References. 1. Russel et al., Operations Managemnt, 4 th edition. Management 3. Dr-Ing. Daniel Kitaw, Industrial Management and Engineering Economy

Transcription

1 Forecasting References 1. Russel et al., Operations Managemnt, 4 th edition 2. Buffa et al., Production and Operations Management 3. Dr-Ing. Daniel Kitaw, Industrial Management and Engineering Economy 4-1

2 OUTLINE Company Profile What Is Forecasting? Forecasting Time Horizons The Influence of Product Life Cycle Types of Forecasts 4-2

3 OUTLINE-CONTINUED The Strategic Importance of Forecasting Forecasting Approaches Overview of Qualitative Methods Overview of Quantitative Methods 4-3

4 OUTLINE-CONTINUED Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment 4-4

5 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 4-5

6 OUTLINE-CONTINUED Monitoring and Controlling Forecasts Adaptive Smoothing Focus Forecasting Forecasting in the Service Sector 4-6

7 FORECASTING AT EEPCO s EEPCo is responsible for generating, transmitting, distributing and selling of electric energy through out the country. The number of electrified towns and rural villages, highly increased for the last five years of the strategic plan period and by July 2011 reached to a total number of 5,866 which brought the electric energy access to 46% 4-7

8 A Simplified Power System Layout CONT D 4-8

9 Progress in Generation Capacity CONT D Tis Abay II Fincha 4 th unit Gilgel Gibe I Awash 7 kilo Thermal Kaliti Diesel Diredawa Diesel Tekeze I Gilgele Gibe II Beles Ashegoda Wind Gibe III Abay Dam, 4-9

10 CONT D Transmission line progress Substations 4-10

11 CONT D Looking at the most determinant factors of energy demand growth factors GDP and Population, the recent good economic performance of the country as demonstrated in the three consecutive years GDP growths of more than 10%. The coming five years growth assumed to be same. Similarly population growth expected to be 2.22 to 1.8%. 4-11

12 Target and Moderate forecast CONT D Analysis made on historical sales and GDP data for the period 1973 to 2007 reveals that the electricity demand has an elasticity of 2.15 to changes in the overall GDP. If an economic growth rate of 7-10% can be achieved in the coming years, it could be translated to an electric energy demand growth rate of about 17% (as projected in the target scenario) based on the above elasticity estimate. 4-12

13 CONT D Yearly demand d growth 4-13

14 CONT D Generates monthly, annual, and 5-year forecasts. Forecast used by labor management, maintenance, operations, finance, and scheduling. Forecast used to adjust the generated energy, required finance, operation hours and staffing level 4-14

15 WHAT IS FORECASTING? Predictions, projections or estimates of future events or conditions in which an enterprise operates. The estimates can be: Demand? Occurrence of an event Timing of happening Magnitude or volume 4-15

16 CONT D The purpose of forecasting is to use the best available information to guide future activities iii toward organizational i goals. Underlying basis of all business decisions Production Inventory Personnel Facilities 4-16

17 FORECASTING TIME HORIZONS Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels Medium-range forecast 3 months to 3 years Sales and production planning, budgeting 4-17

18 FORECASTING TIME HORIZONS Long-range forecast 3 + years New product planning, facility location, research and development 4-18

19 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-termterm forecasts tend to be more accurate than longer-term forecasts 4-19

20 Forecasting system INPUTS Decisions 1. Selection of data 2. Selection of Methods OUTPUT 1. Internal data a. Historical b. Subjective Forecasting Methods c. Survey 1. Predictive 2. Causal 2. Environmental Data 3. Time series a. Economic b. Social, political c. Technological Constraints 1. Data 2. Expertise 3. Time 4. Funds Eti Estimates t of 1. Expected demand 2. Forecast error 4-20

21 INFLUENCE OF PRODUCT LIFE CYCLE Introduction Growth Maturity Decline Introduction and growth require longer forecasts than maturity and decline As product passes through life cycle, forecasts are useful in projecting Staffing levels Inventory levels Factory capacity 4-21

22 PRODUCT LIFE CYCLE Co ompany Strate egy/iss sues Introduction Growth Maturity Decline Best period to increase market share R&D engineering is critical Sales Practical to change price or quality image Strengthen niche Internet search engines ipods Xbox 360 I Phone 3D technology Air Bus Twitter Boeing 787 Poor time to change image, price, or quality Competitive costs become critical USB sticks LCD & plasma TVs Cost control critical ii CD-ROMs Analog TVs Floppy disk 4-22

23 PRODUCT LIFE CYCLE Introduction Growth Maturity Decline OM S trategy y/issues s Product design and development critical Frequent product process design changes Short production runs High production costs Limited models Attention to quality Forecasting Standardization Little product critical Fewer product differentiation Product and changes, more Cost process reliability minor changes minimization Competitive Optimum capacity Overcapacity product Increasing in the industry improvements and stability of Prune line to options process eliminate items Increase capacity Long production not returning Shift toward runs good margin product focus Product Reduce Enhance improvement and capacity distribution cost cutting 4-23

24 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 4-24

25 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 4-25

26 FORECASTING PROCESS 1. Identify the purpose of forecast 2. Collect historical data 3. Plot data and identify patterns 6. Check forecast accuracy with one or more measures 5. Develop/compute forecast for period of historical data 4. Select a forecast model 7. Is accuracy of forecast acceptable? 8b. Select new forecast model or adjust parameters of existing model 8a. Forecast over planning horizon 9. Adjust forecast 10. Monitor results based on additional and measure qualitative information forecast accuracy 4-26

27 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 4-27

28 FORECASTING APPROACHES Qualitative Methods Used when situation ti is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet 4-28

29 FORECASTING APPROACHES Quantitative Methods Used when situation is stable and historical data exist Existing i products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions 4-29

30 OVERVIEW OF QUALITATIVE METHODS 1. Jury of executive opinion 2. Delphi method 3. Sales force composite 4. Consumer Market Survey 4-30

31 JURY OF EXECUTIVE OPINION Involves small group of high-level experts and managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick Group-think disadvantage 4-31

32 DELPHI METHOD Iterative group process, continues until consensus is reached 3 types of participants Decision makers Staff Respondents Staff (What will sales be? survey) Decision Makers (Sales will be 50!) Respondents (Sales will be 45, 50, 55) 4-32

33 SALES FORCE COMPOSITE Each salesperson projects his or her sales Combined at district and national levels l Sales represents customers wants Tends to be overly optimistic 4-33

34 CONSUMER MARKET SURVEY Ask customers about purchasing plans. What consumers say, and what they actually do are often different. Sometimes difficult to answer. 4-34

35 OVERVIEW OF QUANTITATIVE APPROACHES 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-series models Associative model 4-35

36 TIME SERIES FORECASTING Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values, no other variables important Assumes that factors influencing past and present will continue influence in future 4-36

37 TIME SERIES COMPONENTS Trend Cyclical l Seasonal Random 4-37

38 COMPONENTS OF DEMAND Demand for produ uct or se ervice Seasonal peaks Random variation Time (years) Trend component Actual demand line Average demand over 4 years 4-38

39 TREND COMPONENT Persistent, overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration 4-39

40 SEASONAL COMPONENT Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year Number of Period Length Seasons Week Day 7 Month Week Month Day Year Quarter 4 Year Month 12 Year Week

41 CYCLICAL COMPONENT Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships

42 RANDOM COMPONENT Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen events Short duration and non-repeating M T W T F 4-42

43 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 4-43

44 MOVING AVERAGE METHOD MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Moving average = demand in previous n periods n 4-44

45 Moving Average Example Actual 3-Month Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 ( )/3 = 11 2 / 3 ( )/3 = 13 2 / 3 ( )/3 = 16 July 26 ( )/3 = 19 1 /

46 Graph of Moving Average Sales Shed Actual Sales Moving Average Forecast J F M A M J J A S O N D 4-46

47 WEIGHTED MOVING AVERAGE Used when some trend might be present Older data usually less important Weights based on experience and intuition (Weight for period n) x Weighted Moving Average = (Demand in period n) Weights 4-47

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

49 POTENTIAL PROBLEMS WITH MOVING AVERAGE Increasing n smoothes the forecast but makes it less sensitive to changes. Do notforecast trends well. Require extensive historical i data. 4-49

50 MOVING AVERAGE AND WEIGHTED MOVING AVERAGE Sales de emand Actual sales 15 SMoving 10 average Weighted moving average 5 J F M A M J J A S O N D 4-50

51 EXPONENTIAL SMOOTHING Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant t ( ) Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data 4-51

52 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 ) Where F t = new forecast F t 1 = previous forecast = smoothing (or weighting) constant (0 1) 4-52

53 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant =

54 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant =0.20 New forecast = ( ) = = cars 4-54

55 IMPACT OF DIFFERENT 225 Dema and Actual demand = 0.5 = Quarter 4-55

56 IMPACT OF DIFFERENT 225 Dema and Chose high Actual h values of when underlying demand average is likely to change = 0.5 Choose low values of when underlying average is stable = Quarter 4-56

57 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 4-57

58 COMMON MEASURES OF ERROR Mean Absolute Deviation (MAD) MAD = Actual - Forecast n Mean Squared Error (MSE) MSE = (Forecast Errors)2 n 4-58

59 COMMON MEASURES OF ERROR Mean Absolute Percent Error (MAPE) MAPE = n 100 Actualt l i - Forecast /Actual i i i = 1 n 4-59

60 COMPARISON OF FORECAST ERROR Rounded d Absolute Rounded d Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded = 0.10 = 0.10 = 0.50 =

61 COMPARISON OF FORECAST ERROR Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for = deviations Quarter MAD Unloaded a =.10 a =.10 = 0.50 = 0.50 For = 0.10 n = 82.45/ = For = = 98.62/8 =

62 COMPARISON OF FORECAST ERROR Rounded d Absolute Rounded d Absolute Actual (forecast Forecast errors)2 Deviation Forecast Deviation MSE = Tonnage with for with for Quarter Unloaded a =.10 a =.10 = = n = 159 1,526.54/ /8 75 = = 1,561.91/8 = For = 0.10 For = MAD

63 COMPARISON OF FORECAST ERROR n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage 100 deviation with for /actual i with i for Quarter MAPE Unloaded = i = 1 a =.10 a =.10 a =.50 = n For 168 = = 44.75/8 = 5.59% 59% For 190 = = 54.05/ = % MAD MSE

64 COMPARISON OF FORECAST ERROR Actual Rounded Absolute Rounded Absolute Tonnage Forecast Deviation Forecast Deviation Quarter Unloaded = 0.10 = 0.10 = 0.50 = MAD MSE MAPE 5.59% 6.76% 4-64

65 EXPONENTIAL SMOOTHING WITH TREND ADJUSTMENT When a trend is present, exponential smoothing must be modified Forecast Exponentially Exponentially including (FIT t ) = smoothed (F t ) + smoothed (T t ) trend forecast trend F t = (A( t - 1 ) + (1 - )(F t T t - 1 ) T t = (F t - F t - 1 ) + (1 - )T t

66 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t

67 Exponential Smoothing with Trend Adjustment Example for and for Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Step 1: Forecast for Month F 2 = A 1 + (1 - )(F 1 + T 1 ) F 2 = (0.2)(12) + (1-0.2)(11 + 2) 8 28 = = 12.8 units

68 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t Step 2: Trend for Month T 2 = (F 2 - F 1 ) + (1 - )T T 2 = (0.4)( ) + (1-0.4)(2) 8 28 = = 1.92 units

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

70 Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t ) Forecast, F t Trend, T t Trend, FIT t

71 Exponential Smoothing with Trend Adjustment Example 30 Pr roduct demand Actual demand (A t ) Forecast including trend (FIT t ) with = 0.2 and = Time (month) 4-71

72 TREND PROJECTIONS Fitting a trend line to historical data points to project into the medium to long-range Linear trends can be found using the least squares technique ^y = a + bx Where y^ =computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable 4-72

73 LEAST SQUARES METHOD Depend dent Var riable Actual observation (y-value) Deviation 3 Deviation 7 Deviation 5 Deviation 6 Deviation 4 Va alues of Deviation 1 (error) Deviation 2 Trend line, ^ y = a + bx Time period 4-73

74 LEAST SQUARES METHOD Depend dent Var riable Va alues of Actual observation (y-value) Deviation 1 Deviation 3 Deviation 5 Deviation 7 Deviation 6 Least squares method minimizes Deviation 4 the sum of the squared errors (deviations) (error) Deviation 2 Trend line, ^ y = a + bx Time period 4-74

75 LEAST SQUARES METHOD Equations to calculate the regression variables ^ y = a + bx xy y - nxy b = x 2 -nx 2 a = y - bx 4-75

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

77 Least Squares Example Time Electrical Power Year Period (x) Demand x 2 xy The trend 122 line is x = 28 y ^ y = x 2 + = x xy = 3,063 x = 4 y = xy - nxy 3,063 - (7)(4)(98.86) b = = = x 2 - nx (7)(4 2 ) a = y - bx = (4) =

78 Least Squares Example Power de emand Trend line, ^ y = x Year 4-78

79 LEAST SQUARES REQUIREMENTS 1. We always plot the data to insure a linear relationship 2. We do not predict time periods far beyond the database 3. Deviations around the least squares line are assumed to be random 4-79

80 SEASONAL VARIATIONS IN DATA Steps in the process: 1. Find Fndaverage aeragehstorcal 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. Divideid this estimate of total demandd by the number of seasons, then multiply it by the seasonal index for that season 4-80

81 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

82 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Mar Apr Average monthly demand 94 Seasonal index = May Average monthly 123 demand d 94 Jun = 90/ = Jul Aug Sept Oct Nov Dec

83 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

84 Seasonal Index Example Demand Average Average Seasonal Month Monthly Index Jan Feb Mar Forecast 82 for Apr Expected annual demand = 1,200 May Jun , Jul Jan x = Aug ,200 Sept Feb 95 x = Oct Nov Dec

85 Seasonal Index Example Deman nd Forecast 2009 Demand 2008 Demand 2007 Demand 70 J F M A M J J A S O N D Time 4-85

86 CORRELATION How strong is the linear relationship between the variables? Correlation does not necessarily imply causality! Coefficient of correlation, r, measures degree of association Values range from -1 to

87 CORRELATION COEFFICIENT r = nsxys - SxSy S [nsx 2 - (Sx) 2 ][nsy 2 - (Sy) 2 ] 4-87

88 CORRELATION COEFFICIENT y y x (a) Perfect positive correlation: r = +1 x (b) Positive correlation: 0 < r < 1 y y (c) No correlation: r = 0 x (d) Perfect negative correlation: r =-1 x 4-88

89 CORRELATION Coefficient of Determination, r 2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret 4-89

90 MULTIPLE REGRESSION ANALYSIS If more than one independent variable is to be used in the model, linear regression can be extended d to multiple l 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 4-90

91 MONITORING AND CONTROLLING FORECASTS Tracking Signal 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 4-91

92 MONITORING AND CONTROLLING FORECASTS Tracking signal = Cumulative error MAD Tracking signal = (Actual demand in period i Forecast demand in period i) ( Actual - Forecast /n) 4-92

93 TRACKING SIGNAL + 0 MADs Signal exceeding limit Upper control limit Lower control limit Time Tracking signal Acceptable range 4-93

94 ADAPTIVE FORECASTING It s possible to use the computer to continually monitor forecast error and adjust the values of the a and b coefficients used in exponential smoothing to continually minimize forecast error. This technique is called adaptive smoothing. 4-94

95 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 4-95

96 Percent tage of sales20% 15% 10% Fast Food Restaurant Forecast 5% (Lunchtime) (Dinnertime) Hour of day 4-96

97 FedEx Call Center Forecast 12% 10% 8% 6% 4% 2% 0% A.M. P.M. Hour of day 4-97