1. 4 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 4 Forecasting PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl

2. 4 - 2© 2011 Pearson Education, Inc. publishing as Prentice Hall Outline  Global Company Profile: Disney World  What Is Forecasting?  Forecasting Time Horizons  The Influence of Product Life Cycle  Types Of Forecasts

3. 4 - 3© 2011 Pearson Education, Inc. publishing as Prentice Hall Outline – Continued  The Strategic Importance of Forecasting  Human Resources  Capacity  Supply Chain Management  Seven Steps in the Forecasting System

4. 4 - 4© 2011 Pearson Education, Inc. publishing as Prentice Hall Outline – Continued  Forecasting Approaches  Overview of Qualitative Methods  Overview of Quantitative Methods  Time-Series Forecasting  Decomposition of a Time Series  Naive Approach

5. 4 - 5© 2011 Pearson Education, Inc. publishing as Prentice Hall Outline – Continued  Time-Series Forecasting (cont.)  Moving Averages  Exponential Smoothing  Exponential Smoothing with Trend Adjustment  Trend Projections  Seasonal Variations in Data  Cyclical Variations in Data

6. 4 - 6© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

7. 4 - 7© 2011 Pearson Education, Inc. publishing as Prentice Hall Outline – Continued  Monitoring and Controlling Forecasts  Adaptive Smoothing  Focus Forecasting  Forecasting in the Service Sector

8. 4 - 8© 2011 Pearson Education, Inc. publishing as Prentice Hall Learning Objectives When you complete this chapter you should be able to : 1.Understand the three time horizons and which models apply for each use 2.Explain when to use each of the four qualitative models 3.Apply the naive, moving average, exponential smoothing, and trend methods

9. 4 - 9© 2011 Pearson Education, Inc. publishing as Prentice Hall Learning Objectives When you complete this chapter you should be able to : 4.Compute three measures of forecast accuracy 5.Develop seasonal indexes 6.Conduct a regression and correlation analysis 7.Use a tracking signal

10. 4 - 10© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

11. 4 - 11© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

12. 4 - 12© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

13. 4 - 13© 2011 Pearson Education, Inc. publishing as Prentice Hall 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%

14. 4 - 14© 2011 Pearson Education, Inc. publishing as Prentice Hall What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Inventory  Personnel  Facilities ??

15. 4 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Forecasting Time Horizons

16. 4 - 16© 2011 Pearson Education, Inc. publishing as Prentice Hall Distinguishing Differences  Medium/long range  Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes  Short-term  Short-term forecasting usually employs different methodologies than longer-term forecasting  Short-term  Short-term forecasts tend to be more accurate than longer-term forecasts

17. 4 - 17© 2011 Pearson Education, Inc. publishing as Prentice Hall Influence of Product Life Cycle  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 Introduction – Growth – Maturity – Decline

18. 4 - 18© 2011 Pearson Education, Inc. publishing as Prentice Hall Product Life Cycle Best period to increase market share R&D engineering is critical Practical to change price or quality image Strengthen niche Poor time to change image, price, or quality Competitive costs become critical Defend market position Cost control critical IntroductionGrowthMaturityDecline Company Strategy/Issues Figure 2.5 Internet search engines Sales Drive-through restaurants CD-ROMs Analog TVs iPods Boeing 787 LCD & plasma TVs Twitter Avatars Xbox 360

19. 4 - 19© 2011 Pearson Education, Inc. publishing as Prentice Hall Product Life Cycle Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality IntroductionGrowthMaturityDecline OM Strategy/Issues Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focus Enhance distribution Standardization Fewer 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 2.5

20. 4 - 20© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

21. 4 - 21© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

22. 4 - 22© 2011 Pearson Education, Inc. publishing as Prentice Hall Seven Steps in Forecasting 1.Determine the use of the forecast 2.Select the items to be forecasted 3.Determine the time horizon of the forecast 4.Select the forecasting model(s) 5.Gather the data 6.Make the forecast 7.Validate and implement results

23. 4 - 23© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

24. 4 - 24© 2011 Pearson Education, Inc. publishing as Prentice Hall Forecasting Approaches  Used when situation is vague and little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods

25. 4 - 25© 2011 Pearson Education, Inc. publishing as Prentice Hall Forecasting Approaches  Used when situation is ‘stable’ and historical data exist  Existing products  Current technology  Involves mathematical techniques  e.g., forecasting sales of color televisions Quantitative Methods

26. 4 - 26© 2011 Pearson Education, Inc. publishing as Prentice Hall Overview of Qualitative Methods 1.Jury of executive opinion  Pool opinions of high-level experts, sometimes augment by statistical models 2.Delphi method  Panel of experts, queried iteratively

27. 4 - 27© 2011 Pearson Education, Inc. publishing as Prentice Hall Overview of Qualitative Methods 3.Sales force composite  Estimates from individual salespersons are reviewed for reasonableness, then aggregated 4.Consumer Market Survey  Ask the customer

28. 4 - 28© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Jury of Executive Opinion

29. 4 - 29© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

30. 4 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall 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)

31. 4 - 31© 2011 Pearson Education, Inc. publishing as Prentice Hall Consumer Market Survey  Ask customers about purchasing plans  What consumers say, and what they actually do are often different  Sometimes difficult to answer

32. 4 - 32© 2011 Pearson Education, Inc. publishing as Prentice Hall Overview of Quantitative Approaches 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression time-series models associative model

33. 4 - 33© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Time Series Forecasting

34. 4 - 34© 2011 Pearson Education, Inc. publishing as Prentice Hall Trend Seasonal Cyclical Random Time Series Components

35. 4 - 35© 2011 Pearson Education, Inc. publishing as Prentice Hall Components of Demand Demand for product or service |||| 1234 Time (years) Average demand over 4 years Trend component Actual demand line Random variation Figure 4.1 Seasonal peaks

36. 4 - 36© 2011 Pearson Education, Inc. publishing as Prentice Hall  Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration Trend Component

37. 4 - 37© 2011 Pearson Education, Inc. publishing as Prentice Hall  Regular pattern of up and down fluctuations  Due to weather, customs, etc.  Occurs within a single year Seasonal Component Number of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

38. 4 - 38© 2011 Pearson Education, Inc. publishing as Prentice Hall  Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships Cyclical Component 05101520

39. 4 - 39© 2011 Pearson Education, Inc. publishing as Prentice Hall  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating Random Component MTWTFMTWTF

40. 4 - 40© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

41. 4 - 41© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Method Moving average = ∑ demand in previous n periods n

42. 4 - 42© 2011 Pearson Education, Inc. publishing as Prentice Hall January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 Moving Average Example 101213 101213 (10 + 12 + 13)/3 = 11 2 / 3

43. 4 - 43© 2011 Pearson Education, Inc. publishing as Prentice Hall Graph of Moving Average ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Shed Sales 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales Moving Average Forecast

44. 4 - 44© 2011 Pearson Education, Inc. publishing as Prentice Hall  Used when some trend might be present  Older data usually less important  Weights based on experience and intuition Weighted Moving Average Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

45. 4 - 45© 2011 Pearson Education, Inc. publishing as Prentice Hall January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(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 / 2 Weighted Moving Average 101213 131210 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3 3Last month 2 2Two months ago 1 1Three months ago 6Sum of weights

46. 4 - 46© 2011 Pearson Education, Inc. publishing as Prentice Hall  Increasing n smooths the forecast but makes it less sensitive to changes  Do not forecast trends well  Require extensive historical data Potential Problems With Moving Average

47. 4 - 47© 2011 Pearson Education, Inc. publishing as Prentice Hall Moving Average And Weighted Moving Average 30 – 25 – 20 – 15 – 10 – 5 – Sales demand ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Actual sales Moving average Weighted moving average Figure 4.2

48. 4 - 48© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Exponential Smoothing

49. 4 - 49© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing New forecast =Last period’s forecast +  (Last period’s actual demand – Last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1)

50. 4 - 50© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

51. 4 - 51© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= 142 +.2(153 – 142)

52. 4 - 52© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= 142 +.2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

53. 4 - 53© 2011 Pearson Education, Inc. publishing as Prentice Hall Effect of Smoothing Constants Weight Assigned to Most2nd Most3rd Most4th Most5th Most RecentRecentRecentRecentRecent SmoothingPeriodPeriodPeriodPeriodPeriod Constant(  )  (1 -  )  (1 -  ) 2  (1 -  ) 3  (1 -  ) 4  =.1.1.09.081.073.066  =.5.5.25.125.063.031

54. 4 - 54© 2011 Pearson Education, Inc. publishing as Prentice Hall Impact of Different  225 – 200 – 175 – 150 – |||||||||123456789|||||||||123456789 Quarter Demand  =.1 Actual demand  =.5

55. 4 - 55© 2011 Pearson Education, Inc. publishing as Prentice Hall Impact of Different  225 – 200 – 175 – 150 – |||||||||123456789|||||||||123456789 Quarter Demand  =.1 Actual demand  =.5  Chose high values of  when underlying average is likely to change  Choose low values of  when underlying average is stable

56. 4 - 56© 2011 Pearson Education, Inc. publishing as Prentice Hall Choosing  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

57. 4 - 57© 2011 Pearson Education, Inc. publishing as Prentice Hall Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

58. 4 - 58© 2011 Pearson Education, Inc. publishing as Prentice Hall Common Measures of Error Mean Absolute Percent Error (MAPE) MAPE = ∑ 100|Actual i - Forecast i |/Actual i n i = 1

59. 4 - 59© 2011 Pearson Education, Inc. publishing as Prentice Hall Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62

60. 4 - 60© 2011 Pearson Education, Inc. publishing as Prentice Hall Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD = ∑ |deviations| n = 82.45/8 = 10.31 For  =.10 = 98.62/8 = 12.33 For  =.50

61. 4 - 61© 2011 Pearson Education, Inc. publishing as Prentice Hall Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 = 1,526.54/8 = 190.82 For  =.10 = 1,561.91/8 = 195.24 For  =.50 MSE = ∑ (forecast errors) 2 n

62. 4 - 62© 2011 Pearson Education, Inc. publishing as Prentice Hall Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 = 44.75/8 = 5.59% For  =.10 = 54.05/8 = 6.76% For  =.50 MAPE = ∑ 100|deviation i |/actual i n i = 1

63. 4 - 63© 2011 Pearson Education, Inc. publishing as Prentice Hall Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 MAPE5.59%6.76%

64. 4 - 64© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trendExponentially smoothed (F t ) +smoothed(T t ) forecasttrend

65. 4 - 65© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment F t =  (A t - 1 ) + (1 -  )(F t - 1 + T t - 1 ) T t =  (F t - F t - 1 ) + (1 -  )T t - 1 Step 1: Compute F t Step 2: Compute T t Step 3: Calculate the forecast FIT t = F t + T t

66. 4 - 66© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 217 320 419 524 621 731 828 936 10 Table 4.1

67. 4 - 67© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 217 320 419 524 621 731 828 936 10 Table 4.1 F 2 =  A 1 + (1 -  )(F 1 + T 1 ) F 2 = (.2)(12) + (1 -.2)(11 + 2) = 2.4 + 10.4 = 12.8 units Step 1: Forecast for Month 2

68. 4 - 68© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.80 320 419 524 621 731 828 936 10 Table 4.1 T 2 =  (F 2 - F 1 ) + (1 -  )T 1 T 2 = (.4)(12.8 - 11) + (1 -.4)(2) =.72 + 1.2 = 1.92 units Step 2: Trend for Month 2

69. 4 - 69© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.801.92 320 419 524 621 731 828 936 10 Table 4.1 FIT 2 = F 2 + T 2 FIT 2 = 12.8 + 1.92 = 14.72 units Step 3: Calculate FIT for Month 2

70. 4 - 70© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t 11211213.00 21712.801.9214.72 320 419 524 621 731 828 936 10 Table 4.1 15.182.1017.28 17.822.3220.14 19.912.2322.14 22.512.3824.89 24.112.0726.18 27.142.4529.59 29.282.3231.60 32.482.6835.16

71. 4 - 71© 2011 Pearson Education, Inc. publishing as Prentice Hall Exponential Smoothing with Trend Adjustment Example Figure 4.3 |||||||||123456789|||||||||123456789 Time (month) Product demand 35 – 30 – 25 – 20 – 15 – 10 – 5 – 0 – Actual demand (A t ) Forecast including trend (FIT t ) with  =.2 and  =.4

72. 4 - 72© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 x= the independent variable ^

73. 4 - 73© 2011 Pearson Education, Inc. publishing as Prentice Hall Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 (error) Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y-value) Trend line, y = a + bx ^

74. 4 - 74© 2011 Pearson Education, Inc. publishing as Prentice Hall Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 (error) Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y-value) Trend line, y = a + bx ^ Least squares method minimizes the sum of the squared errors (deviations)

75. 4 - 75© 2011 Pearson Education, Inc. publishing as Prentice Hall Least Squares Method Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx

76. 4 - 76© 2011 Pearson Education, Inc. publishing as Prentice Hall Least Squares Example b = = = 10.54 ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(4 2 ) a = y - bx = 98.86 - 10.54(4) = 56.70 TimeElectrical Power YearPeriod (x)Demandx 2 xy 2003174174 20042794158 20053809240 200649016360 2007510525525 2008614236852 2009712249854 ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

77. 4 - 77© 2011 Pearson Education, Inc. publishing as Prentice Hall b = = = 10.54 ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(4 2 ) a = y - bx = 98.86 - 10.54(4) = 56.70 TimeElectrical Power YearPeriod (x)Demandx 2 xy 2003174174 20042794158 20053809240 200649016360 2007510525525 2008614236852 2009712249854 ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86 Least Squares Example The trend line is y = 56.70 + 10.54x ^

78. 4 - 78© 2011 Pearson Education, Inc. publishing as Prentice Hall Least Squares Example ||||||||| 200320042005200620072008200920102011 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – Year Power demand Trend line, y = 56.70 + 10.54x ^

79. 4 - 79© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

80. 4 - 80© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand

81. 4 - 81© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Variations In Data 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 Steps in the process:

82. 4 - 82© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2007200820092007-2009MonthlyIndex

83. 4 - 83© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2007200820092007-2009MonthlyIndex 0.957 Seasonal index = Average 2007-2009 monthly demand Average monthly demand = 90/94 =.957

84. 4 - 84© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Index Example Jan808510590940.957 Feb70858580940.851 Mar80938285940.904 Apr9095115100941.064 May113125131123941.309 Jun110115120115941.223 Jul100102113105941.117 Aug88102110100941.064 Sept85909590940.957 Oct77788580940.851 Nov75728380940.851 Dec82788080940.851 DemandAverageAverage Seasonal Month2007200820092007-2009MonthlyIndex

85. 4 - 85© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Index Example Jan808510590940.957 Feb70858580940.851 Mar80938285940.904 Apr9095115100941.064 May113125131123941.309 Jun110115120115941.223 Jul100102113105941.117 Aug88102110100941.064 Sept85909590940.957 Oct77788580940.851 Nov75728380940.851 Dec82788080940.851 DemandAverageAverage Seasonal Month2007200820092007-2009MonthlyIndex Expected annual demand = 1,200 Janx.957 = 96 1,200 12 Febx.851 = 85 1,200 12 Forecast for 2010

86. 4 - 86© 2011 Pearson Education, Inc. publishing as Prentice Hall Seasonal Index Example 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Time Demand 2010 Forecast 2009 Demand 2008 Demand 2007 Demand

87. 4 - 87© 2011 Pearson Education, Inc. publishing as Prentice Hall San Diego Hospital 10,200 – 10,000 – 9,800 – 9,600 – 9,400 – 9,200 – 9,000 – |||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNovDec 676869707172737475767778 Month Inpatient Days 9530 9551 9573 9594 9616 9637 9659 9680 9702 9724 9745 9766 Figure 4.6 Trend Data

88. 4 - 88© 2011 Pearson Education, Inc. publishing as Prentice Hall San Diego Hospital 1.06 – 1.04 – 1.02 – 1.00 – 0.98 – 0.96 – 0.94 – 0.92 – |||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNovDec 676869707172737475767778 Month Index for Inpatient Days 1.04 1.02 1.01 0.99 1.03 1.04 1.00 0.98 0.97 0.99 0.97 0.96 Figure 4.7 Seasonal Indices

89. 4 - 89© 2011 Pearson Education, Inc. publishing as Prentice Hall San Diego Hospital 10,200 – 10,000 – 9,800 – 9,600 – 9,400 – 9,200 – 9,000 – |||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNovDec 676869707172737475767778 Month Inpatient Days Figure 4.8 9911 9265 9764 9520 9691 9411 9949 9724 9542 9355 10068 9572 Combined Trend and Seasonal Forecast

90. 4 - 90© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

91. 4 - 91© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 ^

92. 4 - 92© 2011 Pearson Education, Inc. publishing as Prentice Hall Associative Forecasting Example SalesArea Payroll ($ millions), y($ billions), x 2.01 3.03 2.54 2.02 2.01 3.57 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll

93. 4 - 93© 2011 Pearson Education, Inc. publishing as Prentice Hall Associative Forecasting Example Sales, y Payroll, xx 2 xy 2.0112.0 3.0399.0 2.541610.0 2.0244.0 2.0112.0 3.574924.5 ∑y = 15.0∑x = 18∑x 2 = 80∑xy = 51.5 x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 b = = =.25 ∑xy - nxy ∑x 2 - nx 2 51.5 - (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx = 2.5 - (.25)(3) = 1.75

94. 4 - 94© 2011 Pearson Education, Inc. publishing as Prentice Hall Associative Forecasting Example y = 1.75 +.25x ^ Sales = 1.75 +.25(payroll) If payroll next year is estimated to be $6 billion, then: Sales = 1.75 +.25(6) Sales = $3,250,000 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Nodel’s sales Area payroll 3.25

95. 4 - 95© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 Figure 4.9 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Nodel’s sales Area payroll 3.25

96. 4 - 96© 2011 Pearson Education, Inc. publishing as Prentice Hall Standard Error of the Estimate wherey=y-value of each data point y c =computed value of the dependent variable, from the regression equation n=number of data points S y,x = ∑(y - y c ) 2 n - 2

97. 4 - 97© 2011 Pearson Education, Inc. publishing as Prentice Hall Standard Error of the Estimate Computationally, this equation is considerably easier to use We use the standard error to set up prediction intervals around the point estimate S y,x = ∑y 2 - a∑y - b∑xy n - 2

98. 4 - 98© 2011 Pearson Education, Inc. publishing as Prentice Hall Standard Error of the Estimate 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Nodel’s sales Area payroll 3.25 S y,x = = ∑y 2 - a∑y - b∑xy n - 2 39.5 - 1.75(15) -.25(51.5) 6 - 2 S y,x =.306 The standard error of the estimate is $306,000 in sales

99. 4 - 99© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Correlation

100. 4 - 100© 2011 Pearson Education, Inc. publishing as Prentice Hall Correlation Coefficient r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

101. 4 - 101© 2011 Pearson Education, Inc. publishing as Prentice Hall Correlation Coefficient r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ] y x (a)Perfect positive correlation: r = +1 y x (b)Positive correlation: 0 < r < 1 y x (c)No correlation: r = 0 y x (d)Perfect negative correlation: r = -1

102. 4 - 102© 2011 Pearson Education, Inc. publishing as Prentice Hall  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 Correlation For the Nodel Construction example: r =.901 r 2 =.81

103. 4 - 103© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

104. 4 - 104© 2011 Pearson Education, Inc. publishing as Prentice Hall Multiple Regression Analysis y = 1.80 +.30x 1 - 5.0x 2 ^ In the Nodel example, including interest rates in the model gives the new equation: 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

105. 4 - 105© 2011 Pearson Education, Inc. publishing as Prentice Hall  Measures how well the forecast is predicting actual values  Ratio of cumulative forecast errors to mean absolute deviation (MAD)  Good tracking signal has low values  If forecasts are continually high or low, the forecast has a bias error Monitoring and Controlling Forecasts Tracking Signal

106. 4 - 106© 2011 Pearson Education, Inc. publishing as Prentice Hall Monitoring and Controlling Forecasts Tracking signal Cumulative error MAD = Tracking signal = ∑(Actual demand in period i - Forecast demand in period i)  ∑|Actual - Forecast|/n)

107. 4 - 107© 2011 Pearson Education, Inc. publishing as Prentice Hall Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range

108. 4 - 108© 2011 Pearson Education, Inc. publishing as Prentice Hall Tracking Signal Example CumulativeAbsolute ActualForecastCummForecastForecast QtrDemandDemandErrorErrorErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2

109. 4 - 109© 2011 Pearson Education, Inc. publishing as Prentice Hall CumulativeAbsolute ActualForecastCummForecastForecast QtrDemandDemandErrorErrorErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2 Tracking Signal Example Tracking Signal (Cumm Error/MAD) -10/10 = -1 -15/7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = +0.5 +35/14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits

110. 4 - 110© 2011 Pearson Education, Inc. publishing as Prentice Hall Adaptive Forecasting  It’s possible to use the computer to continually monitor forecast error and adjust the values of the  and  coefficients used in exponential smoothing to continually minimize forecast error  This technique is called adaptive smoothing

111. 4 - 111© 2011 Pearson Education, Inc. publishing as Prentice Hall Focus Forecasting  Developed at American Hardware Supply, 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

112. 4 - 112© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

113. 4 - 113© 2011 Pearson Education, Inc. publishing as Prentice Hall Fast Food Restaurant Forecast 20% – 15% – 10% – 5% – 11-121-23-45-67-89-10 12-12-34-56-78-910-11 (Lunchtime)(Dinnertime) Hour of day Percentage of sales Figure 4.12

114. 4 - 114© 2011 Pearson Education, Inc. publishing as Prentice Hall FedEx Call Center Forecast Figure 4.12 12% – 10% – 8% – 6% – 4% – 2% – 0% – Hour of day A.M.P.M. 2468101224681012

115. 4 - 115© 2011 Pearson Education, Inc. publishing as Prentice Hall All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.