Forecasting Supply Chain Requirements

Forecasting Supply Chain Requirements

Dr.Burcu Ozcam

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The Importance of Forecasting  Governments forecast unemployment, interest rates, and expected revenues from income taxes for policy purposes  Marketing executives forecast demand, sales, and consumer preferences for strategic planning  College administrators forecast enrollments to plan for facilities and for faculty recruitment  Retail stores forecast demand to control inventory levels, hire employees and provide training Dr.Burcu Ozcam

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What’s Forecasted in the Supply Chain?

•Demand, sales or requirements •Purchase prices •Replenishment and delivery lead times CR (2004) Prentice Hall, Inc. Dr.Burcu Ozcam

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Some Forecasting Method Choices •Historical projection Moving average Exponential smoothing •Causal or associative Regression analysis •Qualitative Surveys Expert systems or rule-based •Collaborative

Dr.Burcu Ozcam

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Forecasting  We focus on using historical data for forecasting demand  This should not diminish the importance of other sources of information and common sense  Information consists of 1. Historical data on our time series 2. Insight/knowledge and common sense

 Don’t confuse information with intuition  Lets try a case study. Forecast a real time series from scratch using intuition! Dr.Burcu Ozcam

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Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800

We’ll guess same as last month

600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Month

Dr.Burcu Ozcam

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Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

We’ll guess same as last month plus a little more for a possible trend

800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

This is easy, who needs forecasting

800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Continue with our successful method: guess the same as last month plus a little more for a possible trend

800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Definitely looks like a trend

800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Trend might be a tad steeper than I thought

800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Opps

800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Momentary deviation, trend will continue

800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

See, I told you this was easy!

800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

Trend will continue

1200 1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Opps, another momentary fluctuation:

800 600 400 Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Trend should continue

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Oh oh!

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200

Sales has leveled off: Lets average last few points

1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200

Oh oh, maybe things are going down hill

1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200

Let’s be conservative and Assume a negative trend

1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200

Thank goodness, we are still basically level

1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200

We’ll guess same as last month

1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

This stuff is easy

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

We have for sure leveled off

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800

Big trouble!!! Chief forecaster Smith and CEO Smothers fired!

1600

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

New chief forecaster points out the obvious trend

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800 1600

Remarkable turnaround in sales. New CEO Smithers given credit

Sales ($1000)

1400 1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

Still looks like a trend to me

1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

Maybe not!

1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

Level except for anomaly

1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

Have things turned around?

1200 1000 800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400

I’ll hedge my bets

1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000

Things have turned around. Perhaps Smithers truly is a genius

1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800

Trend up!

1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800

Not bad!

1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800

Revise trend a tad

1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000

Smithers makes cover of Fortune

1800 1600

Sales ($1000)

1400 1200 1000 800 600

Smithers

400

Smothers

200

Monthly Sales Forecast

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000

This is easy!!

1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800

No big deal, trend continues

1600

Sales ($1000)

1400 1200 1000 800

(in an unrelated matter Smithers cashes out stock options)

600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Heads will surely roll soon

800 600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000

Let’s be cautiously optimistic

800 600 400

Monthly Sales Forecast

200 0

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Month

Monthly Sales and Forecast 2000 1800

Smithers called before board

1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000

Perhaps we over reacted

1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800

We will guess level

600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800

Back to normal!

600 400

Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000 1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

Monthly Sales and Forecast 2000

Smithers fired!

1800 1600

Sales ($1000)

1400 1200 1000 800 600 400 Monthly Sales Forecast

200 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dr.Burcu Ozcam

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Month

What have we learned?  Our Actual sales appears to be a great leading indicator of our forecast • It is supposed to work the other way around!!!!

 If we add up the (absolute value of) our forecast errors, we get 226.2  If we had simply guessed “same as last month” we get 175.1  Our intuition (ability to recognize a pattern) was poor given almost no information or data. Never-the-less we saw patterns.  For monthly data we can be tempted to “over think” forecasting.  Now some additional information: • Source of data is monthly sales of Australian Red Wine • We also have a few years of data LOG301 Dr.Burcu Ozcam

M onthly S ales of A us tralian Red W ine 3500

clear seasonal behavior clear upward trend increase in amplitude

3000

Sales($1000)

2500 2000 1500 1000 500

Dr.Burcu Ozcam

M o n th

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141

134

127

120

113

106

99

92

85

78

71

64

57

50

43

36

29

22

15

8

1

0

Value of Data  Given data, we can forecast this series quite accurately.  This assumes stable behavior  Recommend at least 4 - 5 seasons of data.  Monthly demand thus prefers 4 to 5 years of data  With 2 years of data, we are essentially forecasting on the basis of two points if there is seasonal behavior

Dr.Burcu Ozcam

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Laws of forecasting 1.We assume the future will behave like the past • In the real world, the future often does not behave like the past.

1. Even given that the future behaves like the past, there is a limit to how accurate forecasts can be (or nothing can be predicted with complete accuracy) • The key issue is: How close will the forecast be to the actual value? • It is crucial to attempt to quantify the expected accuracy of a forecast

1. The further into the future you attempt to forecast, the greater will be the forecast error. • Major decisions are often based on long term forecasts. e.g. building a new plant • Considering risk is even more important in these cases

1. Decisions will be based on the forecast (Otherwise there is no need to forecast!) • That is: forecasts have inherent error, thus the decisions based on forecasts have inherent risk

Dr.Burcu Ozcam

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P ast D ata and Future Fore casts 20 15

Now

10

Demand

5 0 -5

Future forecast

Past Data

-10 -15

Dr.Burcu Ozcam

P e rio d

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73

69

65

61

57

53

49

45

41

37

33

29

25

21

17

13

9

5

1

-20

Fore casts with 50% P re diction Inte rv als 20 15 10

Demand

5 0 -5 -10 -15

Dr.Burcu Ozcam

P e rio d

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73

69

65

61

57

53

49

45

41

37

33

29

25

21

17

13

9

5

1

-20

Fore casts with 95% P re diction Inte rv als 20 15 10

Demand

5 0 -5 -10 -15

Dr.Burcu Ozcam

P e rio d

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73

69

65

61

57

53

49

45

41

37

33

29

25

21

17

13

9

5

1

-20

Time-Series Data  Numerical data obtained at regular time intervals  The time intervals can be annually, quarterly, daily, hourly, etc.  Example:

Dr.Burcu Ozcam

Year:

1999 2000 2001 2002 2003

Sales:

75.3 74.2 78.5 79.7 80.2

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Time Series Plot A time-series plot is a two-dimensional plot of time series data  the vertical axis measures the variable of interest

Dr.Burcu Ozcam

Year

2001

1999

1997

1995

1993

1991

1989

1987

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1985

1983

1981

1979

1977

16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 1975

Inflation Rate (%)

 the horizontal axis corresponds to the time periods

U.S. Inflation Rate

Time-Series Components Time-Series Trend Component

Dr.Burcu Ozcam

Seasonal Component

Cyclical Component

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Random Component

Trend Component  Long-run increase or decrease over time (overall upward or downward movement)

 Data taken over a long period of time Sales

Dr.Burcu Ozcam

U

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nd e r t d r pwa

Time

Trend Component

(continued)

 Trend can be upward or downward  Trend can be linear or non-linear

Sales

Sales

Time Downward linear trend Dr.Burcu Ozcam

Time Upward nonlinear trend LOG301

Seasonal Component  Short-term regular wave-like patterns  Observed within 1 year  Often monthly or quarterly Sales Summer Winter Fall

Spring

Time (Quarterly) Dr.Burcu Ozcam

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Cyclical Component  Long-term wave-like patterns  Regularly occur but may vary in length  Often measured peak to peak or trough to trough 1 Cycle Sales

Dr.Burcu Ozcam

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Year

Random Component  Unpredictable, random, “residual” fluctuations  Due to random variations of • Nature • Accidents or unusual events

 “Noise” in the time series

Dr.Burcu Ozcam

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Trend-Based Forecasting  Estimate a trend line using regression analysis

Year

Time Period (t)

1999 2000 2001 2002 2003 2004

1 2 3 4 5 6

Dr.Burcu Ozcam

Sales (y) 20 40 30 50 70 65

 Use time (t) as the independent variable:

yˆ = b0 + b1t

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Trend-Based Forecasting  The linear trend model is: Sales (y)

1999 2000 2001 2002 2003 2004

1 2 3 4 5 6

20 40 30 50 70 65

yˆ = 12.333 + 9.5714 t Sales trend

sales

Year

Time Period (t)

80 70 60 50 40 30 20 10 0 0

Dr.Burcu Ozcam

1

2 LOG301

3

4

Year

5

6

Trend-Based Forecasting

1999 2000 2001 2002 2003 2004 2005

1 2 3 4 5 6 7

20 40 30 50 70 65 ??

yˆ = 12.333 + 9.5714 (7) = 79.33Sales

sales

Time Year Period (t) Sales (y)

 Forecast for time period 7:

80 70 60 50 40 30 20 10 0 0

Dr.Burcu Ozcam

1

2 LOG301

3

4

Year

5

6

7

Comparing Forecast Values to Actual Data  The forecast error or residual is the difference between the actual value in time t and the forecast value in time t:  Error in time t:

e t = y t − Ft

Dr.Burcu Ozcam

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Two common Measures of Fit  Measures of fit are used to gauge how well the forecasts match the actual values MSE (mean squared error) • Average squared difference between yt and Ft

MAD (mean absolute deviation) • Average absolute value of difference between yt and Ft • Less sensitive to extreme values

Dr.Burcu Ozcam

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MSE vs. MAD Mean Absolute Deviation

Mean Square Error

(y ∑ MSE =

t

− Ft )

n

2

|y ∑ MAD =

n

where: yt = Actual value at time t Ft = Predicted value at time t n = Number of time periods Dr.Burcu Ozcam

t

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− Ft |

Moving Averages  Used for smoothing  Series of arithmetic means over time  Result dependent upon choice of L (length of period for computing means)  To smooth out seasonal variation, L should be equal to the number of seasons • For quarterly data, L = 4 • For monthly data, L = 12

Dr.Burcu Ozcam

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Moving Averages

(continued)

 Example: Four-quarter moving average • First average:

Q1 + Q2 + Q3 + Q4 Moving average 1 = 4 • Second average:

Q2 + Q3 + Q4 + Q5 Moving average 2 = 4 • etc… Dr.Burcu Ozcam

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Seasonal Data Sales

1 2 3 4 5 6 7 8 9 10 11 etc…

23 40 25 27 32 48 33 37 37 50 40 etc…

Dr.Burcu Ozcam

Quarterly Sales 60

…

50 40 Sales

Quarter

30 20

…

10 0

1

2

3

4

5

6 Quarter

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7

8

9

10

11

Calculating Moving Averages Quarter

Sales

Average 4-Quarter Period Moving Average 2.5 28.75 3.5 31.00 4.5 33.00 5.5 35.00 6.5 37.50 7.5 38.75 8.5 39.25 9.5 41.00

2.5 =

1+ 2 + 3 + 4 4

1

23

2

40

3

25

4

27

5

32

6

48

7

33

8

37

9

37

 Each moving average is for a consecutive block of 4 quarters

10

50

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Dr.Burcu Ozcam

etc…

28.75 =

23 + 40 + 25 + 27 4

Single Exponential Smoothing  A weighted moving average • Weights decline exponentially • Most recent observation weighted most

 Used for smoothing and short term forecasting

Dr.Burcu Ozcam

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Single Exponential Smoothing(continued)  The weighting factor is α • Subjectively chosen • Range from 0 to 1 • Smaller α gives more smoothing, larger α gives less smoothing

 The weight is: • Close to 0 for smoothing out unwanted cyclical and irregular components • Close to 1 for forecasting

Dr.Burcu Ozcam

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Exponential Smoothing Model  Single exponential smoothing model

Ft +1 = Ft + α( y t − Ft ) or:

Ft +1 = αy t + (1 − α )Ft where: Ft+1 = forecast value for period t + 1 yt = actual value for period t Ft = forecast value for period t α = alpha (smoothing constant) Dr.Burcu Ozcam

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Exponential Smoothing Example  Suppose we use weight α = .2 Quarter (t)

1 2 3 4 5 6 7 8 9 10 etc…

Dr.Burcu Ozcam

Sales (yt) 23 40 25 27 32 48 33 37 37 50 etc…

Forecast from prior period

Forecast for next period (Ft+1 )

NA 23 26.4 26.12 26.296 27.437 31.549 31.840 32.872 33.697 etc…

23 (.2)(40)+(.8)(23)=26.4 (.2)(25)+(.8)(26.4)=26.12 (.2)(27)+(.8)(26.12)=26.296 (.2)(32)+(.8)(26.296)=27.437 (.2)(48)+(.8)(27.437)=31.549 (.2)(48)+(.8)(31.549)=31.840 (.2)(33)+(.8)(31.840)=32.872 (.2)(37)+(.8)(32.872)=33.697 (.2)(50)+(.8)(33.697)=36.958 etc…

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F1 = y1 since no prior information exists

Ft +1 = αy t + (1 − α)Ft

Sales vs. Smoothed Sales 60 50 40

Sales

 Seasonal fluctuations have been smoothed  NOTE: the smoothed value in this case is generally a little low, since the trend is upward sloping and the weighting factor is only .2

30 20 10 0 1

2

3

4

5

Sales Dr.Burcu Ozcam

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6

7

Quarter

8

Smoothed

9

10

Double Exponential Smoothing  Double exponential smoothing is sometimes called exponential smoothing with trend  If trend exists, single exponential smoothing may need adjustment  Add a second smoothing constant to account for trend

Dr.Burcu Ozcam

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Double Exponential Smoothing Model

C t = αy t + (1 − α )(C t −1 + Tt −1 )

Tt = β(C t − C t −1 ) + (1 − β)Tt −1 Ft +1 = C t + Tt where: yt = actual value in time t α = constant-process smoothing constant β = trend-smoothing constant Ct = smoothed constant-process value for period t Tt = smoothed trend value for period t Ft+1 = forecast value for period t + 1 Dr.Burcu Ozcam

t = current time period

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Double Exponential Smoothing  Double exponential smoothing is generally done by computer  Use larger smoothing constants α and β when less smoothing is desired  Use smaller smoothing constants α and β when more smoothing is desired

Dr.Burcu Ozcam

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Exponential Smoothing in Excel  Use tools / data analysis / exponential smoothing • The “damping factor” is (1 - α )

Dr.Burcu Ozcam

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Types of Regression Models Positive Linear Relationship

Relationship NOT Linear

Negative Linear Relationship

Dr.Burcu Ozcam

No Relationship

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Simple Linear Regression Model  Only one independent variable, x  Relationship between x and y is described by a linear function  Changes in y are assumed to be caused by changes in x

Dr.Burcu Ozcam

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Linear Regression The regression model: y intercept Dependent Variable

Slope Coefficient

Independent Variable

y = b 0 + b1x + ε Linear component

Dr.Burcu Ozcam

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Random Error term, or residual

Random Error component

Linear Regression y

y = b 0 + b1x + ε

(continued)

Observed Value of y for xi

εi

Predicted Value of y for xi

Slope = b1 Random Error for this x value

Intercept = b0

x

xi Dr.Burcu Ozcam

LOG301

Least Squares Criterion  b0 and b1 are obtained by finding the values of b0 and b1 that minimize the sum of the squared residuals 2 ˆ ∑ e = ∑ (y −y) 2

=

Dr.Burcu Ozcam

∑ (y − (b

+ b1x))

2

0

LOG301

The Least Squares Equation  The formulas for b1 and b0 are:

b1

( x − x )( y − y ) ∑ = ∑ (x − x) 2

algebraic equivalent:

b1 =

Dr.Burcu Ozcam

and

x∑ y ∑ ∑ xy − n 2 ( x ) ∑ 2 x − ∑ n

b0 = y − b1 x LOG301

Interpretation of the Slope and the Intercept  b0 is the estimated average value of y when the value of x is zero  b1 is the estimated change in the average value of y as a result of a one-unit change in x

Dr.Burcu Ozcam

LOG301

Finding the Least Squares Equation  The coefficients b0 and b1 will usually be found using computer software, such as Excel or Minitab  Other regression measures will also be computed as part of computer-based regression analysis

Dr.Burcu Ozcam

LOG301

Simple Linear Regression Example  A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square feet)  A random sample of 10 houses is selected • Dependent variable (y) = house price in $1000s

• Independent variable (x) = square feet

Dr.Burcu Ozcam

LOG301

Sample Data for House Price Model

Dr.Burcu Ozcam

House Price in $1000s (y)

Square Feet (x)

245

1400

312

1600

279

1700

308

1875

199

1100

219

1550

405

2350

324

2450

319

1425

255

1700 LOG301

Regression Using Excel  Tools / Data Analysis / Regression

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Excel Output Regression Statistics Multiple R

0.76211

R Square

0.58082

Adjusted R Square

0.52842

Standard Error

house price = 98.24833 + 0.10977 (square feet)

41.33032

Observations

ANOVA

The regression equation is:

10 df

SS

MS

Regression

1

18934.9348

18934.9348

Residual

8

13665.5652

1708.1957

Total

9

32600.5000

Coefficients Intercept Square Feet

Dr.Burcu Ozcam

Standard Error

t Stat

F 11.0848

P-value

Significance F 0.01039

Lower 95%

Upper 95%

98.24833

58.03348

1.69296

0.12892

-35.57720

232.07386

0.10977

0.03297

3.32938

0.01039

0.03374

0.18580

LOG301

Graphical Presentation  House price model: scatter plot and regression line 450

Intercept = 98.248

House Price ($1000s)

400

Slope = 0.10977

350 300 250 200 150 100 50 0 0

500

1000

1500

2000

Square Feet

2500

3000

house price = 98.24833 + 0.10977 (square feet) Dr.Burcu Ozcam

LOG301

Actions When Forecasting is Not Appropriate • Seek information directly from customers •Collaborate with other channel members • Apply forecasting methods with caution (may work where forecast accuracy is not critical)

• Delay supply response until demand becomes clear

• Shift demand to other periods for better supply response

• Develop quick response and flexible supply systems

CR (2004) Prentice Hall, Inc. Dr.Burcu Ozcam

LOG301

Collaborative Forecasting

• Demand is lumpy or highly uncertain • Involves multiple participants each with • •

a unique perspective—“two heads are better than one” Goal is to reduce forecast error The forecasting process is inherently unstable

CR (2004) Prentice Hall, Inc. Dr.Burcu Ozcam

LOG301

Collaborative Forecasting: Key Steps • Establish a process champion • Identify the needed Information and collection processes • Establish methods for processing information from multiple

sources and the weights assigned to multiple forecasts • Create methods for translating forecast into form needed by each party • Establish process for revising and updating forecast in real time • Create methods for appraising the forecast • Show that the benefits of collaborative forecasting are obvious and real CR (2004) Prentice Hall, Inc. Dr.Burcu Ozcam

LOG301

Managing Highly Uncertain Demand •Delay forecasting as long as possible •Prioritize supply by product’s degree of uncertainty (supply to the more certain products first)

•Apply the principle of postponement to the most

uncertain products (delay committing to a final product form until an order is received)

•Create flexible supply to changing demand (alter

capacity and output rates through subcontracting, computer technology, multi-purpose processes, etc.)

•Be able to respond quickly to uncertain demand levels CR (2004) Prentice Hall, Inc. Dr.Burcu Ozcam

LOG301

 Ch 2, Problems 1,4,8,9,10  Due 8-12 Oct.

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LOG301