40 41 37 MAD 45 50 43 47 56 52 55 54 557 Ft 0 3 Dt F t 3 00 3 10 1 83 6 72 9 69 0 20 3 86 11 70 4 19 5 94 3 15 49 31 Dt Ft 3 00 3 10 1 83 6 72 9 69 0 20 3 86 11 70 4 19 5 94 3 15 53 39 37 00 37 00 D37 90 t t F 38 83 38 28 n 40 29 53 39 43 20 43 14 11 44 30 4 85 47 81 49 06 50 84



Other Accuracy Measures Other
Mean absolute percent deviation MAPD MAPD Cumulative error E et Average error E

Dt Ft Dt

et
n

Comparison of Forecasts Comparison

FORECAST Exponential smoothing 0 30 0 30 Exponential smoothing 0 50 0 50 Adjusted exponential smoothing 0 50 0 30 0 30 Linear trend line

MAD 4 85 4 04 3 81 2 29

MAPD 9 6 8 5 7 5 4 9

E 49 31 33 21 21 14

E 4 48 3 02 1 92

Forecast Control Forecast
Tracking signal


monitors the forecast to see if it is biased high or low Dt Ft E MAD

Tracking signal MAD 1 MAD 0 8 Control limits of 2 to 5 MADs are used most frequently

Tracking Signal Values Tracking
PERIOD DEMAND Dt FORECAST Ft ERROR Dt Ft E Dt Ft MAD TRACKING SIGNAL

1 2 3 4 5 6 7 8 9 10 11 12

37 40 41 37 45 50 43 47 56 52 55 54

37 00 37 00 3 00 3 00 37 90 3 10 6 10 38 83 1 83 4 27 38 28 6 72 10 99 Tracking signal for period 3 40 29 9 69 20 68 43 20 0 20 6 10 20 48 43 14 TS3 3 86 24 34 2 00 3 05 36 04 44 30 11 70 47 81 4 19 40 23 49 06 5 94 46 17 50 84 3 15 49 32

3 00 3 05 2 64 3 66 4 87 4 09 4 06 5 01 4 92 5 02 4 85

1 00 2 00 1 62 3 00 4 25 5 01 6 00 7 19 8 18 9 20 10 17

Tracking Signal Plot Tracking
3 Tracking signal MAD 2 1 0 1 2 3 Linear trend line Exponential smoothing 0 30

0

1

2

3

4

5

6 Period

7

8

9

10

11

12

Statistical Control Charts Statistical
Using we can calculate Using statistical control limits for the forecast error forecast Control limits are typically set at Control 3

Statistical Control Charts Statistical
2 Dt Ft 2 n 1

Statistical Control Charts Statistical
18 39 18 39 12 24 12 24 6 12 6 12 Errors 0 6 12 6 12 UCL 3

12 24 12 24 18 39 18 39 LCL 3 0 1 2 3 4 5 6 Period 7 8 9 10 11 12

Regression Methods
Linear regression


a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation a measure of the strength of the relationship between independent and dependent variables

Correlation


Linear Regression Linear
y a bx bx
a y bx xy xy b nxy nxy where x2 nx2 nx a intercept b slope of the line slope x x mean of the x data mean n y y n mean of the y data mean

Linear Regression Example Linear
x WINS 4 6 6 8 6 7 5 7 49 y ATTENDANCE ATTENDANCE 36 3 40 1 41 2 53 0 44 0 45 6 39 0 47 5 346 7 xy xy 145 2 240 6 247 2 424 0 264 0 319 2 195 0 332 5 2167 7 x2 16 36 36 64 36 49 25 49 311

Linear Regression Example cont Linear
49 6 125 8 346 9 y 43 36 8 x

xy nxy2 b x2 nx2
2 167 7 8 6 125 43 36 311 8 6 125 2 4 06 a y bx 43 36 4 06 6 125 18 46

Linear Regression Example cont
Regression equation y 18 46 4 06x
60 000 60 000 50 000 50 000 40 000 40 000 Attendance y 30 000 30 000 20 000 20 000 10 000 10 000

Attendance forecast for 7 wins y 18 46 4 06 7 46 88 or 46 880

Linear regression line Linear y 18 46 4 06x

0

1

2

3

4

5 6 Wins x

7

8

9

10

Simple Linear Regression Model Simple
The simple linear regression The simple linear regression model seeks to fit a line model seeks to fit a line tthroughvarious data over hrough various data over ttime ime
Y

a
012345 x Time Is the linear regression model Is the linear regression model

Yt a bx

Yt is the regressed forecast value or dependent variable in the model a is the intercept value of the the regression line and b is similar to the slope of the regression line However since it is calculated with the variability of the data in mind its formulation is not as straight forward as our usual notion of slope

Simple Linear Regression Problem Data Simple
Question Given the data below what is the simple linear Question Given the data below what is the simple linear rregressionmodel that can be used to predict sales in future egression model that can be used to predict sales in future weeks weeks

Week 1 2 3 4 5

Sales 150 157 162 166 177

59

Answer First using the linear regression formulas we Answer First using the linear regression formulas we can compute a and b can compute a and b

W eek Week Week Sales Week Sales 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 3 55 162 4 2499 Average Sum Average Sum xy n y x 2499 5 162 4 3 63 6 3 b 55 5 9 10 x 2 n x 2
a y b x 162 4 6 3 3 143 5

60

The resulting regression model is

Yt 143 5 6 3x

Now if we plot the regression generated forecasts against the actual sales we obtain the following chart 180 175 170 165 Sales 160 155 Forecast 150 145 140 135 1 2 3 4 5 Perio d Sales

Correlation and Coefficient of Determination Determination
Correlation r Correlation
Measure of strength of relationship Varies between 1 00 and 1 00

Coefficient of determination r2 Coefficient
Percentage of variation in dependent Percentage variable resulting from changes in the independent variable independent

Computing Correlation Computing
r n xy x y xy n x2 x 2 n y2 y 2 8 2 167 7 49 346 9 8 311 49 2 8 15 224 7 346 9 2 r 0 947 Coefficient of determination Coefficient r2 0 947 2 0 897 0 947 0 897

r

Multiple Regression Multiple
Study the relationship of demand to two or Study more independent variables more
y 0 1x1 2x2 kxk where 0 the intercept 1 k parameters for the parameters independent variables independent x1 xk independent variables

Question Bowl Question
Which of the following is a classification of a Which basic type of forecasting basic a Transportation method b Simulation c Linear programming d All of the above e None of the above Answer b Simulation There are four types including Qualitative Time Series Analysis Causal Relationships and Simulation

Question Bowl Question
Which of the following is an example of a Which Qualitative type of forecasting technique a b c d e or model or Grass roots Market research Panel consensus All of the above None of the above

Answer d All of the above Also includes Historical Analogy and Delphi Method

Question Bowl Question
Which of the following is an example of a Which Time Series Analysis type of forecasting technique or model technique a Simulation b Exponential smoothing c Panel consensus d All of the above e None of the above
Answer b Exponential smoothing Also includes Simple Moving Average Weighted Moving Average Regression Analysis Box Jenkins Shiskin Time Series and Trend Projections

Question Bowl Question
Which of the following is a reason why a Which firm should choose a particular forecasting model model a Time horizon to forecast b Data availability c Accuracy required d Size of forecasting budget e All of the above Answer e All of the above Also should include availability of qualified personnel

Question Bowl Question
Which of the following are ways to Which choose weights in a Weighted Moving a b c d e Average forecasting model Average Cost Experience Trial and error Only b and c above None of the above

Answer d Only b and c above

Question Bowl Question
Which of the following are reasons why Which the Exponential Smoothing model has been a well accepted forecasting a b c d e methodology methodology It is accurate It is easy to use Computer storage requirements are small All of the above None of the above

Answer d All of the above

Question Bowl Question
The value for alpha or must be between The which of the following when used in an Exponential Smoothing model Exponential 1 to 10 1 to 2 0 to 1 1 to 1 Any number at all

a b c d e

Answer c 0 to 1

Question Bowl Question
Which of the following are sources of error in Which forecasts forecasts a Bias b Random c Employing the wrong trend line d All of the above e None of the above

Answer d All of the above

Question Bowl Question
Which of the following would be the Which best MAD values in an analysis of the accuracy of a forecasting model accuracy a 1000 b 100 c 10 d 1 e 0

Answer e 0

Question Bowl Question
If a Least Squares model is Y 25 5x and x is If equal to 10 what is the forecast value using this model this a 100 b 75 c 50 d 25 e None of the above

Answer b 75 Y 25 5 10 75