1. © 2008 Prentice Hall, Inc.4 – 1 Operations Management Chapter 4 – Forecasting Delivered by: Eng.Mosab I. Tabash Eng.Mosab I. Tabash

2. © 2008 Prentice Hall, Inc.4 – 2 What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Inventory  Personnel  Facilities Sales will be $200 Million!

3. © 2008 Prentice Hall, Inc.4 – 3  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

4. © 2008 Prentice Hall, Inc.4 – 4 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

5. © 2008 Prentice Hall, Inc.4 – 5 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

6. © 2008 Prentice Hall, Inc.4 – 6 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

7. © 2008 Prentice Hall, Inc.4 – 7 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

8. © 2008 Prentice Hall, Inc.4 – 8 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

9. © 2008 Prentice Hall, Inc.4 – 9 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

10. © 2008 Prentice Hall, Inc.4 – 10 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

11. © 2008 Prentice Hall, Inc.4 – 11 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

12. © 2008 Prentice Hall, Inc.4 – 12 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

13. © 2008 Prentice Hall, Inc.4 – 13 Overview of Qualitative Methods  Sales force composite  Estimates from individual salespersons are reviewed for reasonableness, then aggregated  Consumer Market Survey  Ask the customer

14. © 2008 Prentice Hall, Inc.4 – 14  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

15. © 2008 Prentice Hall, Inc.4 – 15 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

16. © 2008 Prentice Hall, Inc.4 – 16 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)

17. © 2008 Prentice Hall, Inc.4 – 17 Consumer Market Survey  Ask customers about purchasing plans  What consumers say, and what they actually and what they actually do are often different  Sometimes difficult to answer How many hours will you use the Internet next week? © 1995 Corel Corp.

18. © 2008 Prentice Hall, Inc.4 – 18 Overview of Quantitative Approaches 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression Time-Series Models Associative Model

19. © 2008 Prentice Hall, Inc.4 – 19  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 Example Year:19931994199519961997 Sales:78.763.589.793.292.1

20. © 2008 Prentice Hall, Inc.4 – 20 Trend Seasonal Cyclical Random Time Series Components

21. © 2008 Prentice Hall, Inc.4 – 21 Components of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation Figure 4.1

22. © 2008 Prentice Hall, Inc.4 – 22  Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration Trend Component Mo., Qtr., Yr. Response © 1984-1994 T/Maker Co.

23. © 2008 Prentice Hall, Inc.4 – 23  Regular pattern of up and down fluctuations  Due to weather, customs, etc.  Occurs within a single year Seasonal Component Mo., Qtr. Response Summer © 1984-1994 T/Maker Co.

24. © 2008 Prentice Hall, Inc.4 – 24  Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships Cyclical Component 05101520

25. © 2008 Prentice Hall, Inc.4 – 25  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating Random Component MTWTFMTWTFMTWTFMTWTF

26. © 2008 Prentice Hall, Inc.4 – 26 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

27. © 2008 Prentice Hall, Inc.4 – 27  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

28. © 2008 Prentice Hall, Inc.4 – 28 January10 February12 March13 April16 May19 June23 July26 Actual3-Month Monthcar 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 (10 + 12 + 13)/3 = 11 2 / 3

29. © 2008 Prentice Hall, Inc.4 – 29 Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Cars Sales 30 30 – 28 28 – 26 26 – 24 24 – 22 22 – 20 20 – 18 18 – 16 16 – 14 14 – 12 12 – 10 10 – Actual Sales Moving Average Forecast

30. © 2008 Prentice Hall, Inc.4 – 30  Used when trend is 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

31. © 2008 Prentice Hall, Inc.4 – 31 January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted Monthcar 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 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

32. © 2008 Prentice Hall, Inc.4 – 32  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

33. © 2008 Prentice Hall, Inc.4 – 33 Moving Average And Weighted Moving Average 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average Figure 4.2

34. © 2008 Prentice Hall, Inc.4 – 34  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

35. © 2008 Prentice Hall, Inc.4 – 35 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)

36. © 2008 Prentice Hall, Inc.4 – 36 You’re organizing a planning meeting. You want to forecast attendance for 2000 using exponential smoothing (α=.10). The1995 forecast was 175. 1995180 1996 168 1997159 1996175 1999190 © 1995 Corel Corp. Exponential Smoothing Example

37. © 2008 Prentice Hall, Inc.4 – 37 F t = F t -1 +  ·  ( A t -1 - F t -1 ) Time Actual Forecast, F t ( α =.10) 1995 180175.00 (Given) 1996168 1997159 1998175 1999190 2000NA 175.00 + Exponential Smoothing Solution

38. © 2008 Prentice Hall, Inc.4 – 38 F t = F t -1 +  ·  ( A t -1 - F t -1 ) TimeActual Forecast,F t ( αααα =.10) 1995180 175.00 (Given) 1996168 175.00 +.10(180 - 175.00) = 175.50 1997159 1998175 1999190 2000NA Exponential Smoothing Solution

39. © 2008 Prentice Hall, Inc.4 – 39 F t = F t -1 +  ·  ( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) 1995180 175.00 (Given) 1996168 175.00 +.10(180 - 175.00) = 175.50 1997159 175.50 +.10(168 - 175.50) = 174.75 1998175 174.75 +.10(159 - 174.75) = 173.18 1999190 173.18 +.10(175 - 173.18) = 173.36 2000NA 173.36 +.10(190 - 173.36) = 175.02 Exponential Smoothing Solution

40. © 2008 Prentice Hall, Inc.4 – 40 Year Sales 140 150 160 170 180 190 939495969798 Actual Forecast Exponential Smoothing Graph

41. © 2008 Prentice Hall, Inc.4 – 41 Forecast error 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

42. © 2008 Prentice Hall, Inc.4 – 42 Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

43. © 2008 Prentice Hall, Inc.4 – 43 Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trend ExponentiallyExponentially smoothed (F t ) +(T t )smoothed forecasttrend

44. © 2008 Prentice Hall, Inc.4 – 44 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

45. © 2008 Prentice Hall, Inc.4 – 45 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

46. © 2008 Prentice Hall, Inc.4 – 46 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

47. © 2008 Prentice Hall, Inc.4 – 47 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

48. © 2008 Prentice Hall, Inc.4 – 48 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 1 FIT 2 = 12.8 + 1.92 = 14.72 units Step 3: Calculate FIT for Month 2

49. © 2008 Prentice Hall, Inc.4 – 49 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

50. © 2008 Prentice Hall, Inc.4 – 50 Exponential Smoothing with Trend Adjustment Example Figure 4.3 |||||||||123456789123456789|||||||||123456789123456789 Time (month) Product demand 35 35 – 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – 0 0 – Actual demand (A t ) Forecast including trend (FIT t ) with  =.2 and  =.4

51. © 2008 Prentice Hall, Inc.4 – 51 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 ^

52. © 2008 Prentice Hall, Inc.4 – 52 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 ^

53. © 2008 Prentice Hall, Inc.4 – 53 Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 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)

54. © 2008 Prentice Hall, Inc.4 – 54 Least Squares Method Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx

55. © 2008 Prentice Hall, Inc.4 – 55 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 2001174174 20022794158 20033809240 200449016360 2005510525525 2005614236852 2007712249854 ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

56. © 2008 Prentice Hall, Inc.4 – 56 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 1999174174 20002794158 20013809240 200249016360 2003510525525 2004614236852 2005712249854  x = 28  y = 692  x 2 = 140  xy = 3,063 x = 4y = 98.86 The trend line is y = 56.70 + 10.54x ^

57. © 2008 Prentice Hall, Inc.4 – 57 Least Squares Example ||||||||| 200120022003200420052006200720082009 160 160 – 150 150 – 140 140 – 130 130 – 120 120 – 110 110 – 100 100 – 90 90 – 80 80 – 70 70 – 60 60 – 50 50 – Year Power demand Trend line, y = 56.70 + 10.54x ^

58. © 2008 Prentice Hall, Inc.4 – 58 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

59. © 2008 Prentice Hall, Inc.4 – 59 Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand

60. © 2008 Prentice Hall, Inc.4 – 60 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:

61. © 2008 Prentice Hall, Inc.4 – 61 Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex

62. © 2008 Prentice Hall, Inc.4 – 62 Seasonal Index Example Jan80851059094 Feb7085858094 Mar8093828594 Apr909511510094 May11312513112394 Jun11011512011594 Jul10010211310594 Aug8810211010094 Sept8590959094 Oct7778858094 Nov7572838094 Dec8278808094 DemandAverageAverage Seasonal Month2005200620072005-2007MonthlyIndex 0.957 Seasonal index = average 2005-2007 monthly demand average monthly demand = 90/94 =.957

63. © 2008 Prentice Hall, Inc.4 – 63 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 Month2005200620072005-2007MonthlyIndex

64. © 2008 Prentice Hall, Inc.4 – 64 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 Month2005200620072005-2007MonthlyIndex Expected annual demand = 1,200 Janx.957 = 96 1,200 12 Febx.851 = 85 1,200 12 Forecast for 2008

65. © 2008 Prentice Hall, Inc.4 – 65 Seasonal Index Example 140 140 – 130 130 – 120 120 – 110 110 – 100 100 – 90 90 – 80 80 – 70 70 – ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Time Demand 2008 Forecast 2007 Demand 2006 Demand 2005 Demand

66. © 2008 Prentice Hall, Inc.4 – 66 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

67. © 2008 Prentice Hall, Inc.4 – 67 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 ^

68. © 2008 Prentice Hall, Inc.4 – 68 Associative Forecasting Example SalesLocal 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

69. © 2008 Prentice Hall, Inc.4 – 69 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

70. © 2008 Prentice Hall, Inc.4 – 70 Associative Forecasting Example 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll 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 3.25

71. © 2008 Prentice Hall, Inc.4 – 71  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

72. © 2008 Prentice Hall, Inc.4 – 72 Correlation Coefficient r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

73. © 2008 Prentice Hall, Inc.4 – 73 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

74. © 2008 Prentice Hall, Inc.4 – 74  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

75. © 2008 Prentice Hall, Inc.4 – 75 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

76. © 2008 Prentice Hall, Inc.4 – 76 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

77. © 2008 Prentice Hall, Inc.4 – 77 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