1. Operations Management Dr. Ron Lembke
FORECASTING
Operations Management
Dr. Ron Lembke

2. Predicting the Future We know the forecast will be wrong.
Try to make the best forecast we can,
Given the time we want to invest
Given the available data
The “Rules” of Forecasting:
The forecast will always be wrong
The farther out you are, the worse your forecast is likely to be.
Aggregate forecasts are more likely to accurate than individual item ones

3. Independent vs Dependent
Independent Demand
Things demanded by end users
Dependent Demand
Demand known, once demand for end items is known

4. Time Horizons
Different decisions require projections about different time periods:
Short-range: who works when, what to make each day (weeks to months)
Medium-range: when to hire, lay off (months to years)
Long-range: where to build plants, enter new markets, products (years to decades)

5. Forecast Impact
Finance & Accounting: budget planning Human Resources: hiring, training, laying off employees Capacity: not enough, customers go away angry, too much, costs are too high Supply-Chain Management: bringing in new vendors takes time, and rushing it can lead to quality problems later

6. Qualitative Methods Sales force composite / Grass Roots
Market Research / Consumer market surveys & interviews
Jury of Executive Opinion / Panel Consensus
Delphi Method
Historical Analogy - DVDs like VCRs
Naïve approach

7. The Human Element
Colbert says you have more nerve endings in your gut than in your brain
Limited ability to include factors
Can’t include everything
If it feels really wrong to your gut, maybe your gut is right

8. Historical Analogy Video sales of Shrek 2
Shrek (2001) did $500m at the box office, and sold almost 50 million DVDs & videos
Shrek2 (2004) did $920m at the box office

9. Video sales of Shrek 2? Assume 1-1 ratio:
920/500 = 1.84
1.84 * 50 million = 92 million videos?
Fortunately, not that dumb.
January 3, 2005: 37 million sold!
March analyst call: 40m by end Q1
March SEC filing: 33.7 million sold. Oops.
May 10 Announcement:
In 2nd public Q, missed earnings targets by 25%.
May 9, word started leaking
Stock dropped 16.7%

10. Lessons Learned Guaranteed Sales: flooded market with DVDs 5 years ago
Promised the retailer they would sell them, or else the retailer could return them
Didn’t know how many would come back
5 years ago
Typical movie 30% of sales in first week
Animated movies even lower than that
2004/ % in first week
Shrek 2: 12.1m in first 3 days
Far Far Away Idol
Had to vote in first week

11. Quantitative Methods Math-based
Relationships, patterns, trends, in previous data
Associative or Causal models
Prediction based on relationship to inputs
Identify independent and dependent variables
Time-Series
Extrapolation – existing patterns will continue

12. New Housing Starts
Who cares?
How predict?

13. Evaluating Forecasts
How far off is the forecast? What do we do with this information?
Forecasts
Demands

14. Forecast Errors
Error: 𝐸 𝑡 = 𝐴 𝑡 − 𝐹 𝑡

15. Naïve Forecast Error Avg Error (14 mos)= -0.4 Avg Error (55 yrs)= 0.02
Month
Total
Naïve
Error
Jan 1959
96.2
Feb 1959
99.0
2.8
Mar 1959
127.7
28.7
Apr 1959
150.8
23.1
May 1959
152.5
1.7
Jun 1959
147.8
-4.7
Jul 1959
148.1
0.3
Aug 1959
138.2
-9.9
Sep 1959
136.4
-1.8
Oct 1959
120.0
-16.4
Nov 1959
104.7
-15.3
Dec 1959
95.6
-9.1
Jan 1960
86.0
-9.6
Feb 1960
90.7
4.7
Avg Error (14 mos)= -0.4
Avg Error (55 yrs)= 0.02

16. Mean Error of 0
That’s good!
not perfect.
Just unbiased

17. Squared Errors No negatives No cancelling Large errors blow up
One bad month and your
method looks terrible
MSE=303.25
Good? Bad?

18. Mean Absolute Error No negatives No cancelling
Large errors do not blow up
What’s a good score?
MAD=12.99
Good? Bad?

19. Mean Absolute Percentage Error
No negatives
No cancelling
Large errors do not blow up
What’s a good score?
MAPE=11.4%
Good? Bad?

20. Evaluating Forecasts
Mean Absolute Deviation Mean Squared Error Percent Error

21. Tracking Signal To monitor, compute tracking signal
If >4 or <-4 something is wrong
Top should sum to 0 over time. If not, forecast is biased.

22. Monitoring Forecast Accuracy
Monitor forecast error each period, to see if it becomes too great 4
Upper Limit
Forecast Error -4
Lower Limit
Forecast Period

23. Scenario 1-Livingston Medical
Month
Math Model
Jury of Executive Opinion
Actual
Jan
13,128
12,500
12,480
Feb
12,009
13,000
11,568
Mar
12,649
13,500
13,244
Apr
16,387
16,000
15,560
May
16,190
16,034
June
23,002
24,000
23,400

24. Math Model - Forecast Errors

25. Jury of Executive Opinion- Forecast Errors

26. Stability vs. Responsiveness
Real-time accuracy
Market conditions
Stable
Forecasts being used throughout the company
Long-term decisions based on forecasts
Don’t whipsaw those folks

27. Causal Forecasting
Linear regression seeks a linear relationship between the input variable and the output quantity.
For example, furniture sales correlates to housing sales
Not easy, multiple sources of error:
Understand and quantify relationship
Someone else has to forecast the x values for you

28. Causal Relationships

29. Computing Values

30. Linear Regression Four methods Fits a trend and intercept to the data.
Type in formulas for trend, intercept
Tools | Data Analysis | Regression
Graph, and R click on data, add a trendline, and display the equation.
Use intercept(Y,X), slope(Y,X) and RSQ(Y,X) commands
Fits a trend and intercept to the data.
R2 measures the percentage of change in y that can be explained by changes in x.
Gives all data equal weight.
Exp. smoothing with a trend gives more weight to recent, less to old.

31. Van Uses – 2,200 clients
-22+( * 2100) = =196 rides

32. Confidence?

33. Assisted Living Facility
-22+( * 2100) = =196 rides

34. Quantitative Methods
Causal Methods 1. Linear Regression Time Series Methods 1. Simple Moving Average 2. Weighted Moving Average 3. Exponential Smoothing 4. Exponential smoothing with trend 5. Linear regression

35. Time Series Forecasting
Assume patterns in data will continue, including:
Trend (T)
Seasonality (S)
Cycles (C)
Random
Variations

36. Moving Average Compute forecast using n most recent periods
Jan Feb Mar Apr May Jun Jul
3 month Moving Avg:
June forecast:
FJun = (AMar + AApr + AMay)/3
If no seasonality, freedom to choose n
If seasonality is N periods, must use N, 2N, 3N etc. number of periods

37. Moving Average Advantages: Disadvantages:
Ignores data that is “too” old
Requires less data than simple average
More responsive than simple average
Disadvantages:
Still lacks behind trend like simple average, (though not as badly)
The larger n is, more smoothing, but the more it will lag
The smaller n is, the more over-reaction

38. Simple and Moving Averages

39. Old Data
Comparison of simple, moving averages clearly shows that getting rid of old data makes forecast respond to trends faster Moving average still lags the trend, but it suggests to us we give newer data more weight, older data less weight.

40. Exponential Smoothing
F10 = F (A9 - F9)
F10 = 0.8 F (A9 - F9)
At-1 Actual demand in period t-1 Ft-1 Forecast for period t-1  Smoothing constant >0, <1 Forecast is old forecast plus a portion of the error of the last forecast. Formulas are equivalent, give same answer

41. Exponential Smoothing
Smoothing Constant between
Easier to compute than moving average
Most widely used forecasting method, because of its easy use
F1 = 1,050,  = 0.05, A1 = 1,000
F2 = F1 + (A1 - F1)
= 1, (1,000 – 1,050)
= 1, (-50) = 1,047.5 units
BTW, we have to make a starting forecast to get started. Often, use actual A1

42. Exponential Smoothing
Alpha = 0.3

43. Exponential Smoothing
Alpha = 0.5

44. Exponential Smoothing
We take:
And substitute in
to get:
and if we continue doing this, we get:
Older demands get exponentially less weight

45. Choosing 
Low : if demand is stable, we don’t want to get thrown into a wild-goose chase, over-reacting to “trends” that are really just short-term variation
High : If demand really is changing rapidly, we want to react as quickly as possible

46. Averaging Methods Simple Average Moving Average
Weighted Moving Average
Exponentially Weighted Moving Average (Exponential Smoothing)
They ALL take an average of the past
With a trend, all do badly
Average must be in-between 30 20 10

47. Trend-Adjusted Ex. Smoothing

48. Trend-Adjusted Ex. Smoothing
Trend-Adjusted Forecast for period 2 was
Suppose actual demand is 115, A2=115

49. Trend-Adjusted Ex. Smoothing
Suppose actual demand is 120, A3=120

50. TAF6=S5+T5 F6 A5 S5

51. Selecting  and β You could:
Try an initial value for each parameter.
Try lots of combinations and see what looks best.
But how do we decide “what looks best?”
Let’s measure the amount of forecast error.
Then, try lots of combinations of parameters in a methodical way.
Let  = 0 to 1, increasing by 0.1
For each  value, try  = 0 to 1, increasing by 0.1

52. Techniques for Trend
Determine how demand increases as a function of time
t = periods since beginning of data
b = Slope of the line
a = Value of yt at t = 0

53. Seasonality
Demand goes up and down on a regular, time-based pattern

54. Washoe Gaming Win, 1993-96 What did they mean when they
said it was down
three quarters
in a row?

55. Seasonality Seasonality is regular up or down movements in the data
Can be hourly, daily, weekly, yearly
Naïve method
N1: Assume January sales will be same as December
N2: Assume this Friday’s ticket sales will be same as last

56. Seasonal Relatives
Seasonal relative for May is 1.20, means May sales are typically 20% above the average
Factor for July is 0.90, meaning July sales are typically 10% below the average

57. Seasonality & Assume No Trend
Avg Relative Spring /257.5 = 0.83 Summer /257.5 = 1.42 Fall /257.5 = 1.20 Winter /257.5 = 0.56 Total 1,000 1,060 1,030 Avg 1,030/4=257.5 Relatives sum to =4.01

58. Seasonality & No Trend
If we expected total demand for the next year to be 1,100, the average per quarter would be 1,100/4=275 Forecast Spring 275 * 0.8 = 220 Summer 275 * 1.4 = 385 Fall 275 * 1.2 = 330 Winter 275 * 0.6 = 165 Total 1,100

59. Scenario 3a
R2=

60. Deseasonalized Van Usage

61. Seasonality with a Trend
Demand goes up and down on a regular, time-based pattern
AND demand is on a long-term upward (or downward) trend

62. Trend & Seasonality Deseasonalize to find the trend
Calculate seasonal relatives
Deseasonalize the demand
Find trend of deseasonalized line
Project trend into the future
Project trend line into future
Multiply trend line by seasonal relatives.

63. Washoe Gaming Win, 1993-96 Looks like a downhill slide
Silver Legacy opened 95Q3
Otherwise, upward trend
Source: Comstock Bank, Survey of Nevada Business & Economics

64. Washoe Win
Definitely a general upward trend, slowed 93-94

67.
Cache
Creek
Thunder
Valley
9/11 CC
Expands

68. BTW

69. Q2 SR

70. 1.Compute Seasonal Relatives
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Avg Q1
240.1
231.6
245.8
244.6
227.9
190.1
187.0
174.1
175.4
179.5
172.1
209.5 Q2
259.3
259.8
269.2
269.7
273.5
237.0
211.9
198.3
192.1
183.3
191.8
191.1
228.1 Q3
279.8
297.4
294.8
284.7
259.0
217.2
209.6
203.9
201.8
207.2
250.0 Q4
246.1
259.6
257.0
257.2
246.4
206.2
186.0
175.6
175.5
166.8
174.6
213.7
Average
225.3
Avg SR Q1
209.5
0.930 Q2
228.1
1.012 Q3
250.0
1.110 Q4
213.7
0.948
Divide by = 0.930

71. 2.Deseasonalize 0.930 1.012 1.110 0.948 Year Quarter Gaming Win
Seasonal Relative
Deseas
2009 1
190,098,500
0.930
204,462,607 2
211,913,667
1.012
209,348,089 3
217,227,445
1.110
195,779,857 4
185,971,111
0.948
196,079,317
2010
187,016,132
201,147,331
198,330,968
195,929,832
209,608,491
188,913,148
175,601,589
185,146,174
2011
174,138,905
187,297,082
192,122,889
189,796,912
203,912,214
183,779,283
175,510,911
185,050,567
2012
175,417,340
188,672,118
183,305,632
181,086,403
201,825,465
181,898,566
166,760,853
175,824,912

72. 3.LR on Deseas data Period Deseasonalized 1 204,462,607 2 209,348,089
195,779,857 4
196,079,317 5
201,147,331 6
195,929,832 7
188,913,148 8
185,146,174 9
187,297,082 10
189,796,912 11
183,779,283 12
185,050,567 13
188,672,118 14
181,086,403 15
181,898,566 16
175,824,912 17
193,041,432 18
189,508,450 19
186,699,574 20
184,133,867 21
185,087,867 22
188,770,074
3.LR on Deseas data

73. 4.Project trend line into future
Q3 is 23rd point in series
199,533, *(-839,033) = 180,235,371

74. 5.Multiply by Seasonal Relatives
Period Q
Linear Trend Line
Seasonal Relative
Seasonalized Forecast 23 3
176,330,767
0.937
165,141,344 24 4
174,654,854
1.020
178,076,517 25 1
172,978,941
1.101
190,514,933 26 2
171,303,027
0.942
161,451,313

77. Housing-Selecting Data
A>F
A<F

78. 1. Seasonal Factors 2009 2010 2011 2012 2013 2014 2015 Avg SF Jan 31.9
38.9
40.2
47.2
58.7
60.7
73.0
50.1
0.776
Feb
39.8
40.7
35.4
49.7
66.1
65.1
61.9
51.2
0.794
Mar
42.7
54.7
49.9
58.0
83.3
80.2
79.7
64.1
0.993
Apr
42.5
62.0
49.0
66.8
76.3
94.9
108.5
71.4
1.107
May
52.2
56.2
54.0
67.8
87.2
92.5
99.6
72.8
1.128
June
59.1
53.8
60.5
74.7
80.7
87.3
112.7
75.5
1.171
July
56.8
51.5
57.6
69.2
84.0
101.0
112.3
76.1
1.179
Aug
52.9
56.3
54.5
69.0
80.4
86.2
66.6
1.032
Sept
52.6
53.0
58.8
75.8
78.4
94.2
68.8
1.066
Oct
44.5
45.4
53.2
77.0
92.0
1.009
Nov
42.3
40.6
62.2
83.8
59.6
0.924
Dec
36.6
33.8
63.2
67.6
73.4
0.820
64.51

79. 2. Deseasonalize Month Starts SF Deseas Jan 2009 31.9 0.776 41.1
Feb 2009
39.8
0.794
50.1
Mar 2009
42.7
0.993
43.0
Apr 2009
42.5
1.107
38.4
May 2009
52.2
1.128
46.3
Jun 2009
59.1
1.171
50.5
Jul 2009
56.8
1.179
48.2
Aug 2009
52.9
1.032
51.3
Sep 2009
52.6
1.066
49.3
Oct 2009
44.5
1.009
44.1
Nov 2009
42.3
0.924
45.8
Dec 2009
36.6
0.820
44.6

80. 3. Linear Regression

81. 4. Project Forward
F(t) = t*0.69

82. 5. Seasonalize

83. Summary Calculate seasonal relatives Deseasonalize Do a LR
Divide actual demands by seasonal relatives
Do a LR
Project the LR into the future
Seasonalize
Multiply straight-line forecast by relatives