1. 4 - 1© 2014 Pearson Education Forecasting Demand PowerPoint presentation to accompany Heizer and Render Operations Management, Global Edition, Eleventh Edition Principles of Operations Management, Global Edition, Ninth Edition PowerPoint slides by Jeff Heyl 4 © 2014 Pearson Education

2. 4 - 2© 2014 Pearson Education Outline ▶ What Is Forecasting? ▶ The Strategic Importance of Forecasting ▶ Seven Steps in the Forecasting System ▶ Forecasting Approaches

3. 4 - 3© 2014 Pearson Education Outline - Continued ▶ Time-Series Forecasting ▶ Associative Forecasting Methods: Regression and Correlation Analysis ▶ Monitoring and Controlling Forecasts

4. 4 - 4© 2014 Pearson Education What is Forecasting? ► Process of predicting a future event ► Underlying basis of all business decisions ► Production ► Inventory ► Personnel ► Facilities ??

5. 4 - 5© 2014 Pearson Education 1.Short-range forecast ► Up to 1 year, generally less than 3 months ► Purchasing, job scheduling, workforce levels, job assignments, production levels 2.Medium-range forecast ► 3 months to 3 years ► Sales and production planning, budgeting 3.Long-range forecast ► 3 + years ► New product planning, facility location, research and development Forecasting Time Horizons

6. 4 - 6© 2014 Pearson Education Distinguishing Differences 1.Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes 2.Short-term forecasting usually employs different methodologies than longer-term forecasting 3.Short-term forecasts tend to be more accurate than longer-term forecasts

7. 4 - 7© 2014 Pearson Education 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

8. 4 - 8© 2014 Pearson Education 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 DVDs Analog TVs Boeing 787 Electric vehicles iPods 3-D game players 3D printers Xbox 360

9. 4 - 9© 2014 Pearson Education 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

10. 4 - 10© 2014 Pearson Education Types of Forecasts 1.Economic forecasts ► Address business cycle – inflation rate, money supply, housing starts, etc. 2.Technological forecasts ► Predict rate of technological progress ► Impacts development of new products 3.Demand forecasts ► Predict sales of existing products and services

11. 4 - 11© 2014 Pearson Education Strategic Importance of Forecasting ► Supply-Chain Management – Good supplier relations, advantages in product innovation, cost and speed to market ► Human Resources – Hiring, training, laying off workers ► Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share

12. 4 - 12© 2014 Pearson Education 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 needed to make the forecast 6.Make the forecast 7.Validate and implement results

13. 4 - 13© 2014 Pearson Education The Realities! ► Forecasts are seldom perfect, unpredictable outside factors may impact the forecast ► Most techniques assume an underlying stability in the system ► Product family and aggregated forecasts are more accurate than individual product forecasts

14. 4 - 14© 2014 Pearson Education 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

15. 4 - 15© 2014 Pearson Education 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

16. 4 - 16© 2014 Pearson Education 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

17. 4 - 17© 2014 Pearson Education Overview of Qualitative Methods 3.Sales force composite ► Estimates from individual salespersons are reviewed for reasonableness, then aggregated 4.Market Survey ► Ask the customer

18. 4 - 18© 2014 Pearson Education ► 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

19. 4 - 19© 2014 Pearson Education 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)

20. 4 - 20© 2014 Pearson Education Sales Force Composite ► Each salesperson projects his or her sales ► Combined at district and national levels ► Sales reps know customers’ wants ► May be overly optimistic

21. 4 - 21© 2014 Pearson Education Market Survey ► Ask customers about purchasing plans ► Useful for demand and product design and planning ► What consumers say, and what they actually do may be different ► May be overly optimistic

22. 4 - 22© 2014 Pearson Education Overview of Quantitative Approaches 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression Time-series models Associative model

23. 4 - 23© 2014 Pearson Education ► 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

24. 4 - 24© 2014 Pearson Education Trend Seasonal Cyclical Random Time-Series Components

25. 4 - 25© 2014 Pearson Education 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

26. 4 - 26© 2014 Pearson Education ► Persistent, overall upward or downward pattern ► Changes due to population, technology, age, culture, etc. ► Typically several years duration Trend Component

27. 4 - 27© 2014 Pearson Education ► Regular pattern of up and down fluctuations ► Due to weather, customs, etc. ► Occurs within a single year Seasonal Component PERIOD LENGTH“SEASON” LENGTHNUMBER OF “SEASONS” IN PATTERN WeekDay7 MonthWeek4 – 4.5 MonthDay28 – 31 YearQuarter4 YearMonth12 YearWeek52

28. 4 - 28© 2014 Pearson Education ► Repeating up and down movements ► Affected by business cycle, political, and economic factors ► Multiple years duration ► Often causal or associative relationships Cyclical Component 05101520

29. 4 - 29© 2014 Pearson Education ► Erratic, unsystematic, ‘residual’ fluctuations ► Due to random variation or unforeseen events ► Short duration and nonrepeating Random Component MTWTFMTWTF

30. 4 - 30© 2014 Pearson Education 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

31. 4 - 31© 2014 Pearson Education ► 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

32. 4 - 32© 2014 Pearson Education Moving Average Example MONTHACTUAL SHED SALES3-MONTH MOVING AVERAGE January10 February12 March13 April16 May19 June23 July26 August30 September28 October18 November16 December14 (10 + 12 + 13)/3 = 11 2 / 3 (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 (19 + 23 + 26)/3 = 22 2 / 3 (23 + 26 + 30)/3 = 26 1 / 3 (29 + 30 + 28)/3 = 28 (30 + 28 + 18)/3 = 25 1 / 3 (28 + 18 + 16)/3 = 20 2 / 3 10 12 13

33. 4 - 33© 2014 Pearson Education ► Used when some trend might be present ► Older data usually less important ► Weights based on experience and intuition Weighted Moving Average Weighted moving average

34. 4 - 34© 2014 Pearson Education Weighted Moving Average MONTHACTUAL SHED SALES3-MONTH WEIGHTED MOVING AVERAGE January10 February12 March13 April16 May19 June23 July26 August30 September28 October18 November16 December14 WEIGHTS APPLIEDPERIOD 3Last month 2Two months ago 1Three months ago 6Sum of the weights Forecast for this month = 3 x Sales last mo. + 2 x Sales 2 mos. ago + 1 x Sales 3 mos. ago Sum of the weights [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 10 12 13

35. 4 - 35© 2014 Pearson Education Weighted Moving Average MONTHACTUAL SHED SALES3-MONTH WEIGHTED MOVING AVERAGE January10 February12 March13 April16 May19 June23 July26 August30 September28 October18 November16 December14 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 10 12 13 [(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 [(3 x 26) + (2 x 23) + (19)]/6 = 23 5 / 6 [(3 x 30) + (2 x 26) + (23)]/6 = 27 1 / 2 [(3 x 28) + (2 x 30) + (26)]/6 = 28 1 / 3 [(3 x 18) + (2 x 28) + (30)]/6 = 23 1 / 3 [(3 x 16) + (2 x 18) + (28)]/6 = 18 2 / 3

36. 4 - 36© 2014 Pearson Education ► Increasing n smooths the forecast but makes it less sensitive to changes ► Does not forecast trends well ► Requires extensive historical data Potential Problems With Moving Average

37. 4 - 37© 2014 Pearson Education Graph of Moving Averages ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Sales demand 30 – 25 – 20 – 15 – 10 – 5 – Month Actual sales Moving average Weighted moving average Figure 4.2

38. 4 - 38© 2014 Pearson Education ► 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

39. 4 - 39© 2014 Pearson Education 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 period’s forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1) A t – 1 =previous period’s actual demand OR F t =  (A t - 1 ) + (1 -  )(F t – 1 )

40. 4 - 40© 2014 Pearson Education Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

41. 4 - 41© 2014 Pearson Education Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= 142 +.2(153 – 142)

42. 4 - 42© 2014 Pearson Education 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

43. 4 - 43© 2014 Pearson Education Effect of Smoothing Constants ▶ Smoothing constant generally.05 ≤  ≤.50 ▶ As  increases, older values become less significant WEIGHT ASSIGNED TO SMOOTHING CONSTANT MOST RECENT PERIOD (  ) 2 ND MOST RECENT PERIOD  (1 –  ) 3 RD MOST RECENT PERIOD  (1 –  ) 2 4 th MOST RECENT PERIOD  (1 –  ) 3 5 th MOST RECENT PERIOD  (1 –  ) 4  =.1.1.09.081.073.066  =.5.5.25.125.063.031

44. 4 - 44© 2014 Pearson Education Impact of Different  225 – 200 – 175 – 150 – |||||||||123456789|||||||||123456789 Quarter Demand  =.1 Actual demand  =.5

45. 4 - 45© 2014 Pearson Education 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

46. 4 - 46© 2014 Pearson Education 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

47. 4 - 47© 2014 Pearson Education Common Measures of Error Mean Absolute Deviation (MAD)

48. 4 - 48© 2014 Pearson Education Determining the MAD QUARTER ACTUAL TONNAGE UNLOADED FORECAST WITH  =.10 FORECAST WITH  =.50 1180175 2168175.50 = 175.00 +.10(180 – 175)177.50 3159174.75 = 175.50 +.10(168 – 175.50)172.75 4175173.18 = 174.75 +.10(159 – 174.75)165.88 5190173.36 = 173.18 +.10(175 – 173.18)170.44 6205175.02 = 173.36 +.10(190 – 173.36)180.22 7180178.02 = 175.02 +.10(205 – 175.02)192.61 8182178.22 = 178.02 +.10(180 – 178.02)186.30 9?178.59 = 178.22 +.10(182 – 178.22)184.15

49. 4 - 49© 2014 Pearson Education Determining the MAD QUARTER ACTUAL TONNAGE UNLOADED FORECAST WITH  =.10 ABSOLUTE DEVIATION FOR a =.10 FORECAST WITH  =.50 ABSOLUTE DEVIATION FOR a =.50 11801755.001755.00 2168175.507.50177.509.50 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 Sum of absolute deviations:82.4598.62 MAD = Σ|Deviations| 10.3112.33 n

50. 4 - 50© 2014 Pearson Education Common Measures of Error Mean Squared Error (MSE)

51. 4 - 51© 2014 Pearson Education Determining the MSE QUARTER ACTUAL TONNAGE UNLOADED FORECAST FOR  =.10 (ERROR) 2 11801755 2 = 25 2168175.50(–7.5) 2 = 56.25 3159174.75(–15.75) 2 = 248.06 4175173.18(1.82) 2 = 3.31 5190173.36(16.64) 2 = 276.89 6205175.02(29.98) 2 = 898.80 7180178.02(1.98) 2 = 3.92 8182178.22(3.78) 2 = 14.29 Sum of errors squared= 1,526.52

52. 4 - 52© 2014 Pearson Education Common Measures of Error Mean Absolute Percent Error (MAPE)

53. 4 - 53© 2014 Pearson Education Determining the MAPE QUARTER ACTUAL TONNAGE UNLOADED FORECAST FOR  =.10 ABSOLUTE PERCENT ERROR 100(ERROR/ACTUAL) 1180175.00100(5/180)= 2.78% 2168175.50100(7.5/168)= 4.46% 3159174.75100(15.75/159)= 9.90% 4175173.18100(1.82/175)= 1.05% 5190173.36100(16.64/190)= 8.76% 6205175.02100(29.98/205)= 14.62% 7180178.02100(1.98/180)= 1.10% 8182178.22100(3.78/182)= 2.08% Sum of % errors= 44.75%

54. 4 - 54© 2014 Pearson Education 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

55. 4 - 55© 2014 Pearson Education Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloadeda =.10a =.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

56. 4 - 56© 2014 Pearson Education Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloadeda =.10a =.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

57. 4 - 57© 2014 Pearson Education Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloadeda =.10a =.10a =.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

58. 4 - 58© 2014 Pearson Education 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%

59. 4 - 59© 2014 Pearson Education Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified MONTHACTUAL DEMANDFORECAST (F t ) FOR MONTHS 1 – 5 1100F t = 100 (given) 2200 F t = F 1 +  (A 1 – F 1 ) = 100 +.4(100 – 100) = 100 3300 F t = F 2 +  (A 2 – F 2 ) = 100 +.4(200 – 100) = 140 4400 F t = F 3 +  (A 3 – F 3 ) = 140 +.4(300 – 140) = 204 5500 F t = F 4 +  (A 4 – F 4 ) = 204 +.4(400 – 204) = 282

60. 4 - 60© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Forecast including (FIT t ) = trendExponentially smoothed (F t ) +smoothed(T t ) forecasttrend F t =  (A t - 1 ) + (1 -  )(F t - 1 + T t - 1 ) T t =  (F t - F t - 1 ) + (1 -  )T t - 1 whereF t = exponentially smoothed forecast average T t = exponentially smoothed trend A t = actual demand  = smoothing constant for average (0 ≤  ≤ 1)  = smoothing constant for trend (0 ≤  ≤ 1)

61. 4 - 61© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Step 1: Compute F t Step 2: Compute T t Step 3: Calculate the forecast FIT t = F t + T t

62. 4 - 62© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example MONTH (t)ACTUAL DEMAND (A t )MONTH (t)ACTUAL DEMAND (A t ) 112621 217731 320828 419936 52410?  =.2  =.4

63. 4 - 63© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example TABLE 4.1 Forecast with  -.2 and  =.4 MONTHACTUAL DEMAND SMOOTHED FORECAST AVERAGE, F t SMOOTHED TREND, T t FORECAST INCLUDING TREND, FIT t 11211213.00 217 320 419 524 621 731 828 936 10— F 2 =  A 1 + (1 –  )(F 1 + T 1 ) F 2 = (.2)(12) + (1 –.2)(11 + 2) = 2.4 + (.8)(13) = 2.4 + 10.4 = 12.8 units Step 1: Average for Month 2 12.80

64. 4 - 64© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example TABLE 4.1 Forecast with  -.2 and  =.4 MONTHACTUAL DEMAND SMOOTHED FORECAST AVERAGE, F t SMOOTHED TREND, T t FORECAST INCLUDING TREND, FIT t 11211213.00 21712.80 320 419 524 621 731 828 936 10— T 2 =  (F 2 - F 1 ) + (1 - b)T 1 T 2 = (.4)(12.8 - 11) + (1 -.4)(2) =.72 + 1.2 = 1.92 units Step 2: Trend for Month 2 1.92

65. 4 - 65© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example TABLE 4.1 Forecast with  -.2 and  =.4 MONTHACTUAL DEMAND SMOOTHED FORECAST AVERAGE, F t SMOOTHED TREND, T t FORECAST INCLUDING TREND, FIT t 11211213.00 21712.801.92 320 419 524 621 731 828 936 10— FIT 2 = F 2 + T 2 FIT 2 = 12.8 + 1.92 = 14.72 units Step 3: Calculate FIT for Month 2 14.72

66. 4 - 66© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example TABLE 4.1 Forecast with  -.2 and  =.4 MONTHACTUAL DEMAND SMOOTHED FORECAST AVERAGE, F t SMOOTHED TREND, T t FORECAST INCLUDING TREND, FIT t 11211213.00 21712.801.9214.72 32015.182.1017.28 41917.822.3220.14 52419.912.2322.14 62122.512.3824.89 73124.112.0726.18 82827.142.4529.59 93629.282.3231.60 10—32.482.6835.16

67. 4 - 67© 2014 Pearson Education Exponential Smoothing with Trend Adjustment Example Figure 4.3 |||||||||123456789|||||||||123456789 Time (months) Product demand 40 – 35 – 30 – 25 – 20 – 15 – 10 – 5 – 0 – Actual demand (A t ) Forecast including trend (FIT t ) with  =.2 and  =.4

68. 4 - 68© 2014 Pearson Education 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 ^

69. 4 - 69© 2014 Pearson Education Least Squares Method 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 ^ Time period Values of Dependent Variable ( y -values) |||||||1234567|||||||1234567 Least squares method minimizes the sum of the squared errors (deviations)

70. 4 - 70© 2014 Pearson Education Least Squares Method Equations to calculate the regression variables

71. 4 - 71© 2014 Pearson Education Least Squares Example YEAR ELECTRICAL POWER DEMANDYEAR ELECTRICAL POWER DEMAND 1745105 2796142 3807122 490

72. 4 - 72© 2014 Pearson Education Least Squares Example YEAR (x) ELECTRICAL POWER DEMAND (y)x2x2 xy 174 1 279 4158 380 9240 49016360 510525525 614236852 712249854 Σx = 28 Σy = 692 Σx 2 = 140 Σxy = 3,063

73. 4 - 73© 2014 Pearson Education Least Squares Example YEAR (x) ELECTRICAL POWER DEMAND (y)x2x2 xy 174 1 279 4158 380 9240 49016360 510525525 614236852 712249854 Σx = 28 Σy = 692 Σx 2 = 140 Σxy = 3,063 Demand in year 8= 56.70 + 10.54(8) = 141.02, or 141 megawatts

74. 4 - 74© 2014 Pearson Education Least Squares Example |||||||||123456789|||||||||123456789 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – Year Power demand (megawatts) Trend line, y = 56.70 + 10.54 x ^ Figure 4.5

75. 4 - 75© 2014 Pearson Education 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

76. 4 - 76© 2014 Pearson Education Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand

77. 4 - 77© 2014 Pearson Education Seasonal Variations In Data 1.Find average historical demand for each month 2.Compute the average demand over all months 3.Compute a seasonal index for each month 4.Estimate next year’s total demand 5.Divide this estimate of total demand by the number of months, then multiply it by the seasonal index for that month Steps in the process for monthly seasons:

78. 4 - 78© 2014 Pearson Education Seasonal Index Example DEMAND MONTHYEAR 1YEAR 2YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND SEASONAL INDEX Jan8085105 Feb7085 Mar809382 Apr9095115 May113125131 June110115120 July100102113 Aug88102110 Sept859095 Oct777885 Nov758283 Dec827880 90 80 85 100 123 115 105 100 90 80 Total average annual demand = 1,128

79. 4 - 79© 2014 Pearson Education Seasonal Index Example DEMAND MONTHYEAR 1YEAR 2YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND SEASONAL INDEX Jan80851059094 Feb7085 8094 Mar8093828594 Apr909511510094 May11312513112394 June11011512011594 July10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7582838094 Dec827880 94 Total average annual demand =1,128 Average monthly demand

80. 4 - 80© 2014 Pearson Education Seasonal Index Example DEMAND MONTHYEAR 1YEAR 2YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND SEASONAL INDEX Jan80851059094 Feb7085 8094 Mar8093828594 Apr909511510094 May11312513112394 June11011512011594 July10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7582838094 Dec827880 94 Total average annual demand =1,128 Seasonal index.957( = 90/94)

81. 4 - 81© 2014 Pearson Education Seasonal Index Example DEMAND MONTHYEAR 1YEAR 2YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND SEASONAL INDEX Jan80851059094.957( = 90/94) Feb7085 8094.851( = 80/94) Mar8093828594.904( = 85/94) Apr9095115100941.064( = 100/94) May113125131123941.309( = 123/94) June110115120115941.223( = 115/94) July100102113105941.117( = 105/94) Aug88102110100941.064( = 100/94) Sept8590959094.957( = 90/94) Oct7778858094.851( = 80/94) Nov7582838094.851( = 80/94) Dec827880 94.851( = 80/94) Total average annual demand =1,128

82. 4 - 82© 2014 Pearson Education Seasonal Index Example MONTHDEMANDMONTHDEMAND Jan 1,200 x.957 = 96 July 1,200 x 1.117 = 112 12 Feb 1,200 x.851 = 85 Aug 1,200 x 1.064 = 106 12 Mar 1,200 x.904 = 90 Sept 1,200 x.957 = 96 12 Apr 1,200 x 1.064 = 106 Oct 1,200 x.851 = 85 12 May 1,200 x 1.309 = 131 Nov 1,200 x.851 = 85 12 June 1,200 x 1.223 = 122 Dec 1,200 x.851 = 85 12 Seasonal forecast for Year 4

83. 4 - 83© 2014 Pearson Education Seasonal Index Example 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Time Demand Year 4 Forecast Year 3 Demand Year 2 Demand Year 1 Demand

84. 4 - 84© 2014 Pearson Education 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

85. 4 - 85© 2014 Pearson Education San Diego Hospital Seasonality Indices for Adult Inpatient Days at San Diego Hospital MONTHSEASONALITY INDEXMONTHSEASONALITY INDEX January1.04July1.03 February0.97August1.04 March1.02September0.97 April1.01October1.00 May0.99November0.96 June0.99December0.98

86. 4 - 86© 2014 Pearson Education 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

87. 4 - 87© 2014 Pearson Education San Diego Hospital Period676869707172 MonthJanFebMarAprMayJune Forecast with Trend & Seasonality 9,9119,2659,1649,6919,5209,542 Period737475767778 MonthJulyAugSeptOctNovDec Forecast with Trend & Seasonality 9,94910,0689,4119,7249,3559,572

88. 4 - 88© 2014 Pearson Education 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

89. 4 - 89© 2014 Pearson Education Adjusting Trend Data Quarter I: Quarter II: Quarter III: Quarter IV:

90. 4 - 90© 2014 Pearson Education 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© 2014 Pearson Education Associative Forecasting Forecasting an outcome based on predictor variables using the least squares technique y = a + bx ^ where y =value of the dependent variable (in our example, sales) a = y -axis intercept b = slope of the regression line x = the independent variable ^

92. 4 - 92© 2014 Pearson Education Associative Forecasting Example NODEL’S SALES (IN $ MILLIONS), y AREA PAYROLL (IN $ BILLIONS), x NODEL’S SALES (IN $ MILLIONS), y AREA PAYROLL (IN $ BILLIONS), x 2.01 2 3.032.01 2.543.57 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Area payroll (in $ billions) Nodel’s sales (in$ millions)

93. 4 - 93© 2014 Pearson Education Associative Forecasting Example SALES, y PAYROLL, x x2x2 xy 2.011 3.0399.0 2.541610.0 2.0244.0 2.011 3.574924.5 Σ y =15.0Σ x =18Σ x 2 =80Σ xy =51.5

94. 4 - 94© 2014 Pearson Education Associative Forecasting Example SALES, y PAYROLL, x x2x2 xy 2.011 3.0399.0 2.541610.0 2.0244.0 2.011 3.574924.5 Σ y =15.0Σ x =18Σ x 2 =80Σ xy =51.5

95. 4 - 95© 2014 Pearson Education Associative Forecasting Example SALES, y PAYROLL, x x2x2 xy 2.011 3.0399.0 2.541610.0 2.0244.0 2.011 3.574924.5 Σ y =15.0Σ x =18Σ x 2 =80Σ xy =51.5 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Area payroll (in $ billions) Nodel’s sales (in$ millions)

96. 4 - 96© 2014 Pearson Education Associative Forecasting Example If payroll next year is estimated to be $6 billion, then: Sales (in $ millions)= 1.75 +.25(6) = 1.75 + 1.5 = 3.25 Sales= $3,250,000

97. 4 - 97© 2014 Pearson Education Associative Forecasting Example If payroll next year is estimated to be $6 billion, then: Sales (in$ millions)= 1.75 +.25(6) = 1.75 + 1.5 = 3.25 Sales= $3,250,000 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Area payroll (in $ billions) Nodel’s sales (in$ millions) 3.25

98. 4 - 98© 2014 Pearson Education 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 Area payroll (in $ billions) Nodel’s sales (in$ millions) 3.25 Regression line,

99. 4 - 99© 2014 Pearson Education Standard Error of the Estimate 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

100. 4 - 100© 2014 Pearson Education 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

101. 4 - 101© 2014 Pearson Education Standard Error of the Estimate The standard error of the estimate is $306,000 in sales 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Area payroll (in $ billions) Nodel’s sales (in$ millions) 3.25

102. 4 - 102© 2014 Pearson Education ► 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

103. 4 - 103© 2014 Pearson Education Correlation Coefficient

104. 4 - 104© 2014 Pearson Education Correlation Coefficient y x (a)Perfect negative correlation y x (c)No correlation y x (d)Positive correlation y x (e)Perfect positive correlation y x (b)Negative correlation HighModerateLow Correlation coefficient values HighModerateLow ||||||||| –1.0–0.8–0.6–0.4–0.200.20.40.60.81.0 Figure 4.10

105. 4 - 105© 2014 Pearson Education Correlation Coefficient yxx2x2 xy y2y2 2.011 4.0 3.0399.0 2.541610.06.25 2.0244.0 2.011 4.0 3.574924.512.25 Σ y =15.0Σ x =18Σ x 2 =80Σ xy =51.5Σy 2 =39.5

106. 4 - 106© 2014 Pearson Education ► 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

107. 4 - 107© 2014 Pearson Education 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 Computationally, this is quite complex and generally done on the computer

108. 4 - 108© 2014 Pearson Education Multiple-Regression Analysis In the Nodel example, including interest rates in the model gives the new equation: An improved correlation coefficient of r =.96 suggests 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

109. 4 - 109© 2014 Pearson Education ► 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

110. 4 - 110© 2014 Pearson Education Monitoring and Controlling Forecasts Tracking signal Cumulative error MAD =

111. 4 - 111© 2014 Pearson Education Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range Figure 4.11

112. 4 - 112© 2014 Pearson Education Tracking Signal Example QTR ACTUAL DEMAND FORECAST DEMANDERROR CUM ERROR ABSOLUTE FORECAST ERROR CUM ABS FORECAST ERRORMAD TRACKING SIGNAL (CUM ERROR/MAD) 190100–10 10 10.0–10/10 = –1 295100–5–155157.5–15/7.5 = –2 3115100+150153010.0/10 = 0 4100110–10 104010.10/10 = –1 5125110+15+5155511.0+5/11 = +0.5 6140110+30+35308514.2+35/14.2 = +2.5 At the end of quarter 6,

113. 4 - 113© 2014 Pearson Education Adaptive Smoothing ► 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

114. 4 - 114© 2014 Pearson Education 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 ► Uses historical data to test multiple forecasting models for individual items ► Forecasting model with the lowest error used to forecast the next demand