Operations Management

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1 Operations Management Chapter 4 Forecasting PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 7e Operations Management, 9e 2008 Prentice Hall, Inc. 4 1

2 Outline Global Company Profile: Disney World What Is Forecasting? Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts 2008 Prentice Hall, Inc. 4 2

3 Outline Continued The Strategic Importance of Forecasting Human Resources Capacity Supply Chain Management Seven Steps in the Forecasting System 2008 Prentice Hall, Inc. 4 3

4 Outline Continued Forecasting Approaches Overview of Qualitative Methods Overview of Quantitative Methods 2008 Prentice Hall, Inc. 4 4

5 Outline Continued Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclical Variations in Data 2008 Prentice Hall, Inc. 4 5

6 Outline Continued Associative Forecasting Methods: Regression and Correlation Analysis Using Regression Analysis for Forecasting Standard Error of the Estimate Correlation Coefficients for Regression Lines Multiple-Regression Analysis 2008 Prentice Hall, Inc. 4 6

7 Outline Continued Monitoring and Controlling Forecasts Adaptive Smoothing Focus Forecasting Forecasting In The Service Sector 2008 Prentice Hall, Inc. 4 7

8 Learning Objectives When you complete this chapter you should be able to : Understand the three time horizons and which models apply for each use Explain when to use each of the four qualitative models Apply the naive, moving average, exponential smoothing, and trend methods 2008 Prentice Hall, Inc. 4 8

9 Learning Objectives When you complete this chapter you should be able to : Compute three measures of forecast accuracy Develop seasonal indexes Conduct a regression and correlation analysis Use a tracking signal 2008 Prentice Hall, Inc. 4 9

10 Forecasting at Disney World Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and Anaheim Revenues are derived from people how many visitors and how they spend their money Daily management report contains only the forecast and actual attendance at each park 2008 Prentice Hall, Inc. 4 10

11 Forecasting at Disney World Disney generates daily, weekly, monthly, annual, and 5-year 5 forecasts Forecast used by labor management, maintenance, operations, finance, and park scheduling Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted 2008 Prentice Hall, Inc. 4 11

12 Forecasting at Disney World 20% of customers come from outside the USA Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year 2008 Prentice Hall, Inc. 4 12

13 Forecasting at Disney World Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world Average forecast error for the 5-year 5 forecast is 5% Average forecast error for annual forecasts is between 0% and 3% 2008 Prentice Hall, Inc. 4 13

14 What is Forecasting? Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities?? 2008 Prentice Hall, Inc. 4 14

15 Forecasting Time Horizons Short-range range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels Medium-range forecast 3 months to 3 years Sales and production planning, budgeting Long-range forecast 3 + years New product planning, facility location, research and development 2008 Prentice Hall, Inc. 4 15

16 Distinguishing Differences Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes Short-termterm forecasting usually employs different methodologies than longer-term forecasting Short-termterm forecasts tend to be more accurate than longer-term forecasts 2008 Prentice Hall, Inc. 4 16

17 Influence of Product Life Cycle Introduction Growth Maturity Decline Introduction and growth require longer forecasts than maturity and decline As product passes through life cycle, forecasts are useful in projecting Staffing levels Inventory levels Factory capacity 2008 Prentice Hall, Inc. 4 17

18 Product Life Cycle Introduction Growth Maturity Decline Company Strategy/Issues Best period to increase market share R&D engineering is critical Sales Practical to change price or quality image Strengthen niche Internet search engines LCD & plasma TVs Xbox 360 ipods Poor time to change image, price, or quality Competitive costs become critical Defend market position Drive-through restaurants Cost control critical CD-ROMs Analog TVs 3 1/2 Floppy disks Figure Prentice Hall, Inc. 4 18

19 Product Life Cycle OM Strategy/Issues Introduction Growth Maturity Decline Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focus Enhance distribution Standardization Less rapid product changes more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Overcapacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Figure Prentice Hall, Inc. 4 19

20 Types of Forecasts Economic forecasts Address business cycle inflation rate, money supply, housing starts, etc. Technological forecasts Predict rate of technological progress Impacts development of new products Demand forecasts Predict sales of existing products and services 2008 Prentice Hall, Inc. 4 20

21 Strategic Importance of Forecasting Human Resources Hiring, training, laying off workers Capacity Capacity shortages can result in undependable delivery, loss of customers, loss of market share Supply Chain Management Good supplier relations and price advantages 2008 Prentice Hall, Inc. 4 21

22 Seven Steps in Forecasting Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results 2008 Prentice Hall, Inc. 4 22

23 The Realities! Forecasts are seldom perfect Most techniques assume an underlying stability in the system Product family and aggregated forecasts are more accurate than individual product forecasts 2008 Prentice Hall, Inc. 4 23

24 Forecasting Approaches Qualitative Methods Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet 2008 Prentice Hall, Inc. 4 24

25 Forecasting Approaches Quantitative Methods Used when situation is stable and historical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions 2008 Prentice Hall, Inc. 4 25

26 Overview of Qualitative Methods Jury of executive opinion Pool opinions of high-level experts, sometimes augment by statistical models Delphi method Panel of experts, queried iteratively 2008 Prentice Hall, Inc. 4 26

27 Overview of Qualitative Methods Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated Consumer Market Survey Ask the customer 2008 Prentice Hall, Inc. 4 27

28 Jury of Executive Opinion Involves small group of high-level experts and managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick Group-think disadvantage 2008 Prentice Hall, Inc. 4 28

29 Sales Force Composite Each salesperson projects his or her sales Combined at district and national levels Sales reps know customers wants Tends to be overly optimistic 2008 Prentice Hall, Inc. 4 29

30 Delphi Method Iterative group process, continues until consensus is reached 3 types of participants Decision makers Staff Respondents Staff (Administering survey) Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments) 2008 Prentice Hall, Inc. 4 30

31 Consumer Market Survey Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer 2008 Prentice Hall, Inc. 4 31

32 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model 2008 Prentice Hall, Inc. 4 32

33 Time Series Forecasting Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values, no other variables important Assumes that factors influencing past and present will continue influence in future 2008 Prentice Hall, Inc. 4 33

34 Time Series Components Trend Cyclical Seasonal Random 2008 Prentice Hall, Inc. 4 34

35 Components of Demand Demand for product or service Seasonal peaks Random variation Trend component Average demand over four years Year Actual demand Figure Prentice Hall, Inc. 4 35

36 Trend Component Persistent, overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration 2008 Prentice Hall, Inc. 4 36

37 Seasonal Component Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year Number of Period Length Seasons Week Day 7 Month Week Month Day Year Quarter 4 Year Month 12 Year Week Prentice Hall, Inc. 4 37

38 Cyclical Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships Prentice Hall, Inc. 4 38

39 Random Component Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen events Short duration and nonrepeating M T W T F 2008 Prentice Hall, Inc. 4 39

40 Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then February sales will be 68 Sometimes cost effective and efficient Can be good starting point 2008 Prentice Hall, Inc. 4 40

41 Moving Average Method MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Moving average = demand in previous n periods demand in previous n periods n 2008 Prentice Hall, Inc. 4 41

42 Moving Average Example Month Actual Shed Sales January 10 February 12 March 13 April 16 May 19 June 23 July 26 3-Month Moving Average ( )/3 = 11 2 / 3 ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / Prentice Hall, Inc. 4 42

43 Graph of Moving Average Shed Sales Moving Average Forecast Actual Sales J F M A M J J A S O N D 2008 Prentice Hall, Inc. 4 43

44 Weighted Moving Average Used when trend is present Older data usually less important Weights based on experience and intuition Weighted moving average = (weight for period n) n x (demand in period n) n weights 2008 Prentice Hall, Inc. 4 44

45 Weights Applied Period Weighted Moving 3 Last Average month 2 Two months ago 1 Three months ago 6 Sum of weights Month Actual Shed Sales January 10 February 12 March 13 April 16 May 19 June 23 July 26 3-Month Weighted Moving Average [(3 x 13) ) + (2 x 12) ) + (10( 10)]/6 = 12 1 / 6 [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / Prentice Hall, Inc. 4 45

46 Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data 2008 Prentice Hall, Inc. 4 46

47 Moving Average And Weighted Moving Average 30 Weighted moving average Sales demand Actual sales Moving average 5 Figure 4.2 J F M A M J J A S O N D 2008 Prentice Hall, Inc. 4 47

48 Exponential Smoothing Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant (α) Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data 2008 Prentice Hall, Inc. 4 48

49 Exponential Smoothing New forecast = Last period s s forecast + α (Last period s s actual demand Last period s s forecast) F t = F t 1 + α(a t 1 - F t 1 ) where F t = new forecast F t 1 = previous forecast α = smoothing (or weighting) constant (0 α 1) 2008 Prentice Hall, Inc. 4 49

50 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant α = Prentice Hall, Inc. 4 50

51 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant α =.20 New forecast = ( ) 2008 Prentice Hall, Inc. 4 51

52 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant α =.20 New forecast = ( ) = = cars 2008 Prentice Hall, Inc. 4 52

53 Effect of Smoothing Constants Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (α) α(1 - α) α(1 - α) 2 α(1 - α) 3 α(1 - α) 4 α = α = Prentice Hall, Inc. 4 53

54 Impact of Different α 225 Demand Actual demand α = Quarter α = Prentice Hall, Inc. 4 54

55 Impact of Different α Demand 225 Actual demand Chose high values of α 200 when underlying average is likely to change 175 Choose low values of Choose low values of α when underlying average is stable Quarter α =.5 α = Prentice Hall, Inc. 4 55

56 Choosing α The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error = Actual demand - Forecast value = A t - F t 2008 Prentice Hall, Inc. 4 56

57 Common Measures of Error Mean Absolute Deviation (MAD) MAD = Actual - Forecast n Mean Squared Error (MSE) MSE = ( Forecast Errors) 2 n 2008 Prentice Hall, Inc. 4 57

58 Common Measures of Error Mean Absolute Percent Error (MAPE) n 100 Actual i - Forecast i /Actual i MAPE = i = 1 n 2008 Prentice Hall, Inc. 4 58

59 Quarter Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Unloaded α =.10 α =.10 α =.50 α = Prentice Hall, Inc. 4 59

60 Quarter Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with n for with for Unloaded α =.10 α =.10 α =.50 α =.50 MAD = deviations For α = = 82.45/ = For α 175 = = 98.62/ = Prentice Hall, Inc. 4 60

61 MSE = Quarter Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with n for with for Unloaded α =.10 α =.10 α =.50 α =.50 For α =.10 (forecast errors) = 1,526.54/ = For α 175 = = 1,561.91/ = MAD Prentice Hall, Inc. 4 61

62 Comparison of Forecast n Error MAPE = Quarter i = 1 Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with n for with for Unloaded α =.10 α =.10 α =.50 α =.50 For α = deviation i /actual i = 44.75/ = % For 175 α = = 54.05/ = % MAD MSE Prentice Hall, Inc. 4 62

63 Comparison of Forecast Error Quarter Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Unloaded α =.10 α =.10 α =.50 α = MAD MSE MAPE 5.59% 6.76% 2008 Prentice Hall, Inc. 4 63

64 Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trend Exponentially smoothed (F t ) + forecast Exponentially (T t ) smoothed trend 2008 Prentice Hall, Inc. 4 64

65 Exponential Smoothing with Trend Adjustment F t = α(a t - 1 ) + (1 - α)( )(F t T t - 1 ) T t = β(f t - F t - 1 ) + (1 - β)t t - 1 Step 1: Compute F t Step 2: Compute T t Step 3: Calculate the forecast FIT t = F t + T t 2008 Prentice Hall, Inc. 4 65

66 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Table Prentice Hall, Inc. 4 66

67 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Step 1: Forecast for Month F 2 = αa 1 + (1 - α)(f 1 + T 1 ) 8 28 F = (.2)(12) + (1 -.2)(11 + 2) 10 = = 12.8 units Table Prentice Hall, Inc. 4 67

68 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Step 2: Trend for Month T 2 = β(f 2 - F 1 ) + (1 - β)t T = (.4)( ) + (1 -.4)(2) 10 = = 1.92 units Table Prentice Hall, Inc. 4 68

69 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Step 3: Calculate FIT for Month FIT 2 = F 2 + T FIT 2 = = units Table Prentice Hall, Inc. 4 69

70 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Table Prentice Hall, Inc. 4 70

71 Exponential Smoothing with Trend Adjustment Example Product demand Actual demand (A t ) Forecast including trend (FIT t ) with α =.2 and β = Time (month) Figure Prentice Hall, Inc. 4 71

72 Trend Projections Fitting a trend line to historical data points to project into the medium to long-range Linear trends can be found using the least squares technique ^ y ^ = a + bx where y = computed value of the variable to be predicted (dependent variable) a = y-axis y intercept b = slope of the regression line x = the independent variable 2008 Prentice Hall, Inc. 4 72

73 Least Squares Method Values of Dependent Variable Actual observation (y value) Deviation 1 (error) Deviation 3 Deviation 2 Deviation 5 Deviation 4 Deviation 7 Deviation 6 Trend line, y ^ = a + bx Time period Figure Prentice Hall, Inc. 4 73

74 Least Squares Method Values of Dependent Variable Actual observation (y value) Deviation 1 Deviation 3 Deviation 2 Deviation 5 Deviation 7 Deviation 6 Least squares method minimizes the sum of the Deviation squared errors 4 (deviations) Trend line, y ^ = a + bx Time period Figure Prentice Hall, Inc. 4 74

75 Least Squares Method Equations to calculate the regression variables y ^ = a + bx b = Σ xy - nxy Σx 2 - nx 2 a = y - bx 2008 Prentice Hall, Inc. 4 75

76 Least Squares Example Year Time Period (x) Electrical Power Demand x 2 xy x = 28 y = 692 x 2 = 140 xy = 3,063 x = 4 y = xy - nxy 3,063 - (7)(4)(98.86) b = = = x 2 - nx (7)(4 2 ) a = y - bx = (4) = Prentice Hall, Inc. 4 76

77 Least Squares Example Year Time Period (x) Electrical Power Demand x 2 xy The trend 3 line is y ^ 5= x Σx = 28 Σy = 692 Σx 2 = 140 Σxy = 3,063 x = 4 y = Σxy - nxy 3,063 - (7)(4)(98.86) b = = = Σx 2 - nx (7)(4 2 ) a = y - bx = (4) = Prentice Hall, Inc. 4 77

78 Least Squares Example Power demand Trend line, 160 y ^ = x Year 2008 Prentice Hall, Inc. 4 78

79 Least Squares Requirements 1. We always plot the data to insure a linear relationship 2. We do not predict time periods far beyond the database 3. Deviations around the least squares line are assumed to be random 2008 Prentice Hall, Inc. 4 79

80 Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand 2008 Prentice Hall, Inc. 4 80

81 Seasonal Variations In Data Steps in the process: 1. Find average historical demand for each season 2. Compute the average demand over all seasons 3. Compute a seasonal index for each season 4. Estimate next year s s total demand 5. Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season 2008 Prentice Hall, Inc. 4 81

82 Seasonal Index Example Demand Average Average Month Monthly Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Seasonal Index 2008 Prentice Hall, Inc. 4 82

83 Seasonal Index Example Demand Average Average Month Monthly Jan Feb Mar average monthly demand 94 Apr Seasonal 90 index 95 = 115 average monthly 100 demand 94 May = 90/94 =.957 Jun Jul Aug Sept Oct Nov Dec Seasonal Index Prentice Hall, Inc. 4 83

84 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Prentice Hall, Inc. 4 84

85 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Forecast 85 for Mar Apr 90 Expected annual demand 100 = 1, May Jun , Jul Jan 113 x = Aug ,200 Sept Feb 95 x = Oct Nov Dec Prentice Hall, Inc. 4 85

86 Seasonal Index Example Demand Forecast 2007 Demand 2006 Demand 2005 Demand J F M A M J J A S O N D Time 2008 Prentice Hall, Inc. 4 86

87 San Diego Hospital Trend Data Inpatient Days 10,200 10,000 9,800 9,600 9, ,200 9,000 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Month Figure Prentice Hall, Inc. 4 87

88 San Diego Hospital Seasonal Indices Index for Inpatient Days Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Month Figure Prentice Hall, Inc. 4 88

89 San Diego Hospital Combined Trend and Seasonal Forecast Inpatient Days 10,200 10,000 9,800 9,600 9,400 9,200 9, Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Month Figure Prentice Hall, Inc. 4 89

90 Associative Forecasting Used when changes in one or more independent variables can be used to predict the changes in the dependent variable Most common technique is linear regression analysis We apply this technique just as we did in the time series example 2008 Prentice Hall, Inc. 4 90

91 Associative Forecasting Forecasting an outcome based on predictor variables using the least squares technique y ^ = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis y intercept b = slope of the regression line x = the independent variable though to predict the value of the dependent variable 2008 Prentice Hall, Inc. 4 91

92 Associative Forecasting Example Sales Local Payroll ($ millions), y ($ billions), x Sales Area payroll 2008 Prentice Hall, Inc. 4 92

93 Associative Forecasting Example Sales, y Payroll, x x 2 xy y = 15.0 x = 18 x 2 = 80 xy = 51.5 x = x/6 = 18/6 = 3 y = y/6 = 15/6 = 2.5 xy - nxy b = = =.25 x 2 - nx (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx x = (.25)(3) = Prentice Hall, Inc. 4 93

94 Associative Forecasting Example y ^ = x Sales = (payroll payroll) If payroll next year is estimated to be $6 billion, then: Sales = (6) Sales = $3,250, Sales Area payroll 2008 Prentice Hall, Inc. 4 94

95 Standard Error of the Estimate A forecast is just a point estimate of a future value This point is actually the mean of a probability distribution Sales Figure Area payroll 2008 Prentice Hall, Inc. 4 95

96 Standard Error of the Estimate S y,x = (y - y c ) 2 n - 2 where y = y-value of each data point y c = computed value of the dependent variable, from the regression equation n = number of data points 2008 Prentice Hall, Inc. 4 96

97 Standard Error of the Estimate Computationally, this equation is considerably easier to use S y,x = y 2 - a y - b xy n - 2 We use the standard error to set up prediction intervals around the point estimate 2008 Prentice Hall, Inc. 4 97

98 Standard Error of the Estimate y,x = y 2 - a y - b xy = n - 2 S y,x (15) -.25(51.5) 6-2 S y,x =.306 The standard error of the estimate is $306,000 in sales Sales Area payroll 2008 Prentice Hall, Inc. 4 98

99 Correlation How strong is the linear relationship between the variables? Correlation does not necessarily imply causality! Coefficient of correlation, r, measures degree of association Values range from -1 to Prentice Hall, Inc. 4 99

100 Correlation Coefficient r = nσxy - ΣxΣy [nσx 2 - (Σx) 2 ][nσy 2 - (Σy) 2 ] 2008 Prentice Hall, Inc

101 y Correlation Coefficient y r = (a) Perfect positive correlation: r = +1 nσxy - ΣxΣy [nσx 2 - (Σx) 2 ][nσy 2 - (Σy) 2 ] x (b) Positive correlation: 0 < r < 1 x y y (c) No correlation: r = 0 x (d) Perfect negative correlation: r = Prentice Hall, Inc x

102 Correlation Coefficient of Determination, r 2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret For the Nodel Construction example: r =.901 r 2 = Prentice Hall, Inc

103 Multiple Regression Analysis If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables y ^ = a + b 1 x 1 + b 2 x 2 Computationally, this is quite complex and generally done on the computer 2008 Prentice Hall, Inc

104 Multiple Regression Analysis In the Nodel example, including interest rates in the model gives the new equation: ^ y = x 1-5.0x 2 An improved correlation coefficient of r =.96 means this model does a better job of predicting the change in construction sales Sales = (6) - 5.0(.12) = 3.00 Sales = $3,000, Prentice Hall, Inc

105 Monitoring and Controlling Forecasts Tracking Signal Measures how well the forecast is predicting actual values Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, the forecast has a bias error 2008 Prentice Hall, Inc

106 Monitoring and Controlling Forecasts Tracking signal Tracking signal = = RSFE MAD (Actual demand in period i - Forecast demand in period i) ( Actual - Forecast /n) 2008 Prentice Hall, Inc

107 Tracking Signal + Signal exceeding limit Upper control limit Tracking signal 0 MADs Acceptable range Lower control limit Time 2008 Prentice Hall, Inc

108 Tracking Signal Example Qtr Actual Demand Forecast Demand Error RSFE Absolute Forecast Error Cumulative Absolute Forecast Error MAD Prentice Hall, Inc

109 Tracking Signal Example Qtr Actual Demand Tracking Signal (RSFE/MAD) Forecast Demand Error RSFE Absolute Forecast Error Cumulative Absolute Forecast Error MAD /100 = / = / = / = / = / = The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits 2008 Prentice Hall, Inc

110 Adaptive Forecasting It s s possible to use the computer to continually monitor forecast error and adjust the values of the α and β coefficients used in exponential smoothing to continually minimize forecast error This technique is called adaptive smoothing 2008 Prentice Hall, Inc

111 Focus Forecasting Developed at American Hardware Supply, focus forecasting is based on two principles: 1. Sophisticated forecasting models are not always better than simple ones 2. There is no single technique that should be used for all products or services This approach uses historical data to test multiple forecasting models for individual items The forecasting model with the lowest error is then used to forecast the next demand 2008 Prentice Hall, Inc

112 Forecasting in the Service Sector Presents unusual challenges Special need for short term records Needs differ greatly as function of industry and product Holidays and other calendar events Unusual events 2008 Prentice Hall, Inc

113 Fast Food Restaurant Forecast Percentage of sales 20% 15% 10% 5% (Lunchtime) (Dinnertime) Hour of day Figure Prentice Hall, Inc

114 FedEx Call Center Forecast 12% 10% 8% 6% 4% 2% 0% A.M. P.M. Hour of day Figure Prentice Hall, Inc