1. Introduction to Operations Management
Forecasting (Ch.3)
Hansoo Kim (金翰秀)
Dept. of Management Information Systems, YUST

2. X X X X X X X X OM Overview Class Overview (Ch. 0)
Operations, Productivity,
and Strategy
(Ch. 1, 2) X
Project Management
(Ch. 17)
Strategic
Capacity
Planning
(Ch. 5, 5S)
Process
Selection/ Facility Layout; LP
(Ch. 6, 6S) X X X
Mgmt of Quality/ Six Sigma Quality
(Ch. 9, 10) X X
Queueing/
Simulation
(Ch. 18)
Supply Chain Management
(Ch 11) X
Location Planning
and Analysis
(Ch. 8)
JIT &
Lean Mfg System
(Ch. 15)
Demand Mgmt Forecasting
(Ch 3)
Aggregated Planning
(Ch. 13)
Inventory Management
(Ch. 12)
MRP & ERP
(Ch 14)
Term Project

3. Today’s Outline What is Forecasting? 수요예측이란? Types of Forecasting 종류
Seven Steps of Forecasting 절차
Qualitative vs. Quantitative Forecasts 정성적/정량적 방법
Various Forecasting Methods 여러 가지 수요예측 방법들
Evaluation Measures 평가방법

4. Terms(용어) Associative models （联合模型） Bias （偏差）
Centered moving average （中心滑动平均数）
Control chart （控制图）
Correlation （想关系数）
Cycles （循环变动）
Delphi method （德尔菲法）
Error （误差）
Exponential smoothing （指数平滑法）
Forecast  (预册)
Irregular variation （不规则变化）
Judgmental forecasts （通过判断作出预测）
Least square line （最小二乘直线）
Linear trend equation （线形趋势模型）
Mean absolute deviation, MAD （绝对平均偏差）
Mean squared error, MSE （标准偏差）
Moving average （滑动平均法）
Naive forecast （简单预测法）
Predictor variable （预测变动）
Random variations （随机变量）
Regression （回归分析）
Seasonal variations （季节性变动）
Time series （时间序列）
Tracking signal （跟踪信号）
Trend （长期趋势变动）
Trend-adjusted exponential smoothing （调整长期趋势后的指数平滑法）

5. Example: Forecasting What is demand in 21st week?
Demand > Products --- Lost Sales
Demand < Products --- Inventory cost 
What is demand in 21st week?

6. What is Forecasting? The art and science of predicting future events,
Using historical data
Underlying basis of all business decisions
Production
Inventory
Personnel
Facilities
Sales will be $200 Million!
CRM: Customer Relation Management

7. Uses of Forecasts Accounting Cost/profit estimates Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services

8. Types of Forecasts by Time Horizon
Short-range forecast (단기 예측)
Up to 1 year; usually less than 3 months
Job scheduling, worker assignments
Medium-range forecast (중기 예측)
3 months to 3 years
Sales & production planning, budgeting
Long-range forecast (장기 예측)
3+ years
New product planning, facility location, R&D

9. Influence of Product Life Cycle
Introduction, Growth, Maturity, Decline
(도입기, 성장기, 성숙기, 쇠퇴기)
Stages of introduction and growth require longer forecasts than maturity and decline
Forecasts useful in projecting
staffing levels,
inventory levels, and
factory capacity
as product passes through life cycle stages

10. Strategy and Issues During a Product’s Life

11. Types of Forecasts (종류)
Economic forecasts (경제예측)
Address business cycle, e.g., inflation rate, money supply etc.
Technological forecasts (기술예측)
Predict rate of technological progress
Predict acceptance of new product
Demand forecasts (수요예측)
Predict sales of existing product

12. Steps in the Forecasting Process
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”

13. Realities of Forecasting
Forecasts are seldom perfect (수요예측은 잘 맞지 않는다!!)
Most forecasting methods assume that there is some underlying stability in the system (신제품 보다는 성숙기에 도달한 제품)
Both product family and aggregated product forecasts are more accurate than individual product forecasts (단일제품 보다는 제품群으로 예측하는 것이 더 정확하다)

14. Forecasting Approaches
Qualitative Methods (정성적방법)
Quantitative Methods (정량적방법)
Used when situation is vague & little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting sales on Internet
Used when situation is ‘stable’ & historical data exist
Existing products
Current technology
Involves mathematical techniques
e.g., forecasting sales of color televisions

15. Overview of Qualitative Methods (정성적인 방법들)
Jury of executive opinion
Pool opinions of high-level executives, sometimes augment by statistical models
Delphi method (델파이 기법)**
Panel of experts, queried iteratively
Sales force composite
Estimates from individual salespersons are reviewed for reasonableness, then aggregated
Consumer Market Survey
Ask the customer

16. Overview of Quantitative Approaches
Naïve approach
Moving averages
Exponential smoothing
Trend projection
Linear regression
Time-series Models
Associative models

17. What is a Time Series? Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values
Assumes that factors influencing past and present will continue influence in future
Example
Year:
Sales:

18. Product Demand Charted over 4 Years with Trend and Seasonality1 2 3 4
Seasonal peaks
Trend component
Actual demand line
Average demand over four years
Demand for product or service
Random variation

19. Time Series Components
Trend
Seasonal
Cyclical
Random

20. Trend Component Persistent, overall upward or downward pattern
Due to population, technology etc.
Several years duration
Mo., Qtr., Yr.
Response
© T/Maker Co.

21. Seasonal Component Regular pattern of up & down fluctuations
Due to weather, customs etc.
Occurs within 1 year
Mo., Qtr.
Response
Summer
© T/Maker Co.

22.  Cyclical Component Repeating up & down movements
Due to interactions of factors influencing economy
Usually 2-10 years duration
Mo., Qtr., Yr.
Response
Cycle 

23. Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Union strike
Tornado
Short duration & nonrepeating
© T/Maker Co.

24. Overview of Qualitative Methods (정량적인 방법들)
Naïve Approach
Moving Average (MA) 滑动平均法
Weighted Moving Average
Exponential Smoothing Method (指数平滑法 )
Exponential Smoothing with Trend Adjustment (调整长期趋势后的指数平滑法 )

25. Naive Approach (简单预测法)
Assumes demand in next period is the same as demand in most recent period
e.g., If May sales were 48, then June sales will be 48
Sometimes cost effective & efficient
© 1995 Corel Corp.

26. Moving Average (MA) Method 滑动平均法
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time
Equation MA n  
Demand in
Previous
Periods

27. Moving Average where Ft = Forecast for time period t
MAn = n period moving average
At – 1 = Actual value in period t – 1
n = Number of periods (data points) in the moving average
For example, MA3 would refer to a three-period moving average forecast, and MA5 would refer to a five-period moving average forecast.

28. Moving Average Example
You’re manager of a museum store that sells historical replicas. You want to forecast sales for 2008 using a 3-period moving average
© 1995 Corel Corp.

29. Moving Average Solution

30. Weighted Moving Average Method
Used when trend is present
Older data usually less important
Weights based on intuition
Often lay between 0 & 1, & sum to 1.0
Equation
Σ(Weight for period n) (Demand in period n)
WMA =
ΣWeights

31. Actual Demand, Moving Average, Weighted Moving Average
Actual sales
Moving average

32. Disadvantages of Moving Average Methods
Increasing n makes forecast less sensitive to changes
Do not forecast trend well
Require much historical
data

33. Measure for Forecasting Error
Mean Square Error (MSE,标准偏差)
Mean Absolute Deviation (MAD,绝对平均偏差 )
Mean Absolute Percent Error (MAPE)

34. Exponential Smoothing Method (指数平滑法)
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Subjectively chosen
Involves little record keeping of past data

35. Exponential Smoothing Equations
Ft = At -1 + (1- )At -2 + (1- )2·At (1- )3At (1- )t-1·A0
Ft = Forecast value
At = Actual value
 = Smoothing constant
Ft = Ft-1 + (At-1 - Ft-1) = At-1+(1- ) Ft-1
Use for computing forecast

36. Exponential Smoothing Example
During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. ( = .10). The first quarter forecast was 175..
Quarter Actual
6 205
7 180
8 182
9 ?
Find the forecast for the 9th quarter.

37. Exponential Smoothing Solution
Ft = Ft (At-1 - Ft-1)
Forecast, F
Quarter
Actual t ( α
= .10) 1
180
(Given) 2
168
( ) = 3
159
( ) = 4
175
( ) = 5
190
( ) = 6
205
( ) =

38. Exponential Smoothing Solution
Ft = Ft (At-1 - Ft-1)
Forecast, F
Time
Actual t ( α
= .10) 4
175
( ) = 5
190
( ) =
205 6
( ) = 7
180
( ) = 8
182
( ) = 9 ?
( ) =

39. Forecast Effects of Smoothing Constant 
Ft =  At (1- ) At (1- )2At
= At-1+(1- ) Ft-1
Weights
Prior Period 
2 periods ago
(1 - )
3 periods ago
(1 - )2 =
= 0.10
= 0.90
10% 9%
8.1%
90% 9%
0.9%

40. Impact of 

41. Choosing  Seek to minimize the Mean Absolute Deviation (MAD)
If: Forecast error = demand - forecast
Then:

42. Exponential Smoothing with Trend Adjustment
Forecast including trend (FITt)
= exponentially smoothed forecast (Ft)
+ exponentially smoothed trend (Tt)

43. Exponential Smoothing with Trend Adjustment - continued
Ft = exponentially smoothed forecast of the data series in period t
Tt = exponentially smoothed trend in period t
At = actual demand in period t
 = smoothing constant for the average
 = smoothing constant for the trend

44. Exponential Smoothing with Trend Adjustment - continued
Ft =  (Actual Demand of last period) + (1-)(Forecast last period’s actual + Trend Estimates last Period) or
Ft = (At-1) + (1-  )(Ft-1 + Tt-1)
Tt = (Forecast this period - Forecast last period)
+ (1-)(Trend estimate last period) or
Tt = (Ft - Ft-1) + (1- )Tt-1
Forecast including trend (FITt) = Ft + Tt

45. Using MS-Excel
Naïve MA
WMA
Exponential Smoothing Method

46. Associative Model: Regression (회기분석,回归分析 )
Actual observation
Deviation
Deviation
Deviation
Deviation
Point on regression line
Deviation
Values of Dependent Variable
Deviation
Deviation
Time

47. Actual and the Least Squares Line
This slide illustrates a regression line along with the actual demand. You might wish to highlight the actual deviations.

48. Linear Trend Projection
Used for forecasting linear trend line
Assumes relationship between response variable, Y, and time, X, is a linear function
Estimated by least squares method
Minimizes sum of squared errors i Y a bX = +

49. Linear Trend Projection ModelY
b > 0 a
b < 0 a
Time, X

50. Least Squares Equations
Slope:
Y-Intercept:

51. Computation Table (계산표)X i Y 2 1 : n Σ
This slide illustrates how one might do, by hand, the calculations required to solve for the linear trend coefficients. If you are expecting students to solve even the simplest linear trend or regression problems using a computer program, you may wish to skip this slide.

52. Using Regression Model
The demand for electrical power at N.Y.Edison over the years 2000 – 2006 is given at the left. Find the overall trend.
Year Demand

53. Calculation for finding a and b
Year
Time Period
Power Demand x2 xy
2000 1 74
2001 2 79 4
158
2002 3 80 9
240
2003 90 16
360
2004 5
105 25
525
2005 6
142 36
852
2006 7
122 49
854
x=28
y=692
x2=140
xy=3,063

54. The Trend Line Equation

55. Actual and Trend Forecast

56. Correlation (상관관계)
Answers: ‘how strong is the linear relationship between the variables?’
Coefficient of correlation Sample correlation coefficient denoted r
Values range from -1 to +1
Measures degree of association
Used mainly for understanding
This slide can frame the start of a discussion of correlation.. You should probably expect to add to this a discussion of cause and effect, emphasizing in particular that correlation does not imply a cause and effect relationship. Ask student to suggest examples of significant correlation of unrelated phenomenon.

57. Sample Coefficient of Correlation (想关系数)
Here again an explanation of each variable is probably useful.

58. Coefficient of Correlation and Regression ModelY X i = a + b ^
This slide presents additional examples of the meaning of the correlation coefficient.
r2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation

59. Guidelines for Selecting Forecasting Model
You want to achieve:
No pattern or direction in forecast error
Error (or Bias) = (Yi - Yi) = (Actual - Forecast)
Seen in plots of errors over time
Smallest forecast error
Mean square error (MSE)
Mean absolute deviation (MAD) ^
This slide introduces overall guideline for selecting a forecasting model. You may also wish to re-emphasize the role of scatter plots, and discuss the role of “understanding what is going on” (especially in limiting one’s choice of model).

60. Pattern of Forecast Error
Trend Not Fully Accounted for
Desired Pattern
Time (Years)
Error
Time (Years)
Error
This slide illustrates both possible patterns in forecast error, and the merit of making a scatter plot of forecast error.

61. Selecting Forecasting Model Example
You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use?
Actual Linear Model Exponential
Smoothing Year Sales Forecast Forecast (.9)
This slide begins an example of choosing a model.

62. Linear Model EvaluationY i 1 2 4 ^
0.6
1.3
2.0
2.7
3.4
Year
2003
2004
2005
2006
2007
Total
0.4
-0.3
0.0
-0.7
Error
0.16
0.09
0.00
0.49
0.36
1.10
Error2
0.3
0.7
|Error|
Actual
0.40
0.30
0.35
0.15
1.20
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240

63. Exponential Smoothing Model Evaluation
Year
2003
2004
2005
2006
2007
Total Y i 1 2 4
1.0
0.0
1.9
0.1
2.0
3.8
0.2
0.3 ^
Error
0.00
0.01
0.04
0.05
Error2
|Error|
Actual
0.10
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02

64. Exponential Smoothing Model Evaluation (어떤 모델이 더 좋은가?)
Linear Model:
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240
Exponential Smoothing Model:
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02
This slide presents the result of the calculations of MSE and MAD for the Linear and Exponential Smoothing models.
Students should be asked to choose the “better” model.
Students should also be asked to consider the differences between the values calculated for the error measures for a given model, and between the two models. Do these differences tell us more than simply that one model is preferable to the other? (For example, is the exponential smoothing model 22 times better than the linear model?)

65. Tracking Signal (跟踪信号)
Measures how well the forecast is predicting actual values
Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) = RSFE/MAD
Good tracking signal has low values
Should be within upper and lower control limits

66. Tracking Signal Equation

67. Tracking Signal ComputationMo
Fcst
Act
Error
RSFE
Abs
Cum
MAD TS 1
100 90 2 95 3
115 4 5
125 6
140
|Error|

68. Tracking Signal ComputationMo
Forc
Act
Error
RSFE
Abs
Cum
MAD TS 1
100 90 2 95 3
115 4 5
125 6
140
-10 10
10.0 -1 -5
-15 15
7.5 -2
|Error|
TS = RSFE/MAD = -15/7.5 = -2
This slide illustrates the last step in the calculation of a tracking signal for a simple example problem. The PowerPoint slide presentation contains this as the last of a sequence of slides - the others stepping through the actual calculation process.

69. Plot of a Tracking Signal
Signal exceeded limit
Tracking signal
Upper control limit +
MAD
Acceptable range
This slide illustrates a graph of a tracking signal form a “practical” problem. -
Lower control limit
Time

70. The % of Points included within the Control Limits for a range of 1 to 4 MAD3 2 4
±1 MAD
±2 MAD
±3 MAD
±4 MAD
Number of MAD
Related STDEV % ±1
0.798
57.048% ±2
1.596
88.946% ±3
2.394
98.334% ±4
3.192
99.895%

71. Formula Review

72. Summary What is Forecasting? Types of Forecasting Evaluation Measures
Qualitative Methods
Quantitative Methods
Naïve MA
Exponential Smoothing
Regression
Evaluation Measures
MSE, MAD, MAPE

73. What to do HW
Example 1, 2, 3, 8, 9, 10
Solved Problems 1, 6, 7