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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 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 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 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-term forecasting usually employs different methodologies than longer-term forecasting Short-term 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 Best period to Practical to change Poor time to Cost control Company Strategy/Issues increase market price or quality change image, critical share image price, or quality R&D engineering is Strengthen niche Competitive costs critical become critical Defend market position CD-ROMs Internet search engines Analog TVs Drive-through LCD & plasma TVs restaurants Sales iPods 3 1/2” Xbox 360 Floppy disks Figure 2.5© 2008 Prentice Hall, Inc. 4 – 18
- 19. Product Life Cycle Introduction Growth Maturity Decline Product design Forecasting Standardization Little product and critical Less rapid differentiation development Product and product changes Cost OM Strategy/Issues critical process – more minor minimization Frequent reliability changes Overcapacity product and Competitive Optimum in the process design product capacity industry changes improvements Increasing Prune line to Short production and options stability of eliminate runs Increase capacity process items not High production returning Shift toward Long production costs good margin product focus runs Limited models Reduce Enhance Product capacity Attention to distribution improvement and quality cost cutting Figure 2.5© 2008 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 Decision Makers (Evaluate process, responses and continues until make decisions) consensus is reached Staff 3 types of (Administering survey) participants Decision makers Staff Respondents (People who can Respondents 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 Time-Series 3. Exponential Models smoothing 4. Trend projection Associative 5. Linear regression 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 Trend component Demand for product or service Seasonal peaks Actual demand Average demand over Random four years variation | | | | 1 2 3 4 Year Figure 4.1© 2008 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 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52© 2008 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 0 5 10 15 20© 2008 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 ∑ demand in previous n periods Moving average = n© 2008 Prentice Hall, Inc. 4 – 41
- 42. Moving Average Example Actual 3-Month Month Shed Sales Moving Average January 10 February 12 March 13 April 16 (10 + 12 + 13)/3 = 11 2/3 May 19 (12 + 13 + 16)/3 = 13 2/3 June 23 (13 + 16 + 19)/3 = 16 July 26 (16 + 19 + 23)/3 = 19 1/3© 2008 Prentice Hall, Inc. 4 – 42
- 43. Graph of Moving Average Moving Average 30 – 28 – Forecast 26 – Actual 24 – Sales Shed Sales 22 – 20 – 18 – 16 – 14 – 12 – 10 – | | | | | | | | | | | | 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 ∑ (weight for period n) Weighted x (demand in period n) moving average = ∑ weights© 2008 Prentice Hall, Inc. 4 – 44
- 45. Weights Applied Period Weighted Moving Last month 3 Average 2 Two months ago 1 Three months ago 6 Sum of weights Actual 3-Month Weighted Month Shed Sales Moving Average January 10 February 12 March 13 April 16 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 June 23 [(3 x 19) + (2 x 16) + (13)]/6 = 17 July 26 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2© 2008 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 Weighted moving 30 – average 25 – Sales demand 20 – Actual sales 15 – Moving 10 – 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 Smoothingt = Last period’s forecast + α (Last period’s actual demand – Last period’s forecast) Ft = Ft – 1 + α (At – 1 - Ft – 1) where Ft = new forecast Ft – 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 = .20© 2008 Prentice Hall, Inc. 4 – 50
- 51. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant α = .20 New forecast = 142 + .2(153 – 142)© 2008 Prentice Hall, Inc. 4 – 51
- 52. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant α = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 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 ) α (1 - α ) α (1 - α )4 2 3 α = .1 .1 .09 .081 .073 .066 α = .5 .5 .25 .125 .063 .031© 2008 Prentice Hall, Inc. 4 – 53
- 54. Impact of Different α 225 – Actual α = .5 200 – demand Demand 175 – 150 – α = .1 | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter© 2008 Prentice Hall, Inc. 4 – 54
- 55. Impact of Different α 225 – Actual α = .5 Chose high values of α 200 – demand when underlying average Demand is likely to change 175 – Choose low values of α when underlying average 150 – α = .1 is stable| | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter© 2008 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 = At - F t© 2008 Prentice Hall, Inc. 4 – 56
- 57. Common Measures of Error Mean Absolute Deviation (MAD) ∑ |Actual - Forecast| MAD = n Mean Squared Error (MSE) ∑ (Forecast Errors)2 MSE = n© 2008 Prentice Hall, Inc. 4 – 57
- 58. Common Measures of Error Mean Absolute Percent Error (MAPE) n ∑ 100|Actuali i=1 - Forecasti|/Actuali MAPE = n© 2008 Prentice Hall, Inc. 4 – 58
- 59. Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62© 2008 Prentice Hall, Inc. 4 – 59
- 60. Comparison of Forecast Error ∑ |deviations| Rounded Absolute Rounded Absolute MAD = Actual Forecast Deviation Forecast Deviation Tonnage n with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 For α180.10 175 = 5.00 175 5.00 2 168 = 82.45/8 = 10.31 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 For α175.50 173.18 = 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 = 98.62/8 175.02 = 12.33 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62© 2008 Prentice Hall, Inc. 4 – 60
- 61. Comparison of Forecast Error ∑ (forecast errors)2 Rounded Absolute Rounded Absolute MSE = Actual Forecast Deviation Forecast Deviation Tonnage n with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 For α180.10 175 = 5.00 175 5.00 2 168 1,526.54/8 = 190.82 = 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 For α175.50 173.18 = 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 2051,561.91/8 = 175.02 = 195.24 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33© 2008 Prentice Hall, Inc. 4 – 61
- 62. Comparison of Forecast n Error i=1 ∑ 100|deviationi|/actuali Rounded Absolute Rounded Absolute MAPE = Actual Forecast Deviation Forecast Deviation Tonnage with Quarter Unloaded α = .10 n α for = .10 with α = .50 for α = .50 1 α For 180= .10 175 5.00 175 5.00 2 168 = 44.75/8 = 7.50 175.5 5.59% 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 For α= 175 .50 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 = 54.05/8 = 6.76% 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24© 2008 Prentice Hall, Inc. 4 – 62
- 63. Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24 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 Exponentially Exponentially including (FITt) = smoothed (Ft) + (Tt) smoothed trend forecast trend© 2008 Prentice Hall, Inc. 4 – 64
- 65. Exponential Smoothing with Trend Adjustment Ft = α (At - 1) + (1 - α )(Ft - 1 + Tt - 1) Tt = β (Ft - Ft - 1) + (1 - β )Tt - 1 Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt = Ft + Tt© 2008 Prentice Hall, Inc. 4 – 65
- 66. Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Table 4.1© 2008 Prentice Hall, Inc. 4 – 66
- 67. Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 Step 1: Forecast for Month 2 6 21 7 31 F2 = αA1 + (1 - α)(F1 + T1) 8 28 9 36 F2 = (.2)(12) + (1 - .2)(11 + 2) 10 = 2.4 + 10.4 = 12.8 units Table 4.1© 2008 Prentice Hall, Inc. 4 – 67
- 68. Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 3 20 4 19 5 24 Step 2: Trend for Month 2 6 21 7 31 T2 = β(F2 - F1) + (1 - β)T1 8 28 9 36 T2 = (.4)(12.8 - 11) + (1 - .4)(2) 10 = .72 + 1.2 = 1.92 units Table 4.1© 2008 Prentice Hall, Inc. 4 – 68
- 69. Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 3 20 4 19 5 24 Step 3: Calculate FIT for Month 2 6 21 7 31 FIT2 = F2 + T1 8 28 FIT2 = 12.8 + 1.92 9 36 10 = 14.72 units Table 4.1© 2008 Prentice Hall, Inc. 4 – 69
- 70. Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 14.72 3 20 15.18 2.10 17.28 4 19 17.82 2.32 20.14 5 24 19.91 2.23 22.14 6 21 22.51 2.38 24.89 7 31 24.11 2.07 26.18 8 28 27.14 2.45 29.59 9 36 29.28 2.32 31.60 10 32.48 2.68 35.16 Table 4.1© 2008 Prentice Hall, Inc. 4 – 70
- 71. Exponential Smoothing with Trend Adjustment Example 35 – Actual demand (At) 30 – Product demand 25 – 20 – 15 – 10 – Forecast including trend (FITt) with α = .2 and β = .4 5 – 0 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 Figure 4.3 Time (month)© 2008 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 intercept b = slope of the regression line© 2008 Prentice Hall, Inc. x = the independent variable 4 – 72
- 73. Values of Dependent Variable Least Squares Method Actual observation Deviation7 (y value) Deviation5 Deviation6 Deviation3 Deviation4 Deviation1 (error) Deviation2 ^ Trend line, y = a + bx Time period Figure 4.4© 2008 Prentice Hall, Inc. 4 – 73
- 74. Values of Dependent Variable Least Squares Method Actual observation Deviation7 (y value) Deviation5 Deviation6 Deviation3 Least squares method minimizes the sum of the Deviation squared errors (deviations) 4 Deviation1 Deviation2 ^ Trend line, y = a + bx Time period Figure 4.4© 2008 Prentice Hall, Inc. 4 – 74
- 75. Least Squares Method Equations to calculate the regression variables ^ y = a + bx Σ xy - nxy b= Σ x2 - nx2 a = y - bx© 2008 Prentice Hall, Inc. 4 – 75
- 76. Least Squares Example Time Electrical Power Year Period (x) Demand x2 xy 2001 1 74 1 74 2002 2 79 4 158 2003 3 80 9 240 2004 4 90 16 360 2005 5 105 25 525 2005 6 142 36 852 2007 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x=4 y = 98.86 ∑xy - nxy 3,063 - (7)(4)(98.86) b= = = 10.54 ∑x - nx 2 2 140 - (7)(4 ) 2 a = y - bx = 98.86 - 10.54(4) = 56.70© 2008 Prentice Hall, Inc. 4 – 76
- 77. Least Squares Example Time Electrical Power Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 The trend line is 80 2001 3 9 240 2002 4 90 16 360 2003 ^= y 5 56.70 + 10.54x 105 25 525 2004 6 142 36 852 2005 7 122 49 854 Σ x = 28 Σ y = 692 Σ x2 = 140 Σ xy = 3,063 x=4 y = 98.86 Σ xy - nxy 3,063 - (7)(4)(98.86) b= = = 10.54 Σ x - nx 2 2 140 - (7)(4 ) 2 a = y - bx = 98.86 - 10.54(4) = 56.70© 2008 Prentice Hall, Inc. 4 – 77
- 78. Least Squares Example Trend line, 160 – ^ 150 – y = 56.70 + 10.54x 140 – Power demand 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – | | | | | | | | | 2001 2002 2003 2004 2005 2006 2007 2008 2009 Year© 2008 Prentice Hall, Inc. 4 – 78
- 79. Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand© 2008 Prentice Hall, Inc. 4 – 80
- 80. 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 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
- 81. Seasonal Index Example Demand Average Average Seasonal Month 2005 2006 2007 2005-2007 Monthly Index Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 Jun 110 115 120 115 94 Jul 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov 75 72 83 80 94 Dec 82 78 80 80 94© 2008 Prentice Hall, Inc. 4 – 82
- 82. Seasonal Index Example Demand Average Average Seasonal Month 2005 2006 2007 2005-2007 Monthly Index Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 Mar 80 93 average 2005-2007 monthly demand 82 85 94 Seasonal index = 115 Apr 90 95 100 94 average monthly demand May 113 125 131 123 94 = 90/94 = .957 Jun 110 115 120 115 94 Jul 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov 75 72 83 80 94 Dec 82 78 80 80 94© 2008 Prentice Hall, Inc. 4 – 83
- 83. Seasonal Index Example Demand Average Average Seasonal Month 2005 2006 2007 2005-2007 Monthly Index Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851© 2008 Prentice Hall, Inc. 4 – 84
- 84. Seasonal Index Example Demand Average Average Seasonal Month 2005 2006 2007 2005-2007 Monthly Index Jan 80 85 105 90 94 0.957 Feb 70 85 Forecast for 2008 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90Expected annual demand = 1,200 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 1,200 115 94 1.223 Jul Jan 100 102 113 12 x .957 = 96 94 105 1.117 Aug 88 102 110 100 94 1.064 1,200 Sept 85 Feb 90 95 x90 .851 = 85 94 0.957 Oct 77 78 85 12 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851© 2008 Prentice Hall, Inc. 4 – 85
- 85. Seasonal Index Example 2008 Forecast 140 – 2007 Demand 130 – 2006 Demand 2005 Demand 120 – Demand 110 – 100 – 90 – 80 – 70 – | | | | | | | | | | | | J F M A M J J A S O N D Time© 2008 Prentice Hall, Inc. 4 – 86
- 86. San Diego Hospital Trend Data 10,200 – 10,000 – Inpatient Days 9745 9,800 – 9702 9616 9659 9573 9724 9766 9,600 – 9530 9680 9594 9637 9551 9,400 – 9,200 – | | | | | | | | | | | | 9,000 – Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month Figure 4.6© 2008 Prentice Hall, Inc. 4 – 87
- 87. San Diego Hospital Seasonal Indices 1.06 – 1.04 1.04 Index for Inpatient Days 1.04 – 1.03 1.02 1.02 – 1.01 1.00 1.00 – 0.99 0.98 0.98 – 0.99 0.96 – 0.97 0.97 0.96 0.94 – | | | | | | | | | | | | 0.92 – Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month Figure 4.7© 2008 Prentice Hall, Inc. 4 – 88
- 88. San Diego Hospital Combined Trend and Seasonal Forecast 10,200 – 10068 9949 10,000 – 9911 Inpatient Days 9764 9724 9,800 – 9691 9572 9,600 – 9520 9542 9,400 – 9411 9265 9355 9,200 – | | | | | | | | | | | | 9,000 – Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month Figure 4.8© 2008 Prentice Hall, Inc. 4 – 89
- 89. 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
- 90. 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 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
- 91. Associative Forecasting Example Sales Local Payroll ($ millions), y ($ billions), x 2.0 1 3.0 3 2.5 4 4.0 – 2.0 2 2.0 1 3.0 – 3.5 7 Sales 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Area payroll© 2008 Prentice Hall, Inc. 4 – 92
- 92. Associative Forecasting Example Sales, y Payroll, x x2 xy 2.0 1 1 2.0 3.0 3 9 9.0 2.5 4 16 10.0 2.0 2 4 4.0 2.0 1 1 2.0 3.5 7 49 24.5 ∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5 ∑xy - nxy 51.5 - (6)(3)(2.5) x = ∑x/6 = 18/6 = 3 b= = = .25 ∑x - nx 2 2 80 - (6)(32) y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75© 2008 Prentice Hall, Inc. 4 – 93
- 93. Associative Forecasting Example ^ y = 1.75 + .25x Sales = 1.75 + .25(payroll) If payroll next year 4.0 – is estimated to be $6 billion, then: 3.25 – 3.0 Sales 2.0 – Sales = 1.75 + .25(6) 1.0 – Sales = $3,250,000 | | | | | | | 0 1 2 3 4 5 6 7 Area payroll© 2008 Prentice Hall, Inc. 4 – 94
- 94. Standard Error of the Estimate A forecast is just a point estimate of a future value This point is 4.0 – actually the 3.25 – 3.0 mean of a Sales probability 2.0 – distribution 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Area payroll Figure 4.9© 2008 Prentice Hall, Inc. 4 – 95
- 95. Standard Error of the Estimate ∑(y - yc)2 Sy,x = n-2 where y = y-value of each data point yc = computed value of the dependent variable, from the regression equation n = number of data© 2008 Prentice Hall, Inc. points 4 – 96
- 96. Standard Error of the Estimate Computationally, this equation is considerably easier to use ∑y2 - a∑y - b∑xy Sy,x = n-2 We use the standard error to set up prediction intervals around the point estimate© 2008 Prentice Hall, Inc. 4 – 97
- 97. Standard Error of the Estimate ∑y2 - a∑y - b∑xy = 39.5 - 1.75(15) - .25(51.5) Sy,x = n-2 6-2 Sy,x = .306 4.0 – 3.25 – 3.0 Sales The standard error 2.0 – of the estimate is 1.0 – $306,000 in sales | | | | | | | 0 1 2 3 4 5 6 7 Area payroll© 2008 Prentice Hall, Inc. 4 – 98
- 98. 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 +1© 2008 Prentice Hall, Inc. 4 – 99
- 99. Correlation Coefficient nΣ xy - Σ xΣ y r= [nΣ x2 - (Σ x)2][nΣ y2 - (Σ y)2]© 2008 Prentice Hall, Inc. 4 – 100
- 100. y Correlation Coefficient y nΣ xy - Σ xΣ y r= [nΣ x2 - (Σ x)2][nΣ y2 - (Σ y)2] (a) Perfect positive x (b) Positive x correlation: correlation: r = +1 0<r<1 y y (c) No correlation: x (d) Perfect negative x r=0 correlation: r = -1© 2008 Prentice Hall, Inc. 4 – 101
- 101. Correlation Coefficient of Determination, r2, 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 r2 = .81© 2008 Prentice Hall, Inc. 4 – 102
- 102. 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 ^=a+bx +bx … y 1 1 2 2 Computationally, this is quite complex and generally done on the computer© 2008 Prentice Hall, Inc. 4 – 103
- 103. Multiple Regression Analysis In the Nodel example, including interest rates in the model gives the new equation: ^ y = 1.80 + .30x1 - 5.0x2 An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales Sales = 1.80 + .30(6) - 5.0(.12) = 3.00 Sales = $3,000,000© 2008 Prentice Hall, Inc. 4 – 104
- 104. 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. 4 – 105
- 105. Monitoring and Controlling Forecasts Tracking RSFE signal = MAD ∑(Actual demand in period i - Forecast demand Tracking in period i) signal = ( ∑|Actual - Forecast|/n)© 2008 Prentice Hall, Inc. 4 – 106
- 106. Tracking Signal Signal exceeding limit Tracking signal Upper control limit + 0 MADs Acceptable range – Lower control limit Time© 2008 Prentice Hall, Inc. 4 – 107
- 107. Tracking Signal Example Cumulative Absolute Absolute Actual Forecast Forecast Forecast Qtr Demand Demand Error RSFE Error Error MAD 1 90 100 -10 -10 10 10 10.0 2 95 100 -5 -15 5 15 7.5 3 115 100 +15 0 15 30 10.0 4 100 110 -10 -10 10 40 10.0 5 125 110 +15 +5 15 55 11.0 6 140 110 +30 +35 30 85 14.2© 2008 Prentice Hall, Inc. 4 – 108
- 108. Tracking Signal Example Cumulative Tracking Absolute Absolute Actual Signal Forecast Forecast Forecast (RSFE/MAD) Qtr Demand Demand Error RSFE Error Error MAD 1 90 100 -1 -10 -10/10 = -10 10 10 10.0 2 95 100 -2 -5 -15/7.5 = -15 5 15 7.5 3 115 0/10 = 0 +15 100 0 15 30 10.0 4 100 110 -1 -10 -10/10 = -10 10 40 10.0 5 125 110 +15 +5/11 = +0.5 +5 15 55 11.0 6 140 110 +2.5 +35/14.2 = +30 +35 30 85 14.2 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits© 2008 Prentice Hall, Inc. 4 – 109
- 109. Adaptive Forecasting It’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. 4 – 110
- 110. 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. 4 – 111
- 111. 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. 4 – 112
- 112. Fast Food Restaurant Forecast 20% – Percentage of sales 15% – 10% – 5% – 11-12 1-2 3-4 5-6 7-8 9-10 12-1 2-3 4-5 6-7 8-9 10-11 (Lunchtime) (Dinnertime) Hour of day Figure 4.12© 2008 Prentice Hall, Inc. 4 – 113
- 113. FedEx Call Center Forecast 12% – 10% – 8% – 6% – 4% – 2% – 0% – 2 4 6 8 10 12 2 4 6 8 10 12 A.M. P.M. Hour of day Figure 4.12© 2008 Prentice Hall, Inc. 4 – 114

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