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Session17
Course: BUAD 311, Spring 2008School: USC
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Word Count: 1687
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Management Session Operations 17: Forecasting Session 17 Operations Management 1 Forecasting Objectives Introduce the basic concepts of forecasting and its importance within an organization. Present several of the more common forecasting methods. Measure and assess the errors that exist in forecasts. Session 17 Operations Management 2 Managerial Issues Recognizing the increased importance of...
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Management
Session Operations 17: Forecasting
Session 17
Operations Management
1
Forecasting Objectives
Introduce the basic concepts of forecasting and its importance within an organization.
Present several of the more common forecasting methods.
Measure and assess the errors that exist in forecasts.
Session 17
Operations Management
2
Managerial Issues
Recognizing the increased importance of forecasting in both manufacturing and services. How to go about implementing forecasting at all levels in the organization.
Session 17
Operations Management
3
Types of Forecasting
Qualitative Techniques
Non-quantitative forecasting techniques based on expert opinions and intuition. Typically used when there is no data available. Analyzing data by time periods to determine if trends or patterns occur. Relating demand to an underlying factor other than time. (Regression)
Time Series Analysis
Causal Relationship Forecasting
Session 17
Operations Management
4
Qualitative Techniques
Subjective, judgmental Based on intuition, estimates, and opinions
Expert Opinions
Market Research
Historical Analogies
Session 17
Operations Management
5
Time Series Methods
Moving average Exponential smoothing More sophisticated techniques available
Session 17
Operations Management
6
Causal Relationship
Multiple Regression Models
It is assumed that you've learned about them in your statistics class, i.e., we will not discuss them.
Session 17
Operations Management
7
Characteristics of Forecasts
They are usually wrong. The longer the forecast horizon, the less accurate the forecast will be.
Group forecasts are more accurate than individual forecasts.
A good forecast says something about its likely error size.
Session 17
Operations Management
8
Time Series Models
Models for short-term decisions Inventory decisions
Stock levels of Gameboys Production planning decisions
Call center scheduling Fast food chain
Staffing decisions
Session 17
Operations Management
9
Components of Demand
Average Demand for the Period Trends Seasonal/Cyclical Influence
Random Variation
Session 17
Operations Management
10
Moving Average
Appropriate when demand for a product is neither growing nor declining rapidly and there are no seasonal characteristics.
Forecast for period t: the average of the previous n periods
Ft
At
1
At
2
... At
n
n
Operations Management 11
Actual demand realized last period and the one before. Actual demand realized n periods ago.
Session 17
Moving Average
Week 1 2 3 4 5 6 7 8 9 10 11
Session 17
Demand
358 952 623 186 714 53 893 425 535 47 956 257
Let's develop 3-week and 6-week moving average forecasts for demand.
12
Operations Management
12
(358+952+623)/3 (358+952+623+186+714+53)/6
Week 1 2 3 Demand 358 952 623 3-week MA 6-week MA
4
5 6
186
714 53
644.33
587.00 507.67
7
8 9 10 11 12
893
425 535 47 956 257
317.67
553.33 457.00 617.67 335.67 512.67 Operations Management
481.00
570.17 482.33 467.67 444.50 484.83
Session 17
.... 13
MA Comparison
1200
1000
800 Demand 600 3-week MA 6-week MA 400
200
0 Week
Session 17
Operations Management
14
Moving Average:
6-week MA is smoother than 3-week MA, which appears to result in better predictions.
How do we measure which one is doing better?
Session 17
Operations Management
15
Forecast Errors
How do we measure errors?
Mean absolute deviation
n
| Ai MAD
i 1
Fi |
n
Session 17
Operations Management
16
There is a Distribution Around the Forecasted Value
Standard Deviation of Error = 1.25*MAD
Error is assumed to be NORMALLY DISTRIBUTED with MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25*MAD
Session 17
Operations Management
17
MAD calculation
Week 1 2 3 Demand 358 952 623 3-week MA AD 6-week MA AD
4
5
186
714
644.33
587.00
458.33
127.00
6
7
53
893
507.67
317.67
454.67
575.33 481.00 412.00
8
9
425
535
553.33
457.00
128.33
78.00
570.17
482.33
145.17
52.67
10
11
47
956
617.67
335.67
570.67
620.33
467.67
444.50
420.67
511.50
12
Session 17
257
512.67
255.67
484.83
277.83
18
Operations Management
Moving Average Comparison
How many periods should we use for forecasting?
6-week MAD is 294.97
3-week MAD is 363.15
6-week MAD is lower than 3-week MAD
As many as possible?
Session 17
Operations Management
19
Moving Average
Week Demand
1
2
650
678
3
4
720
785
5
6
859
920
Let's again develop 3-week and 6-week moving average forecasts for demand for a different example.
7
8
1000
1015
9
10
1025
1100
11
12
Session 17
1109
1210
Operations Management 20
The Forecasts
Week 1 2 3 4 Demand 650 678 720 785 682.67 3-week MA 6-week MA
5 6
7 8 9 10 11 12
859 920
1000 1015 1025 1100 1109 1210
727.67 788.00
854.67 926.33 978.33 1013.33 1046.67 1078.00 Operations Management 768.67 827.00 883.17 934.00 986.50 1028.17 21
Session 17
MAD calculation
Week 1 Demand 650 3-week MA AD 6-week MA AD
2
3
678
720
4
5 6 7 8 9 10 11
Session 17
785
859 920 1000 1015 1025 1100 1109 1210
682.67
727.67 788.00 854.67 926.33 978.33 1013.33 1046.67 1078.00
102.33
131.33 132.00 145.33 88.67 46.67 86.67 62.33 132.00 768.67 827.00 883.17 934.00 986.50 1028.17 231.3333 188.00 141.83 166.00 122.50 181.83
22
12
Operations Management
MA comparison
Note that MAD is now lower for the 3-week MA than for the 6-week MA.
3-week MAD is 103.04
6-week MAD is 171.92
What is going on?
Session 17
Operations Management
23
MA comparison
1400 1200 1000 800 600 400 200 0 1 2 3 4 5 6 7 8 9 10 11 12 3-week MA 6-week MA Demand
Session 17
Operations Management
24
Moving Average: Observations
A large number of observations will cause the moving average to respond slowly to changes.
Therefore, when there is a trend in the data, using more observations results in a forecast with larger error.
Bottom line: there is a trade-off between using more observations to smooth out random variations and using less observations to more closely follow trends.
Session 17
Operations Management 25
How to decide the time window?
Try many different time window sizes and choose the one with the lowest MAD.
Session 17
Operations Management
26
Time Series Methods
Moving Average Exponential Smoothing More sophisticated techniques available
Session 17
Operations Management
27
How did we use data
Moving average
Discard old records
Assign same weight for recent records
Advantage? Disadvantage? Assign different weights
Weighted moving average
For example
Ft
Session 17
0.4 At
1
0.3 At
2
0.2 At
3
0.1At
4
Operations Management
28
Exponential Smoothing
Ft = = Prior Value) + (1 ) Past Forecast
At1 + (1 ) Ft1
Exponentially smoothed forecast for period t Exponentially smoothed forecast for prior period Actual demand in the prior period Desired response rate or smoothing constant
Ft = Ft1 = At1 = =
Session 17
Operations Management
29
Exponential Smoothing
Brings into account our previous forecast and past demand.
Session 17
Operations Management
30
Exponential Smoothing
Ft = Ft1 =
At1 + (1 ) Ft1 At2 + (1 ) Ft2, etc
Ft = At1+(1 ) At2+(1 )2Ft2 = At1+(1 ) At2+(1 )2 At3 +(1 )3 At4 +(1 )4 At5+(1 )5 At6 +(1 )6 At7+... "Age" of data is 1/
Session 17
Operations Management
31
How do we pick ?
Large
When does it work? When does it not?
Small
When does it work? When does it not?
Session 17
Operations Management
32
Go Back to Spread Sheet
The following table lists demands for an item for the past 8 weeks.
Week
1 2
Demand
200 250
Forecast
3
4 5
175
186 225
6
7 8
Session 17
Operations Management
285
305 190
33
Exponential Smoothing
What is the forecast for week 9?
Decide on a value for
0.1
If no history before week 1, we can not forecast the demand for week 1 using the formula.
At the end of period, we get demand = 200.
What is the forecast number week for 2?
Session 17
Operations Management
34
Exponential Smoothing
Week Demand
Forecast
1 2
200 250 200
3 4 5
6 7
Session 17
175 186 225
285 305
Operations Management
8
190
35
Exponential Smoothing
F3 1
Week
F2
A2
0.9 * 200 0.1* 250 205
Demand Forecast 200 205
1
2 3
200
250 175
4
5 6
186
225 285
7
8
Session 17
305
190
Operations Management 36
Exponential Smoothing
F4 1
Week 1
F3
A3
0.9 * 205 0.1*175 202
Demand 200 Forecast
2
3 4
250
175 186
200
205 202
5
6 7
225
285 305
8
Session 17
190
Operations Management 37
Exponential Smoothing
Similarly we get:
Week 1 2 3 Demand 200 250 175 200 205 Forecast
4
5
186
225
202
200
6
7
285
305
203
211
8
Session 17
190
Operations Management
220
38
Exponential Smoothing
Two important questions?
How to choose ? Which is better: exponential smoothing
or moving average?
Session 17
Operations Management
39
Exponential Smoothing: = 0.4
Week 1 2 Demand 200 250 200 Forecast
3 4 5
6 7
Session 17
175 186 225
285 305
Operations Management
220 202 196
207 238 265
40
8
190
Comparison
350 300 250 200 150 100 50 0 1 2 3 4 5 6 7 8 week Operations Management Demand alpha = 0.1 alpha = 0.4
Session 17
41
Comparison
As becomes larger, the predicted values exhibit more variation because they are more responsive to the demand in the previous period.
A large
seems to track the series better.
Value of stability.
This parallels our observation regarding MA: there is a trade-off between responsiveness and smoothing out demand fluctuations.
Session 17
Operations Management 42
Comparison
Week 1 2 3 4 5 6 7 8 Demand 200 250 175 186 225 285 305 190 200.00 205.00 202.00 200.40 202.86 211.07 220.47 50.00 30.00 16.00 24.60 82.14 93.93 30.47 46.73
Session 17
Operations Management
Forecast for 0.1 alpha
AD
Forecast for 0.4 alpha
AD
200.00 220.00 202.00 195.60 207.36 238.42 265.05
50.00 45.00 16.00 29.40 77.64 66.58 75.05 51.38
Choose the forecast with lower MAD.
43
Which
to choose?
In general, you want to calculate MAD for many different values of and choose the one with the lowest MAD.
Same idea to determine if Exponential Smoothing or MA is preferred.
Note that one advantage of exponential smoothing is that it requires less data storage to implement.
Session 17
Operations Management
44
Comparison: Exponential Smoothing and Moving Average
Which is better?
If we set 1/ = (N+1)/2, then both systems are equivalent.
What does it mean that the two systems are equivalent?
The variances of the errors are identical. Does it mean that the two systems have the same forecasts?
Exponential smoothing requires less data storage to implement.
Session 17
Operations Management
45
Forecasts and Probability Distributions: How many to stock?
A firm produces Red and Blue T-Shirts
Month/demand January February March April May June July August September October Red Shirts 909.9 616.7 1073.3 1382.9 1359.5 1519.9 344.9 Blue Shirts 1185.0 546.2 1229.5 1248.7 1337.9 1539.6 1300.8
Session 17
Operations Management
46
Forecasts and Probability Distributions ( = 0.3)
Month
January
T-Shirt Demand
909.9
Forecast 909.9
821.94
February
March
616.7
1073.3
April
May June July August September October
1382.9
1359.5 1519.9 344.9 929.7 1328.5 674
Operations Management
897.348
1043.014 1137.96 1252.542 980.2492 965.0844 1074.109
November
Session 17
954.0764
47
Forecasts and Probability Distributions
Suppose the company stocks 954 T-shirts, the forecasted number. What is the probability the company will have a stockout, that is, that there will not be enough T-shirts to satisfy demand?
The company does not want to have unsatisfied demand, as that would be lost revenue. So the company overstocks. Suppose the company stocks 1,026 units. What is the probability that the actual demand will be larger than 1,026?
Session 17
Operations Management
48
There is a Distribution Around the Forecasted Sale
Standard Deviation of Error = 1.25*MAD
Error is assumed to be NORMALLY DISTRIBUTED with MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25*MAD
Session 17
Operations Management
49
Forecasts and Probability Distributions ( = 0.3)
Month
January
T-Shirt Demand
909.9
Forecast 909.9
821.94
AD 293.2
251.36
February
March
616.7
1073.3
April
May June July August September October
1382.9
1359.5 1519.9 344.9 929.7 1328.5 674
897.348
1043.014 1137.96 1252.542 980.2492 965.0844 1074.109
485.552
316.4864 381.9405 907.6417 50.54916 363.4156 400.1091
50
November
Session 17
954.0764
Operations Management
How many to stock?
Suppose the company wants the probability of not being able to meet its demand to be 2.5%
P ( Nov. demand amt. stocked) P ( N(954,1.25 MAD) amt. stocked) amt. stocked - 954 P N(0,1) 1.25 MAD 0.025 amt. stocked - 954 when 1.96 1.25 MAD
Session 17
Operations Management
Look it up on Normal tables
51
How many to stock?
Amt. stocked 954 1.96 1.25 MAD implies Amt. stocked 1.96 1.25 MAD 954 1892
Note that MAD=383 in this example.
Session 17
Operations Management
52
The Forecast for Blue Products ( = 0.3)
January February March April May June July August September October
Session 17
1185.0 546.2 1229.5 1248.7 1337.9 1539.6 1300.8 1084.4 1211.8 965.6
1185.0 993.3 1064.2 1119.5 1185.1 1291.4 1294.2 1231.3 1225.4 1147.5
638.7429 236.1592 184.5132 218.4141 354.516 9.349969 209.8464 19.48862 259.8598 236.7656
53
Operations Management
Blue Product Inventory Level
The stocking level of blue products for period 11 is:
1148+1.96*(1.25*237)=1728 Recall that:
amt. stocked = forecast + 1.96x1.25xMAD implies the probability of not satisfying demand is P( demand > amt. stocked ) = 0.025.
Session 17
Operations Management 54
Total Inventory Level
The total inventory for Red and Blue is:
1892 + 1728 = 3620
P( Red demand > # of Red T-shirts stocked ) = 0.025 P( Blue demand > # of Blue T-shirts stocked ) = 0.025
Session 17
Operations Management
55
Aggregate Forecasts
Can we more accurately forecast the combined demand?
Session 17
Operations Management
56
Forecasting Gray Products
Suppose we can make Gray Shirt and then dye the T-shirts either red or blue. What is the Demand for Gray Shirts?
We look at the sum of the demands in the past
We forecast the demand for the two products combined We compute the MAD for the aggregate forecast
Session 17
Operations Management
57
Forecast for the Aggregate Demand
Month/demand January February March April May June July August September October November Red Shirts Blue Shirts Gray Shirts 909.9 1185.0 2094.9 616.7 546.2 1162.9 1073.3 1229.5 2302.8 1382.9 1248.7 2631.6 1359.5 1337.9 2697.5 1519.9 1539.6 3059.5 344.9 1300.8 1645.7 929.7 1084.4 2014.1 1328.5 1211.8 2540.3 674.0 965.6 1639.5
Forecast 2094.9 1815.292 1961.535 2162.565 2323.031 2543.976 2274.489 2196.378 2299.549 2101.549 AD 931.9782 487.4767 670.1002 534.888 736.4826 898.2896 260.3722 343.9045 660.0016 613.722
Inventory of Gray = 2102 + 1.96*1.25*614 = 3603
Session 17
Operations Management 58
Aggregate Demand Forecast Conclusions
By stocking 3603 Gray T-shirts, we ensure P( T-shirt demand > # stocked ) = 0.025 Otherwise, we needed to stock 1892 blue T-shirts and 1728 red T-shirts for a combined number of 1892+1728 = 3620 T-shirts to ensure that P( red T-shirt demand > # red shirts stocked) = P( blue T-shirt demand > # blue shirts stocked) = 0.025 3603 < 3620 ... we need to stock less T-shirts to ensure a given stockout probability (2.5% in this example) when we have an aggregate forecast.
Session 17
Operations Management 59
Summary
Time Series Techniques
Moving Averages Exponential Smoothing Error measure Error can be thought of as the distribution around the average or prediction.
Forecast is not a single number
Forecast variability increases with forecast horizon.
Session 17
Operations Management
60
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Rhode Island - ECN - 327
Rhode Island - ECN - 202
Rhode Island - ECN - 327
Rhode Island - ECN - 327
Rhode Island - ECN - 327
Rhode Island - GEO - 100
Chapter 7: Coastal Zones and ProcessesNature of the CoastlineOne factor that influences the geometry of a coastline is plate tectonics. Continental margins can be described as active or passive in a tectonic sense, depending on whether there is or
Rhode Island - ECN - 327
Rhode Island - GEO - 100
Chapter 11: Soil as a ResourceSoil Defined in different ways for different purposes: - Engineering Geologists define soil very broadly to include all unconsolidated materialoverlying bedrock.- Soil Scientists restrict the term soil to those mate
Rhode Island - ECN - 305
Lecture NotesThe Worldly Philosophers IntroductionWorldly activity: drive for wealth Economics: search for order and meaning of social history Age of economists: last 200 yearsIntroduction Economists: powerful ideas (thus the importance of econom
Rhode Island - GEO - 100
Chapter 2: Rocks and Minerals A First LookElements, Isotopes, and Ions:Nucleus At the center of the atom and contains one or more particles with a + (positive) electrical charge (protons) and usually some particles of similar mass that have no ch
Rhode Island - GEO - 100
Chapter 8: Mass Movements Factors Influencing Slope Stability - Mass Movements occur whenever the downward pull of gravity overcomes theforces (usually frictional) resisting it.- The down-slope pulling tendency causes mass movements.Shearing Stre
Rhode Island - ECN - 327
Rhode Island - ECN - 202
Rhode Island - FRN - 101
Chapitre 1: Qui tes-vous?p. 22 26: Introducing YourselfLe verbe tre et les pronoms sujets: tre (to be), can be used to describe yourself and others and to say where someone is from.Conjugation of treSingular Pluralje tu il / elle / on -sui
Rhode Island - ECN - 337
Chapter 2: The Firm and Its CostsCosts are a key determinant of firm behavior such as pricing. You need to understand various types of costs in order to predict a firms behavior.Section 2.1: The Neoclassical FirmTraditional Neoclassical Firm A f
Rhode Island - FRN - 101
Chapitre Prliminairep. 4 7: Greetings, Introductions, and CourtesyUsing tu or vous when greeting someone: Tu is used in farmiliar contexts, such as: o Among friends o Among family o With children o With students your own age Vous is used in forma
Rhode Island - ECN - 337
Chapter 1 : IntroductionThe field of Industrial Organization developed as an offshoot of traditional Microeconomics. o Differs from traditional Microeconomics, as it analyzes the Firms within an industry, rather than the Industry as a whole (Traditi