1. Competing on Cost
PART IV

2. Forecasting Demand
CHAPTER 10

3. Outline Learning Objectives Forecasting Demand Qualitative Approaches
Quantitative Approaches
Forecast Accuracy
Techniques for Trends
Techniques for Seasonality
Associative Models
Summary
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10.3

4. Learning Objectives
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10.4

5. After reading the chapter, you will be able to:
List the most popular qualitative approaches and mention their advantages and disadvantages
Identify the various components of a time series
Develop forecasts based on time series models: moving averages, weighted moving averages, exponential smoothing, and trend projections
Adjust forecasts for trend and seasonality
Modulate the stability and responsiveness of a forecast
Assess the accuracy of forecasts
Develop forecasts based on associative models
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10.5

6. Figure 10.1 – Mind Map With Focus on Cost
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10.6

7. Forecasting Demand Qualitative approaches Quantitative approaches
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10.7

8. Forecasting Demand
A demand forecast is a prediction of the future demand
Two main approaches to forecasting demand:
Qualitative 質化(性)
Relies on subjective human inputs and judgment
Quantitative 量化
Time series models project historical demand into the future
Associative models use multiple variables to predict demand
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10.8

9. Qualitative Approaches
Jury of executive opinion
Delphi method
Consumer market surveys
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10.9

10. Jury of Executive Opinion
Technique mostly used for new products or services or when unusual events warrant revisions of existing forecasts
Relies on opinions, judgment, knowledge of high-level executives
Advantages
Incorporates experts’ opinions
Yields fast results
Disadvantages
Prone to biases from influential executives
Potential waste of executives’ time
台大癌症中心
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10.10

11. Delphi Method 德菲法 Used for long-term forecasting
Aggregates experts’ demand estimates in an iterative fashion
Anonymous aggregated estimates are sent back to experts who can revise their own estimates. The process is repeated until a consensus is reached
Advantages
Experts’ anonymity helps eliminate biases
Forecast is built on consensus
Disadvantage
May be extremely time consuming
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10.11

12. Consumer Market Surveys
Surveys used to obtain consumers’ intentions to buy products or services
Advantage
Can provide useful input to forecasting demand
Disadvantage
May produce overly optimistic estimates as opposed to actual demand
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10.12

13. Quantitative Approaches
Time series models
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10.13

14. Time Series Models
A time series is a sequence of past data points that are spaced at even time intervals (每小時、每日、每星期 …)
Models
Naïve approach (直覺式)
Simple moving average
Weighted moving average
Exponential smoothing
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10.14

15. Components of a Time Series
Trend: long-term, upward or downward movement of demand
Cycle: pattern that occurs every several years
Seasonality: movement of data that repeats itself at a particular interval (day, week, month, quarter, etc.)
Irregular movement: a random variation that occurs by chance
Trend
Seasonal peak
Average demand

16. Figure 10.3 – Time Series of Stent Surgeries
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10.16

17. Stability and Responsiveness
Stability is the ability of a forecast to not overreact to simple, random fluctuations
Responsiveness is the ability of a forecast to react quickly to true changes in demand
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10.17

18. Naïve Approach 直覺
Demand in the next time period is equal to the demand in the current period
Produces extremely responsive forecasts
Advantages
Simplicity
Cost
Disadvantages
Problematic
if random fluctuations
are large
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10.18

19. Simple Moving Average SMAt = (At − n + … +At−2 + At−1) n
 where SMAt is the simple moving average forecast for period t
n is the number of periods included in the average
At−1 is the actual demand in the previous period
At−2 and At−n are the actual demand two periods ago
and n periods ago, respectively
Increasing the number of periods in the model increases stability and decreases responsiveness
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20. Figure 10.4 – Comparison of Actual Demand With 3-Month and 5-Month Moving Averages
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10.20

21. Weighted Moving Average
WMAt = wt−1(At−1) + wt−2(At−2)+ …. + wt−n(At−n)
 where WMAt is the weighted moving average forecast for period t
At−1 is the actual demand in the previous period
wt−1 is the weight assigned to the actual demand in the previous
period
At−2 and At−n are the actual demand two periods ago and n
periods ago, respectively
wt−2 and wt−n are the weights assigned to the actual demand two periods ago and n periods ago, respectively
The weights help place more emphasis on the most recent demand, thereby increasing responsiveness
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22. Figure 10.5 – Comparison of Actual Demand With Weighted Moving Averages (Weights: 0.5, 0.3, 0.2, and 0.7, 0.3)
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10.22

23. Exponential Smoothing
ESt = α At−1 + (1 – α) ESt−1
 where ESt is the exponentially smoothed forecast for
period t
ESt−1 is the exponentially smoothed forecast for
the previous period
At−1 is the actual demand in the previous period
α is the smoothing constant (0 ≤ α ≤ 1)
The importance of past demand decreases exponentially
Large values of α produce more responsive forecasts; small values produce more stable forecasts
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10.23

24. Figure 10.6 – Comparison of Actual Demand With Exponentially Smoothed Forecasts (α = 0.4 and α =0.8)
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10.24

25. Forecast Accuracy Mean absolute deviation Mean squared error
Mean absolute percentage error
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26. Mean Absolute Deviation (MAD) 平均絕對誤差
Forecast Error = Actual Demand – Forecast
Mean Absolute Deviation
MAD = 𝐀𝐜𝐭𝐮𝐚𝐥 𝐝𝐞𝐦𝐚𝐧𝐝 − 𝐅 𝐨𝐫𝐞𝐜𝐚𝐬𝐭| 𝒏
where n is the number of periods included in computing the sum of errors
取「絕對值」表示預測過高、過低，不能互相抵銷。
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10.26

27. Mean Absolute Deviation (cont.)
Month
Actual Demand
SMAt
(n=3)
Abs. Error
Jan.
128
Feb
122
Mar.
134
Apr.
118
128.00
10.00
May
140
124.67
15.33
Jun.
136
130.67
5.33
Jul.
146
131.33
14.67
Aug.
152
140.67
11.33
Sep.
154
144.67
9.33
Oct.
150.67
22.67
Nov.
124
20.67
Dec.
135.33
13.33
MAD
13.63
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10.27

28. Mean Squared Error (MSE) 誤差平方之平均 (均方差)
Squaring the error term penalizes larger errors to a greater extent
小錯不斷 OK
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10.28

29. Mean Squared Error (cont.)
Month
Actual Demand
SMAt
(n=3)
(Error)2
Jan.
128
Feb
122
Mar.
134
Apr.
118
128.00
100.00
May
140
124.67
235.11
Jun.
136
130.67
28.44
Jul.
146
131.33
215.11
Aug.
152
140.67
128.44
Sep.
154
144.67
87.11
Oct.
150.67
513.78
Nov.
124
427.11
Dec.
135.33
177.78
MSE
212.54
16 * 16 =256
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10.29

30. Mean Absolute Percentage Error (MAPE) 平均絕對誤差百分比
The deviations are expressed as a percentage of actual demand; they are not sensitive to the volume of the items being forecast (e.g. dollars vs. millions of dollars)
0.0143
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31. Mean Absolute Percentage Error (cont.)
Month
Actual Demand
SMAt
(n=3)
Abs.% error
Jan.
128
Feb
122
Mar.
134
Apr.
118
128.00
8.47
May
140
124.67
10.95
Jun.
136
130.67
3.92
Jul.
146
131.33
10.05
Aug.
152
140.67
7.46
Sep.
154
144.67
6.06
Oct.
150.67
17.71
Nov.
124
16.67
Dec.
135.33
10.93
MAPE
10.25%
|118−128| 118
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32. Techniques for Trends Trend-adjusted exponential smoothing
Linear trend projections
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10.32

33. Trend-Adjusted Exponential Smoothing
TAESt = Ft + Tt [10.8]
Ft = α At−1 + (1 – α) TAESt−1 [10.9]
Tt = β (Ft – Ft−1) + (1 – β) (Tt−1) [10.10]
where
TAESt is the trend-adjusted exponentially smoothed forecast for period t Ft is the exponentially smoothed forecast for period t Tt is the exponentially smoothed trend estimate for period t At−1 is the actual demand in the previous period TAESt−1 is the trend-adjusted exponentially smoothed forecast for the previous period Ft−1 is the exponentially smoothed forecast for the previous period Tt−1 is the exponentially smoothed trend estimate for the previous period
α is the smoothing constant for the average (0 ≤ α ≤ 1)
β is the smoothing constant for the trend (0 ≤ β ≤ 1)
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34. Trend-Adjusted Exponential Smoothing (cont.)
Steps to compute a trend-adjusted exponentially smoothed forecast
Compute the exponentially smoothed forecast for period t, Ft
Compute the exponentially smoothed trend estimate, Tt
Compute the trend-adjusted exponentially smoothed forecast for period t, TAESt, by adding the values calculated in Steps 1 and 2
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10.34

35. Trend-Adjusted Exponential Smoothing (cont.)
Initial forecast is 125, and initial trend value is 1
Year
Month
Actual Demand
Exponentially Smoothed Forecast, Ft
(α = 0.4)
Exponentially Smoothed Trend Estimate, Tt
(β = 0.3)
Trend-Adjusted Forecast, TAESt 3
Jan.
128
125.00 1
126.00
Feb.
122
126.80
1.24
128.04
Mar.
134
125.62
0.52
126.14
Apr.
118
129.28
1.46
130.74
May
140
125.65
−0.07
125.57
Jun.
136
131.34
1.66
133.01
Jul.
146
134.20
2.02
136.22
Aug.
152
140.13
3.19
143.33
Sep.
154
146.80
4.23
151.03
Oct.
152.22
4.59
156.81
Nov.
124
145.28
1.13
146.42
Dec.
137.45
−1.56
135.89 4
130.34
−3.22
127.11
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36. Figure 10.7 – Comparison of Actual Demand With Trend-Adjusted Exponentially Smoothed Forecasts (α = 0.4 and β =0.3)
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10.36

37. Linear Trend Projections
Version of the linear regression technique
𝐲 = a + bx
Where
𝐲 is the predicted value of the dependent variable, that is, demand a is the y-intercept b is the slope x is the value of the independent variable, that is, time period
a and b can be computed using the following formulas:
a = y –b x
b = 𝒙𝒚 − 𝒏 𝒙 𝒚 𝒙 𝟐 − 𝒏 𝒙 𝟐
𝒚 is the average of the y values
𝒙 is the average of the x values
n is the number of data points used to compute b
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38. Linear Trend Projections (cont.)
TABLE 10.9 – Computations for Trend Line Equations
Year
Quarter
Actual Demand, y xy x2 1
155 2
198
396 4 3
250
750 9
210
840 16 5
299
1495 25 6
312
1872 36 7
370
2590 49 8
290
2320 64
384
3456 81 10
394
3940
100 11
452
4972
121 12
374
4488
144
Sum 78
3,688
27,274
650
計算 a, b 值
𝐲 = a + bx
x = 𝑥 𝑛 = = 6.5
𝑦 = 𝑦 𝑛 = 3, =
b = 𝑥𝑦 − 𝑛 𝑥 𝑦 𝑥 2 − 𝑛 𝑥 2 = 27,274 − (12)(6.5)(307.33) 650−(12) = 23.09
a = 𝑦 – 𝑥 = – (23.09)(6.5) =
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10.38

39. Figure 10.8 – Trend Line Fitted to Actual Demand and Projections for Quarters 13–15
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10.39

40. Techniques for Seasonality
Computing seasonal indices
Decomposing a time series using least- squares regression
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10.40

41. Seasonality
In time series, seasonality is expressed as the amount of deviation between actual demand and the average value of the series
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10.41

42. Types of seasonal patterns
Additive model: certain amount added to and subtracted from the average
夏天時，每天較平均值多3個
Multiplicative model: seasonality is a percentage of the average value or trend
冬天時，每天較平均值多 3%

43. Computing Seasonal Indices and Forecasting
Steps (先找出季節參數)
Calculate the average demand for each season.
the average demand for Quarter 1 is ( )/3 =
Calculate the overall average demand per season.
This is done by averaging the average demand for each season (computed in Step 1).
In our case, the overall average quarterly demand is ( )/4 =
Calculate the seasonal index.
This is done by dividing
the average demand per season (Step 1) by
the overall average demand per season (Step 2).
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10.42

44. Computing Seasonal Indices and Forecasting (cont.)
Step 1
Step 3
Quarter
Year 1
Year 2
Year 3
Quarter Average
Seasonal Index 1
155
299
384
279.33
0.91 2
198
312
394
301.33
0.98 3
250
370
452
357.33
1.16 4
210
290
374
291.33
0.95
Total
813
1,271
1,604
 Overall Average Demand per
Quarter
Step 2
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10.43

45. Computing Seasonal Indices and Forecasting (cont.)
Steps (cont.) (再預測需求、然後作季節調整)
Calculate the average demand in the next periods for which you want to obtain demand forecasts. The actual demand seems to increase by about 400 surgeries per year. With this upward trend in mind, we predict that the surgery volume in Year 4 will be about 2,000, or 500 per quarter.
Multiply the average demand projections by the seasonal indices.
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10.44

46. Computing Seasonal Indices and Forecasting (cont.)
Step 5
Quarter
Year 1
Year 2
Year 3
Quarter Average
Seasonal Index
Forecast (Year 4) 1
155
299
384
279.33
0.91
500 × 0.91 = 455 2
198
312
394
301.33
0.98
500 × 0.98 = 490 3
250
370
452
357.33
1.16
500 × 1.16 = 580 4
210
290
374
291.33
0.95
500 × 0.95 = 475
Total
813
1,271
1,604
2,000
Overall Average Demand per
Quarter
Step 4
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10.45

47. Decomposing a Time Series Using Least Squares Regression
Steps (與前一做法相同、先找出季節參數、然後去除季節因數)
Calculate the seasonal index as described in Steps 1, 2, and 3 of the previous section. In other words, we compute the average demand for each quarter based on our 3 years of data. Then we compute the overall average demand per quarter. Finally, we divide the average demand for each quarter by the overall average.
Deseasonalize the actual demand by dividing each original data point by the appropriate seasonal index. For example, the demand in the first quarter of Year 1 is 155. When we divide it by the seasonal index for Quarter 1, we obtain 155/0.91 =
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48. Decomposing a Time Series Using Least Squares Regression (cont.)
Step 1
Step 2
Year
Quarter
Actual Demand, y
Seasonal
Index
Deseasonalized Demand 1
155
0.91
155/0.91 = 2
198
0.98
198/0.98 = 3
250
1.16
250/1.16 = 4
210
0.95
210/0.95 =
299
299/0.91 =
312
312/0.98 =
370
370/1.16 =
290
290/0.95 =
384
384/0.91 =
394
394/0.98 =
452
452/1.16 =
374
374/0.95 =
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49. Decomposing a Time Series Using Least Squares Regression (cont.)
Steps (cont.) (找出迴歸方程式、預測需求、做季節因數調整)
Develop a regression equation for the deseasonalized data. The deseasonalized data are the dependent or y variable. The quarter numbers (1–12 over 3 years) are the independent or x variable. Using Excel, we obtain the following regression equation: y = x.
Use the regression equation to project demand in future periods.
Adjust the trend forecasts for seasonality by multiplying the trend value by the appropriate seasonal index.
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10.48

50. Decomposing a Time Series Using Least Squares Regression (cont.)
Step 4
Step 5
Year
Quarter
Actual Demand, y
Seasonal Index
Deseasonalized Demand
Trend,
Forecasts 1
155
0.91
155/0.91 =
184.47
× 0.91 = 2
198
0.98
198/0.98 =
206.80
× 0.98 = 3
250
1.16
250/1.16 =
229.13
× 1.16 = 4
210
0.95
210/0.95 =
251.46
× 0.95 =
299
299/0.91 =
273.79
× 0.91 =
312
312/0.98 =
296.12
× 0.98 =
370
370/1.16 =
318.45
× 1.16 =
290
290/0.95 =
340.78
× 0.95 =
384
384/0.91 =
363.11
× 0.91 =
394
394/0.98 =
385.44
× 0.98 =
452
452/1.16 =
407.77
× 1.16 =
374
374/0.95 =
430.10
× 0.95 =
1 (13)
452.43
× 0.91 =
2 (14)
474.76
× 0.98 =
3 (15)
497.09
× 1.16 =
4 (16)
519.42
× 0.95 =
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51. Figure 10.9 – Comparison of Actual Demand With Forecasts Adjusted for Trend and Seasonality
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10.50

52. Associative Models Multiple linear regression
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10.51

53. Multiple Linear Regression
Effect of predictor (independent) variables on an dependent variable
𝐲 = a + b1x1 + b2x2 + … + bnxn
where
𝐲 is the predicted value of the dependent variable, that is, demand a is the y-intercept, a constant b1, b2, and bn are the regression coefficients of x1, x2, and xn,
respectively x1, x2, and xn are the values of the first, second, and nth independent
variables
Example: see Table 10.12
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54. Figure 10.10 – Partial Excel Output for Nursing Home Beds
Coefficient of multiple determination
y = pop people below pov. level
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10.53

55. Summary Connecting concepts
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10.54

56. Figure 10.11 – Mind Map With Demand Forecasts Linking the Competitive Priorities
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10.55