Transcript Forecasting
Chapter 4 – Forecasting PowerPoint presentation to accompany Heizer/Render Operations Management, 8e © 2006 Prentice Hall, Inc. PSM10 4–1 What is Forecasting? Process of predicting a future event Underlying basis of all business decisions ?? Production Inventory Personnel Facilities PSM10 4–2 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 Long-range forecast 3+ years New product planning, facility location, research and development PSM10 4–3 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 PSM10 4–4 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 PSM10 4–5 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 product PSM10 4–6 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 advance PSM10 4–7 Seven Steps in Forecasting 1. Determine the use of the forecast 2. Select the items to be forecasted 3. Determine the time horizon of the forecast 4. Select the forecasting model(s) 5. Gather the data 6. Make the forecast 7. Validate and implement results PSM10 4–8 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 PSM10 4–9 Forecasting Approaches Qualitative Methods Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet PSM10 4 – 10 Forecasting Approaches Quantitative Methods Used when situation is ‘stable’ and historical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions PSM10 4 – 11 Overview of Qualitative Methods Jury of executive opinion Pool opinions of high-level executives, sometimes augment by statistical models Delphi method Panel of experts, queried iteratively PSM10 4 – 12 Overview of Qualitative Methods Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated Consumer Market Survey Ask the customer PSM10 4 – 13 Jury of Executive Opinion Involves small group of high-level managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick ‘Group-think’ disadvantage PSM10 4 – 14 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 PSM10 4 – 15 Delphi Method Iterative group process, continues until consensus is reached Staff (Administering 3 types of survey) participants Decision makers Staff Respondents PSM10 Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments) 4 – 16 Consumer Market Survey Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer PSM10 4 – 17 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages Time-Series Models 3. Exponential smoothing 4. Trend projection 5. Linear regression PSM10 Associative Model 4 – 18 Time Series Forecasting Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values Assumes that factors influencing past and present will continue influence in future PSM10 4 – 19 Time Series Components Trend Cyclical Seasonal Random PSM10 4 – 20 Demand for product or service Components of Demand Trend component Seasonal peaks Actual demand Average demand over four years Random variation | 1 | 2 | 3 | 4 Year PSM10 4 – 21 Trend Component Persistent, overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration PSM10 4 – 22 Seasonal Component Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year Period Length Number of Seasons Week Month Month Year Year Year Day Week Day Quarter Month Week 7 4-4.5 28-31 4 12 52 PSM10 4 – 23 Cyclical Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships 0 PSM10 5 10 15 20 4 – 24 Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and nonrepeating M PSM10 T W T F 4 – 25 Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If May sales were 48, then June sales will be 48 Sometimes cost effective and efficient PSM10 4 – 26 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 ∑ demand in previous n periods Moving average = n PSM10 4 – 27 Moving Average Example Month Actual Shed Sales 3-Month Moving Average January February March April May June July 10 12 13 16 19 23 26 (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 PSM10 4 – 28 Shed Sales Graph of Moving Average 30 28 26 24 22 20 18 16 14 12 10 Moving Average Forecast – – – – – – – – – – – Actual Sales | J | F | M | A | M | J PSM10 | J | A | S | O | N | D 4 – 29 Weighted Moving Average Used when trend is present Older data usually less important Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) PSM10 ∑ weights 4 – 30 Weighted Moving Average Weights Applied Period 3 2 1 6 Month Actual Shed Sales January February March April May June July 10 12 13 16 19 23 26 Last month Two months ago Three months ago Sum of weights 3-Month Weighted Moving Average [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2 PSM10 4 – 31 Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data PSM10 4 – 32 Moving Average And Weighted Moving Average Weighted moving average Sales demand 30 – 25 – 20 – Actual sales 15 – Moving average 10 – 5 – | J | F | M | A | M | J PSM10 | J | A | S | O | N | D 4 – 33 Exponential Smoothing 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 PSM10 4 – 34 Exponential Smoothing New forecast = last period’s forecast + (last period’s actual demand – last period’s forecast) Ft = Ft – 1 + (At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast = smoothing (or weighting) constant (0 1) PSM10 4 – 35 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant = .20 PSM10 4 – 36 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant = .20 New forecast = 142 + .2(153 – 142) PSM10 4 – 37 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 PSM10 4 – 38 Effect of Smoothing Constants Weight Assigned to Smoothing Constant Most Recent Period () 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Period Period Period Period 2 3 (1 - ) (1 - ) (1 - ) (1 - )4 = .1 .1 .09 .081 .073 .066 = .5 .5 .25 .125 .063 .031 PSM10 4 – 39 Impact of Different Demand 225 – = .5 Actual demand 200 – 175 – = .1 150 – | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Quarter PSM10 4 – 40 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 = At - Ft PSM10 4 – 41 Other interpretation Ft = Ft – 1 + (At - Ft – 1) – forecast for the t+1st period, At – demand of the t-th period Ft At ( 1 )Ft 1 At ( 1 ) At 1 ( 1 )Ft 2 At ( 1 ) At 1 ( 1 )2 Ft 2 At ( 1 ) At 1 ( 1 )2 Ar t 2 ( 1 )Ft 3 At ( 1 ) At 1 ( 1 )2 At 2 ( 1 )3 Ft 3 ... α 1 α i At i i 0 Exponential smoothing is the weighted average of the complete historic demand. The weights are decreasing exponentially from period to period. PSM10 4 – 42 Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |actual - forecast| n Mean Squared Error (MSE) MSE = ∑ (forecast errors)2 n PSM10 4 – 43 Common Measures of Error Mean Absolute Percent Error (MAPE) n 100 ∑ |actuali - forecasti|/actuali MAPE = i=1 n PSM10 4 – 44 Comparison of Forecast Error Quarter Actual Tonnage Unloaded Rounded Forecast with = .10 Absolute Deviation for = .10 Rounded Forecast with = .50 1 2 3 4 5 6 7 8 180 168 159 175 190 205 180 182 175 176 175 173 173 175 178 178 5 8 16 2 17 30 2 4 84 175 178 173 166 170 180 193 186 PSM10 Absolute Deviation for = .50 5 10 14 9 20 25 13 4 100 4 – 45 Comparison of Forecast Error ∑ |deviations| Rounded Absolute MADActual = Quarter Tonage Unloaded Forecast n with = .10 Deviation for = .10 For 180 = .10 175 168 = 84/8 176 = 10.50 1 2 3 4 For 5 6 7 8 159 175 175 = .50 173 190 173 205 = 100/8 175 = 180 178 182 178 5 8 16 2 17 12.5030 2 4 84 PSM10 Rounded Forecast with = .50 175 178 173 166 170 180 193 186 Absolute Deviation for = .50 5 10 14 9 20 25 13 4 100 4 – 46 Comparison of Forecast Error ∑ (forecast errors)2 MSE = Actual Quarter Tonage Unloaded Rounded Forecast n with = .10 Absolute Deviation for = .10 For 180 = .10 175 5 168 176 = 1,558/8 = 194.758 1 2 3 4 For 5 6 7 8 159 175 175 = .50 173 190 173 = 1,612/8175= 205 180 178 182 178 16 2 17 201.50 30 2 4 84 MAD 10.50 PSM10 Rounded Forecast with = .50 175 178 173 166 170 180 193 186 Absolute Deviation for = .50 5 10 14 9 20 25 13 4 100 12.50 4 – 47 Comparison of Forecast Error n 100 ∑ |deviationi|/actuali i =Rounded 1 Forecast Tonage with Unloaded = .10 MAPE = Actual Quarter 1 2 3 4 5 6 7 8 n Absolute Deviation for = .10 For 180 = .10 175 5 168 176 8 = 45.62/8 = 5.70% 159 For 175 = 190 205 180 182 175 .50 173 173 = 54.8/8 175 178 178 MAD MSE 16 2 17 = 6.85% 30 2 4 84 10.50 194.75 PSM10 Rounded Forecast with = .50 175 178 173 166 170 180 193 186 Absolute Deviation for = .50 5 10 14 9 20 25 13 4 100 12.50 201.50 4 – 48 Comparison of Forecast Error Quarter Actual Tonnage Unloaded Rounded Forecast with = .10 1 2 3 4 5 6 7 8 180 168 159 175 190 205 180 182 175 176 175 173 173 175 178 178 MAD MSE MAPE Absolute Deviation for = .10 5 8 16 2 17 30 2 4 84 10.50 194.75 5.70% PSM10 Rounded Forecast with = .50 175 178 173 166 170 180 193 186 Absolute Deviation for = .50 5 10 14 9 20 25 13 4 100 12.50 201.50 6.85% 4 – 49 Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast exponentially exponentially including (FITt) = smoothed (Ft) + (Tt) smoothed trend forecast trend PSM10 4 – 50 Exponential Smoothing with Trend Adjustment Ft At 1 1 Ft 1 Tt 1 Tt Ft Ft 1 1 Tt 1 Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt = Ft + Tt PSM10 4 – 51 Exponential Smoothing with Trend Adjustment Example Month(t) 1 2 3 4 5 6 7 8 9 10 Actual Demand (At) 12 17 20 19 24 21 31 28 36 Smoothed Forecast, Ft 11 PSM10 Smoothed Trend, Tt 2 Forecast Including Trend, FITt 13.00 4 – 52 Exponential Smoothing with Trend Adjustment Example Month(t) 1 2 3 4 5 6 7 8 9 10 Forecast Including Trend, FITt 13.00 Actual Smoothed Smoothed Demand (At) Forecast, Ft Trend, Tt 12 11 2 17 20 19 Step 1: Forecast for Month 2 24 21 F2 = A1 + (1 - )(F1 + T1) 31 28 F2 = (.2)(12) + (1 - .2)(11 + 2) 36 = 2.4 + 10.4 = 12.8 units PSM10 4 – 53 Exponential Smoothing with Trend Adjustment Example Month(t) 1 2 3 4 5 6 7 8 9 10 Forecast Including Trend, FITt 13.00 Actual Smoothed Smoothed Demand (At) Forecast, Ft Trend, Tt 12 11 2 17 12.80 20 19 Step 2: Trend for Month 2 24 21 T2 = (F2 - F1) + (1 - )T1 31 28 T2 = (.4)(12.8 - 11) + (1 - .4)(2) 36 = .72 + 1.2 = 1.92 units PSM10 4 – 54 Exponential Smoothing with Trend Adjustment Example Month(t) 1 2 3 4 5 6 7 8 9 10 Forecast Including Trend, FITt 13.00 Actual Smoothed Smoothed Demand (At) Forecast, Ft Trend, Tt 12 11 2 17 12.80 1.92 20 19 Step 3: Calculate FIT for Month 2 24 21 FIT2 = F2 + T1 31 28 FIT2 = 12.8 + 1.92 36 = 14.72 units PSM10 4 – 55 Exponential Smoothing with Trend Adjustment Example Month(t) 1 2 3 4 5 6 7 8 9 10 Actual Demand (At) 12 17 20 19 24 21 31 28 36 Smoothed Forecast, Ft 11 12.80 15.18 17.82 19.91 22.51 24.11 27.14 29.28 32.48 PSM10 Smoothed Trend, Tt 2 1.92 2.10 2.32 2.23 2.38 2.07 2.45 2.32 2.68 Forecast Including Trend, FITt 13.00 14.72 17.28 20.14 22.14 24.89 26.18 29.59 31.60 35.16 4 – 56 Exponential Smoothing with Trend Adjustment Example 35 – Product demand 30 – Actual demand (At) 25 – 20 – 15 – Forecast including trend (FITt) 10 – 5 – 0 – | 1 | 2 | 3 | 4 | 5 | 6 Time (month) PSM10 | 7 | 8 | 9 4 – 57 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 (regression analysis) y^ = a + bx ^ = computed value of the variable to where y be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable PSM10 4 – 58 Values of Dependent Variable Least Squares Method Actual observation (y value) Deviation7 Deviation5 Deviation6 Deviation3 Deviation4 Deviation1 Deviation2 Trend line, y^ = a + bx Time period PSM10 4 – 59 Values of Dependent Variable Least Squares Method Actual observation (y value) Deviation7 Deviation5 Deviation6 Least squares method minimizes the sum of the Deviation squared errors (deviations) Deviation3 4 Deviation1 Deviation2 Trend line, y^ = a + bx Time period PSM10 4 – 60 Least Squares Method Equations to calculate the regression variables y^ = a + bx b= Sxy - nxy Sx2 - nx2 a = y - bx PSM10 4 – 61 Least Squares Example Year 1999 2000 2001 2002 2003 2004 2005 Time Period (x) 1 2 3 4 5 6 7 ∑x = 28 x=4 Electrical Power Demand 74 79 80 90 105 142 122 ∑y = 692 y = 98.86 x2 xy 1 4 9 16 25 36 49 ∑x2 = 140 74 158 240 360 525 852 854 ∑xy = 3,063 3,063 - (7)(4)(98.86) ∑xy - nxy b= = = 10.54 140 - (7)(42) ∑x2 - nx2 a = y - bx = 98.86 - 10.54(4) = 56.70 PSM10 4 – 62 Least Squares Example Time Period (x) Electrical Power Demand x2 xy 1999 1 74 1 2000 2 79 4 line is 80 2001The trend 3 9 2002 4 90 16 2003 105 25 y^ 5= 56.70 + 10.54x 2004 6 142 36 2005 7 122 49 Sx = 28 Sy = 692 Sx2 = 140 x=4 y = 98.86 74 158 240 360 525 852 854 Sxy = 3,063 Year 3,063 - (7)(4)(98.86) Sxy - nxy b= = = 10.54 140 - (7)(42) Sx2 - nx2 a = y - bx = 98.86 - 10.54(4) = 56.70 PSM10 4 – 63 Power demand Least Squares Example 160 150 140 130 120 110 100 90 80 70 60 50 Trend line, y^ = 56.70 + 10.54x – – – – – – – – – – – – 141= 56.7+8*10.54 | 1999 | 2000 | 2001 | 2002 PSM10 | 2003 Year | 2004 | 2005 | 2006 | 2007 4 – 64 Seasonal Variations In Data The multiplicative seasonal model can modify trend data to accommodate seasonal variations in demand 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 PSM10 4 – 66 Seasonal Index Example Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand 2003 2004 2005 80 70 80 90 113 110 100 88 85 77 75 82 85 85 93 95 125 115 102 102 90 78 72 78 Average 2003-2005 Average Monthly 90 80 85 100 123 115 105 100 90 80 80 80 94 94 94 94 94 94 94 94 94 94 94 94 105 85 82 115 131 120 113 110 95 85 83 80 PSM10 Seasonal Index 4 – 67 Seasonal Index Example Month Demand 2003 2004 2005 Average 2003-2005 Average Monthly Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 average 82 85 monthly demand 94 2003-2005 Seasonal90index95= 115 Apr 100 94 average monthly demand May 113 125 131 123 94 = 90/94 = .957 Jun 110 115 120 115 94 Jul 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov 75 72 83 80 94 Dec 82 78 80 80 94 PSM10 Seasonal Index 0.957 4 – 68 Seasonal Index Example Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand 2003 2004 2005 80 70 80 90 113 110 100 88 85 77 75 82 85 85 93 95 125 115 102 102 90 78 72 78 Average 2003-2005 105 85 82 115 131 120 113 110 95 85 83 80 90 80 85 100 123 115 105 100 90 80 80 80 1,128 PSM10 Average Monthly Seasonal Index 94 94 94 94 94 94 94 94 94 94 94 94 0.957 0.851 0.904 1.064 1.309 1.223 1.117 1.064 0.957 0.851 0.851 0.851 4 – 69 Seasonal Index Example Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand 2003 2004 2005 Average 2003-2005 Average Monthly 80 85 105 90 94 for802006 70 85 Forecast 85 94 80 93 82 85 94 annual demand = 1,200 90Expected 95 115 100 94 113 125 131 123 94 110 115 120 1,200 115 94 Jan 113 x .957 = 96 94 100 102 105 12 88 102 110 100 94 1,200 85 90 95 Feb x90 .851 = 85 94 77 78 85 12 80 94 75 72 83 80 94 82 78 80 80 94 PSM10 Seasonal Index 0.957 0.851 0.904 1.064 1.309 1.223 1.117 1.064 0.957 0.851 0.851 0.851 4 – 70 Seasonal Index Example Jan 95,70 Feb 85,10 Mar 90,40 Apr 106,40 140,00 May 130,90 120,00 Jun 122,30 Jul 111,70 Aug 106,40 Sept 95,70 Oct 85,10 Nov 85,10 Dec 85,10 100,00 80,00 60,00 1 PSM10 2 3 4 5 6 7 8 9 10 11 12 4 – 71 Seasonal Index Example 2006 Forecast 2005 Demand 2004 Demand 2003 Demand 140 – 130 – Demand 120 – 110 – 100 – 90 – 80 – 70 – | J | F | M | A | M | J | J Time PSM10 | A | S | O | N | D 4 – 72 Monitoring and Controlling Forecasts Tracking Signal Measures how well the forecast is predicting actual values Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, the forecast has a bias error PSM10 4 – 73 Monitoring and Controlling Forecasts RSFE Tracking = signal MAD ∑(actual demand in period i forecast demand in period i) Tracking signal = ∑|actual - forecast|/n) PSM10 4 – 74 Tracking Signal Signal exceeding limit Tracking signal + Upper control limit Acceptable range 0 MADs – Lower control limit Time PSM10 4 – 75 Tracking Signal Example Qtr Actual Demand Forecast Demand Error RSFE Absolute Forecast Error 1 2 3 4 5 6 90 95 115 100 125 140 100 100 100 110 110 110 -10 -5 +15 -10 +15 +30 -10 -15 0 -10 +5 +35 10 5 15 10 15 30 PSM10 Cumulative Absolute Forecast Error MAD 10 15 30 40 55 85 10.0 7.5 10.0 10.0 11.0 14.2 4 – 76 Tracking Signal Example Qtr 1 2 3 4 5 6 Tracking Actual Signal Forecast (RSFE/MAD) Demand Demand Error RSFE Absolute Forecast Error 90-10/10 100= -1 -10 95 -15/7.5 100= -2 -5 115 0/10 100 = 0 +15 100-10/10 110= -1 -10 125 +5/11110 = +0.5+15 140 +35/14.2 110= +2.5 +30 -10 -15 0 -10 +5 +35 10 5 15 10 15 30 Cumulative Absolute Forecast Error MAD 10 15 30 40 55 85 10.0 7.5 10.0 10.0 11.0 14.2 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits PSM10 4 – 77 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 PSM10 4 – 78 Questions Answer the following questions How would you rate the time horizon for long range forecast in the field of mobile information technologies? Which of the Seven Steps in Forecasting is the most interesting for you? Did you ever use the method of “Jury of Executive Opinion” when discussing family affairs at home? Which week sides if the Delphi method would you identify? Under which circumstances do the Weighted Moving Average method and the method of exponential smoothing coincide? Can the two methods of exponential smoothing ever coincide? Look for the various opportunities of using forecast methods by Excel. Let the demand follow the function d(t) = 10 + 2t and apply the simple weighted average forecast method with n = 2. What can you say about the tracking signal? PSM10 4 – 79 Questions Homework No. 3: Create an Excel Spreadsheet to solve the following problem! Sales of music stands at Johnny Ho’s music store, in Columbus, Ohio, over the past 10 weeks are shown in the table below. Week Demand Week Demand 1 20 6 29 2 21 7 36 3 28 8 22 4 37 9 25 5 25 10 2? Put here the last digit of your university ID card number. a) Forecast demand for each week, including week 10, using exponential smoothing with α = 0.3 (initial forecast F1 = 20) b) Compute the MAD. c) Compute the tracking signal. Submit your solution file via E-Mail to [email protected] (term: 29.04.2010). Don’t forget to indicate your university ID card number. PSM10 4 – 80