Heizer om10 ch04

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Heizer om10 ch04

  1. 1. 10/16/2010 4 Forecasting Outline Global Company Profile: Disney World What Is Forecasting? PowerPoint presentation to accompany Heizer and Render Forecasting Time Horizons F ti Ti H i Operations Management, 10e Principles of Operations Management, 8e The Influence of Product Life Cycle PowerPoint slides by Jeff Heyl Types Of Forecasts© 2011 Pearson Education, Inc. publishing as Prentice Hall 4-1 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4-2 Outline – Continued Outline – Continued The Strategic Importance of Forecasting Approaches Forecasting Overview of Qualitative Methods Human Resources Overview of Quantitative Methods Capacity Time-Series Forecasting Supply Chain Management Decomposition of a Time Series Seven Steps in the Forecasting Naive Approach System© 2011 Pearson Education, Inc. publishing as Prentice Hall 4-3 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4-4 Outline – Continued Outline – Continued Time-Series Forecasting (cont.) Associative Forecasting Methods: Regression and Correlation Moving Averages Analysis Exponential Smoothing Using Regression Analysis for g g y Exponential Smoothing with Trend Forecasting Adjustment Standard Error of the Estimate Trend Projections Correlation Coefficients for Seasonal Variations in Data Regression Lines Cyclical Variations in Data Multiple-Regression Analysis© 2011 Pearson Education, Inc. publishing as Prentice Hall 4-5 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4-6 1
  2. 2. 10/16/2010 Outline – Continued Learning Objectives Monitoring and Controlling When you complete this chapter you Forecasts should be able to : Adaptive Smoothing 1. Understand the three time horizons Focus Forecasting F F ti and which models apply for each use Forecasting in the Service Sector 2. Explain when to use each of the four qualitative models 3. Apply the naive, moving average, exponential smoothing, and trend methods© 2011 Pearson Education, Inc. publishing as Prentice Hall 4-7 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4-8 Learning Objectives Forecasting at Disney World When you complete this chapter you Global portfolio includes parks in Hong should be able to : Kong, Paris, Tokyo, Orlando, and Anaheim 4. Compute three measures of forecast accuracy Revenues are derived from people – how many visitors and how they spend their 5. Develop seasonal indexes money 6. Conduct a regression and correlation Daily management report contains only analysis the forecast and actual attendance at 7. Use a tracking signal each park© 2011 Pearson Education, Inc. publishing as Prentice Hall 4-9 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 10 Forecasting at Disney World Forecasting at Disney World Disney generates daily, weekly, monthly, 20% of customers come from outside the annual, and 5-year forecasts USA Forecast used by labor management, Economic model includes gross maintenance, operations, finance, maintenance operations finance and domestic product, cross-exchange rates, product rates park scheduling arrivals into the USA Forecast used to adjust opening times, A staff of 35 analysts and 70 field people rides, shows, staffing levels, and guests survey 1 million park guests, employees, admitted and travel professionals each year© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 11 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 12 2
  3. 3. 10/16/2010 Forecasting at Disney World What is Forecasting? Inputs to the forecasting model include Process of predicting airline specials, Federal Reserve a future event policies, Wall Street trends, vacation/holiday schedules for 3,000 Underlying basis of all business ?? school districts around the world decisions Average forecast error for the 5-year Production forecast is 5% Inventory Average forecast error for annual Personnel forecasts is between 0% and 3% Facilities© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 13 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 14 Forecasting Time Horizons Distinguishing Differences Short-range forecast Up to 1 year, generally less than 3 months Medium/long range forecasts deal with Purchasing, job scheduling, workforce more comprehensive issues and support levels, job assignments, production levels management decisions regarding planning and products, plants and Medium-range forecast g processes 3 months to 3 years Short- Short-term forecasting usually employs Sales and production planning, budgeting different methodologies than longer-term Long-range forecast forecasting 3+ years Short- Short-term forecasts tend to be more New product planning, facility location, accurate than longer-term forecasts research and development© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 15 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 16 Influence of Product Life Product Life Cycle Cycle Introduction Growth Maturity Decline Best period to Practical to change Poor time to Cost control Introduction – Growth – Maturity – Decline increase market price or quality change image, critical egy/Issues share image price, or quality R&D engineering is Strengthen niche Competitive costs Introduction and growth require longer critical become critical Defend market forecasts than maturity and decline Company Strate position Drive-through Internet search engines restaurants As product passes through life cycle, iPods CD-ROMs LCD & forecasts are useful in projecting Xbox 360 plasma TVs Sales Staffing levels Avatars Inventory levels Boeing 787 Analog TVs Factory capacity Twitter Figure 2.5© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 17 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 18 3
  4. 4. 10/16/2010 Product Life Cycle Types of Forecasts Introduction Growth Maturity Decline Product design and Forecasting critical Standardization Little product differentiation Economic forecasts Fewer product development Product and changes, more Cost Address business cycle – inflation rate, y/Issues critical process minor changes minimization Frequent reliability Optimum Overcapacity money supply, housing starts, etc. product and Competitive capacity in the process design product d t industry i d t Technological forecasts OM Strategy changes Increasing improvements stability of Prune line to Short production and options process eliminate Predict rate of technological progress runs Increase capacity items not Long production High production Shift toward runs returning Impacts development of new products costs product focus good margin Limited models Enhance Product improvement Reduce Demand forecasts Attention to distribution and cost cutting capacity quality Predict sales of existing products and services Figure 2.5© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 19 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 20 Strategic Importance of Seven Steps in Forecasting Forecasting 1. Determine the use of the forecast 2. Select the items to be forecasted Human Resources – Hiring, training, laying off workers 3. Determine the time horizon of the forecast o ecast Capacity – C C it Capacity shortages can it h t result in undependable delivery, loss 4. Select the forecasting model(s) of customers, loss of market share 5. Gather the data Supply Chain Management – Good supplier relations and price 6. Make the forecast advantages 7. Validate and implement results© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 21 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 22 The Realities! Forecasting Approaches Qualitative Methods Forecasts are seldom perfect Used when situation is vague Most techniques assume an and little data exist underlying stability in the system New products Product family and aggregated forecasts are more accurate than New technology individual product forecasts Involves intuition, experience e.g., forecasting sales on Internet© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 23 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 24 4
  5. 5. 10/16/2010 Forecasting Approaches Overview of Qualitative Methods Quantitative Methods 1. Jury of executive opinion Used when situation is ‘stable’ and historical data exist Pool opinions of high-level experts, sometimes augment by statistical Existing products models Current technology 2. Delphi method Involves mathematical techniques Panel of experts, queried iteratively e.g., forecasting sales of color televisions© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 25 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 26 Overview of Qualitative Jury of Executive Opinion Methods Involves small group of high-level experts and managers 3. Sales force composite Group estimates demand by working Estimates from individual together salespersons are reviewed for l i df reasonableness, then aggregated Combines managerial experience with statistical models 4. Consumer Market Survey Relatively quick Ask the customer ‘Group-think’ disadvantage© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 27 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 28 Sales Force Composite Delphi Method Iterative group Decision Makers Each salesperson projects his or process, (Evaluate her sales continues until responses and consensus is make decisions) Combined at district and national reached levels Staff 3 types of (Administering Sales reps know customers’ wants participants survey) Tends to be overly optimistic Decision makers Staff Respondents (People who can Respondents make valuable judgments)© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 29 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 30 5
  6. 6. 10/16/2010 Consumer Market Survey Overview of Quantitative Approaches Ask customers about purchasing plans 1. Naive approach What consumers say, and what 2. Moving averages time-series time series they actually do are often different 3. Exponential models Sometimes difficult to answer smoothing 4. Trend projection 5. Linear regression associative model© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 31 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 32 Time Series Forecasting Time Series Components Set of evenly spaced numerical data Obtained by observing response Trend Cyclical variable at regular time periods Forecast based only on past values, no other variables important Assumes that factors influencing past and present will continue Seasonal Random influence in future© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 33 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 34 Components of Demand Trend Component Trend component Persistent, overall upward or downward pattern Demand for product or service Seasonal peaks Changes due to population, o Actual demand technology, age, culture, etc. t h l lt t line Typically several years Average demand over 4 years duration Random variation | | | | 1 2 3 4 Time (years) Figure 4.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 35 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 36 6
  7. 7. 10/16/2010 Seasonal Component Cyclical Component Regular pattern of up and down fluctuations Repeating up and down movements Due to weather, customs, etc. Affected by business cycle, political, and economic factors Occurs within a single year Multiple years duration Number of Period Length Seasons Often causal or Week Day 7 associative Month Week 4-4.5 Month Day 28-31 relationships Year Quarter 4 Year Month 12 Year Week 52 0 5 10 15 20© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 37 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 38 Random Component Naive Approach Erratic, unsystematic, ‘residual’ Assumes demand in next fluctuations period is the same as demand in most recent period Due to random variation or unforeseen events e g , Ja ua y sales e e e.g., If January sa es were 68, t e then February sales will be 68 Short duration Sometimes cost effective and and nonrepeating efficient Can be good starting point M T W T F© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 39 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 40 Moving Average Method Moving Average Example MA is a series of arithmetic means Actual 3-Month Month Shed Sales Moving Average Used if little or no trend January 10 Used often for smoothing y February 12 March 13 Provides overall impression of data April 16 (10 + 12 + 13 = 11 2/3 10 13)/3 over time May 19 (12 + 13 + 16)/3 = 13 2/3 June 23 (13 + 16 + 19)/3 = 16 July 26 (16 + 19 + 23)/3 = 19 1/3 ∑ demand in previous n periods Moving average = n© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 41 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 42 7
  8. 8. 10/16/2010 Graph of Moving Average Weighted Moving Average Moving Used when some trend might be Average 30 28 – – Forecast present Actual 26 – Sales Older data usually less important 24 – Shed Sales 22 20 – – Weights b W i ht based on experience and d i d 18 – intuition 16 – 14 – ∑ (weight for period n) 12 – Weighted x (demand in period n) 10 – | | | | | | | | | | | | moving average = ∑ weights J F M A M J J A S O N D© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 43 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 44 Weights Applied Period Weighted Moving Last month 3 Average Potential Problems With 2 1 Two months ago Three months ago Moving Average 6 Sum of weights Increasing n smooths the forecast Actual 3-Month Weighted but makes it less sensitive to Month Shed Sales Moving Average changes January 10 February 12 Do not forecast trends well March 13 April 16 [(3 x 13 + (2 x 12 + (10 13) 12) 10)]/6 = 121/6 Require extensive historical data May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 June 23 [(3 x 19) + (2 x 16) + (13)]/6 = 17 July 26 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 45 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 46 Moving Average And Exponential Smoothing Weighted Moving Average Weighted Form of weighted moving average 30 – moving average Weights decline exponentially 25 – Most recent data weighted most and Sales dema 20 – Actual sales Requires smoothing constant (α) 15 – Moving Ranges from 0 to 1 10 – average Subjectively chosen 5 – Involves little record keeping of past | | | | | | | | | | | | J F M A M J J A S O N D data Figure 4.2© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 47 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 48 8
  9. 9. 10/16/2010 Exponential Smoothing Exponential Smoothing Example New forecast = Last period’s forecast + α (Last period’s actual demand Predicted demand = 142 Ford Mustangs – Last period’s forecast) Actual demand = 153 Smoothing constant α = .20 Ft = Ft – 1 + α(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast α = smoothing (or weighting) constant (0 ≤ α ≤ 1)© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 49 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 50 Exponential Smoothing Exponential Smoothing Example Example Predicted demand = 142 Ford Mustangs Predicted demand = 142 Ford Mustangs Actual demand = 153 Actual demand = 153 Smoothing constant α = .20 Smoothing constant α = .20 New forecast = 142 + .2(153 – 142) New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 51 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 52 Effect of Impact of Different α Smoothing Constants 225 – Weight Assigned to Actual α = .5 200 – demand Most 2nd Most 3rd Most 4th Most 5th Most nd Deman Recent R t Recent R t Recent R t Recent R t Recent R t Smoothing Period Period Period Period Period Constant (α) α(1 - α) α(1 - α)2 α(1 - α)3 α(1 - α)4 175 – α = .1 .1 .09 .081 .073 .066 α = .5 .5 .25 .125 .063 .031 α = .1 150 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 53 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 54 9
  10. 10. 10/16/2010 Impact of Different α Choosing α 225 – The objective is to obtain the most Actual α = .5 accurate forecast no matter the Chose high values of α 200 – demand technique when underlying average nd Deman is likely to change We generally do this by selecting the 175 – Choose low values of α model that gives us the lowest forecast when underlying average error α = .1 is stable| 150 – | | | | | | | | Forecast error = Actual demand - Forecast value 1 2 3 4 5 6 7 8 9 Quarter = At - Ft© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 55 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 56 Common Measures of Error Common Measures of Error Mean Absolute Deviation (MAD) Mean Absolute Percent Error (MAPE) ∑ |Actual - Forecast| MAD = n n ∑100|Actuali - Forecasti|/Actuali Mean Squared Error (MSE) MAPE = i=1 n ∑ (Forecast Errors)2 MSE = n© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 57 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 58 Comparison of Forecast Comparison of Forecast Error Error Rounded Absolute Rounded Absolute ∑ |deviations| Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation MAD = Actual Forecast Deviation Forecast Deviation Tonnage with for with for Tonnage n with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 180 175 5.00 175 5.00 1 For α180.10 175 = 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 2 168 = 82.45/8 = 10.31 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 4 For α175.50 173.18 = 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 6 205 = 98.62/8 = 12.33 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 8 182 178.22 3.78 186.30 4.30 82.45 98.62 82.45 98.62© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 59 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 60 10
  11. 11. 10/16/2010 Comparison of Forecast Comparison of Forecast Error2 n Error ∑100|deviation |/actual ∑ (forecast errors) i i Rounded Absolute Rounded Absolute Rounded Absolute Rounded Absolute MSE = Actual Forecast Deviation Forecast Deviation MAPE = i = 1 Actual Forecast Deviation Forecast Deviation Tonnage n with for with for Tonnage with n for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 Quarter Unloaded α = .10 α = .10 α = .50 α = .50 1 For α180.10 175 = 5.00 175 5.00 1 α= For 180 .10 175 5.00 175 5.00 2 168 1,526.54/8 = 190.82 = , 175.5 7.50 177.50 9.50 2 168 = 44.75/8 = 7.50 % 175.5 5.59% 177.50 9.50 3 159 174.75 15.75 172.75 13.75 3 159 174.75 15.75 172.75 13.75 4 For α175.50 173.18 = 1.82 165.88 9.12 4 α= For 175 .50 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 5 190 173.36 16.64 170.44 19.56 6 = 1,561.91/8 = 195.24 205 175.02 29.98 180.22 24.78 6 205 = 54.05/8 = 6.76% 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 8 182 178.22 3.78 186.30 4.30 82.45 98.62 82.45 98.62 MAD 10.31 12.33 MAD 10.31 12.33 MSE 190.82 195.24© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 61 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 62 Comparison of Forecast Exponential Smoothing with Error Trend Adjustment Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = .10 α = .10 α = .50 α = .50 When a trend is present, exponential 1 180 175 5.00 175 5.00 smoothing must be modified 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 Forecast Exponentially Exponentially 5 190 173.36 16.64 170.44 19.56 including (FITt) = smoothed (Ft) + smoothed (Tt) 6 205 175.02 29.98 180.22 24.78 trend forecast trend 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24 MAPE 5.59% 6.76%© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 63 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 64 Exponential Smoothing with Exponential Smoothing with Trend Adjustment Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt Ft = α(At - 1) + (1 - α)(Ft - 1 + Tt - 1) 1 12 11 2 13.00 2 17 Tt = β(Ft - Ft - 1) + (1 - β)Tt - 1 3 4 20 19 5 24 6 21 Step 1: Compute Ft 7 31 Step 2: Compute Tt 8 28 9 36 Step 3: Calculate the forecast FITt = Ft + Tt 10 Table 4.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 65 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 66 11
  12. 12. 10/16/2010 Exponential Smoothing with Exponential Smoothing with Trend Adjustment Example Trend Adjustment Example Forecast Forecast Actual Smoothed Smoothed Including Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 1 12 11 2 13.00 2 17 2 17 12.80 3 20 3 20 4 19 4 19 5 24 Step 1: Forecast for Month 2 5 24 Step 2: Trend for Month 2 6 21 6 21 7 31 F2 = αA1 + (1 - α)(F1 + T1) 7 31 T2 = β(F2 - F1) + (1 - β)T1 8 28 F2 = (.2)(12) + (1 - .2)(11 + 2) 8 28 T2 = (.4)(12.8 - 11) + (1 - .4)(2) 9 36 9 36 10 = 2.4 + 10.4 = 12.8 units 10 = .72 + 1.2 = 1.92 units Table 4.1 Table 4.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 67 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 68 Exponential Smoothing with Exponential Smoothing with Trend Adjustment Example Trend Adjustment Example Forecast Forecast Actual Smoothed Smoothed Including Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 1 12 11 2 13.00 2 17 12.80 1.92 2 17 12.80 1.92 14.72 3 20 3 20 15.18 2.10 17.28 4 19 4 19 17.82 2.32 20.14 5 24 Step 3: Calculate FIT for Month 2 5 24 19.91 2.23 22.14 6 21 6 21 22.51 2.38 24.89 7 31 FIT2 = F2 + T2 7 31 24.11 2.07 26.18 8 28 FIT2 = 12.8 + 1.92 8 28 27.14 2.45 29.59 9 36 9 36 29.28 2.32 31.60 10 = 14.72 units 10 32.48 2.68 35.16 Table 4.1 Table 4.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 69 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 70 Exponential Smoothing with Trend Projections Trend Adjustment Example Fitting a trend line to historical data points 35 – to project into the medium to long-range 30 – Actual demand (At) Linear trends can be found using the least mand 25 – squares technique Product dem 20 – ^ y = a + bx 15 – ^ where y = computed value of the variable to 10 – Forecast including trend (FITt) with α = .2 and β = .4 be predicted (dependent variable) 5 – a = y-axis intercept 0 – | | | | | | | | | b = slope of the regression line 1 2 3 4 5 6 7 8 9 x = the independent variable Figure 4.3 Time (month)© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 71 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 72 12
  13. 13. 10/16/2010 Least Squares Method Least Squares Method Values of Dependent Variable Values of Dependent Variable Actual observation Deviation7 Actual observation Deviation7 (y-value) (y-value) Deviation5 Deviation6 Deviation5 Deviation6 Deviation3 Deviation3 Least squares method minimizes the sum of the Deviation4 squared errors (deviations) Deviation 4 Deviation1 Deviation1 (error) Deviation2 (error) Deviation2 ^ Trend line, y = a + bx ^ Trend line, y = a + bx Time period Figure 4.4 Time period Figure 4.4© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 73 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 74 Least Squares Method Least Squares Example Time Electrical Power Year Period (x) Demand x2 xy Equations to calculate the regression variables 2003 1 74 1 74 2004 2 79 4 158 2005 3 80 9 240 ^ y = a + bx 2006 4 90 16 360 2007 5 105 25 525 2008 6 142 36 852 Σxy - nxy 2009 7 122 49 854 b= ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 Σx2 - nx2 x=4 y = 98.86 ∑xy - nxy 3,063 - (7)(4)(98.86) a = y - bx b= = = 10.54 ∑x2 - nx2 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 75 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 76 Least Squares Example Least Squares Example Time Electrical Power Year Period (x) Demand x2 xy Trend line, 160 – ^ 2003 1 74 1 74 150 – y = 56.70 + 10.54x 2004 2 79 4 158 140 – The trend line is 80 2005 3 9 240 emand 130 – 2006 4 90 16 360 120 – 2007 ^ 5 56 70 + 10 54x y = 56.70 10.54x 105 25 525 Power de 110 – 2008 6 142 36 852 100 – 2009 7 122 49 854 90 – ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 80 – x=4 y = 98.86 70 – 60 – ∑xy - nxy 3,063 - (7)(4)(98.86) b= = = 10.54 50 – ∑x2 - nx2 140 - (7)(42) | | | | | | | | | 2003 2004 2005 2006 2007 2008 2009 2010 2011 a = y - bx = 98.86 - 10.54(4) = 56.70 Year© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 77 © 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 78 13

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