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# OM 300- Forecasting OM 300

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This 83 page Class Notes was uploaded by Samantha on Sunday April 12, 2015. The Class Notes belongs to OM 300 at University of Alabama - Tuscaloosa taught by William Petty in Winter2015. Since its upload, it has received 239 views.

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Date Created: 04/12/15

Forecasting 2014 P eeee on Education Inc Learning Objectives When you complete this chapter you should be able to 1 2 9 N991 Understand the three time horizons and which models apply for each use Explain when to use each of the four qualitative models Apply the naive moving average exponential smoothing and trend methods Compute three measures of forecast accuracy Develop seasonal indexes Conduct a regression analysis Use a tracking signal What is Forecasting PI OCGSS Of predicting a future event 9 Underlying basis of all business decisions production inventorv gersonnel iacm es Forecasting Time Horizons 9 Short range forecast 9 Up to 1 year generally less than 3 months 9 Purchasing job scheduling workforce levels job assignments production levels 9 Medium range forecast O 3 months to 3 years 9 Sales and production planning budgeting 9 Long range forecast 9 3 years 9 New product planning facility location research and development Distinguishing Differences O Mediumlong range forecasts deal with more comprehensive issues and support management decisions regarding planning and products plants and processes 9 Short term forecasting usually employs different methodologies than longerterm forecasting O Short term forecasts tend to be more accurate than longerterm forecasts Influence of Product Life Cycle Introduction Growth Maturity Decline Introduction and growth require longer forecasts than maturity and decline 9 As product passes through life cycle forecasts are useful in projecting 9 Staffing levels 9 Inventory levels Factory capacity 4 l gt Hquotwalpi Types of Forecasts Economic forecasts 9 Address business cycle inflation rate money supply housing starts etc Technological forecasts O Predict rate of technological progress 9 Impacts development of new products Demand forecasts O Predict sales of existing products and services Strategic Importance of Forecasting Human Resources Hiring training laying oil workers 9 Capacity Capacity shortages can result in undependable delivery loss of customers loss of market share Supply Chain Management GOOCI supplier relations and price advantages Seven Steps in Forecasting 1 2 9 N979 Determine the use of the forecast the items to be Select forecasted Determine the time horizon forecast Select the forecasting model 3 Gather the data Make the forecast and implement results of the Validate The Realities p Forecasts are seldom perfect unpredictable outside factors may impact the forecast gt Most techniques assume an underlying stability in the system gt Product family and aggregated forecasts are more accurate than individual product forecasts Forecasting Approaches Qualitative MethOdS 9 Used when situation is vague and data eXiSt use when no past to look at New products New technology 9 Involves iiiiiiiiion experience 9 eg forecasting sales on Internet Forecasting Approaches Quantitative OdS 9 Used when situation is stable and historical data exist 9 Existing products 9 Current technology 9 Involves mathematical techniques 9 eg forecasting sales of color televisions Overview of Qualitative Methods 1 Jury of executive opinion 9 Pool opinions of highlevel experts sometimes augmented by statistical models 2 Delphi method 9 Panel of experts queried iterativey questioned repeatedly Overview of Qualitative Methods 3 Sales fOrCG composite 9 Estimates from individual salespersons are reviewed for reasonableness then aggregated 4 Consumer market Survey 9 Ask the customer 99 O O O Jury of Executive Opinion Involves small group of highlevel experts and managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick groupthink disadvantage Delphi Method Interactive 9 r0 U D process continues un lconsensusis reached i quotS Consensus is not average 3 types 0f Staff participants Administering surve O Decnsnon makers Y 9 Staff 9 Respondents 39l ecision Makers can ma uable judgments Sales Force Composite 9 Each salesperson projects his or her sales 9 Combined at district and national levels 9 Sales reps know customers wants Tends to be overly optimistic Consumer Market Survey 9 Ask customers about purchasing plans 9 What consumers say and what they actually do are often different 9 Sometimes difficult to answer Overview of Quantitative Approaches Naive approach Moving averag Exponen al smoothing Trend projection Linear regression associative model timeseries models Time Series Forecasting 9 Set of evenly spaced numerical data 9 Obtained by observing response variable at regular time periods 9 Forecast based only on past values no other variables important 9 Assumes that factors influencing past and present will continue influence in future Time Series Components ex need more peOple during 9X3 more Cmst 0 fr39day football games longer term Cyclical ex not fall winteretc could be a week month min or hours Demand for product or service Components of Demand Trend component J 9 Actual demand line Seasonal peaks 1 Average demand over 4 years A A Random variation 1 2 3 4 Time years Figure 4 1 Trend Component p Persistent overall upward or Wpattem p Changes due to population technology age culture etc gt Typically several years duration Seasonal Component gt Regular pattern of up and dawn fluctuations gt Due to weather customs etc gt Occurs within a single unit PERIOD LENGTH SEASON LENGTH NUMBER OF SEASONS IN PATTERN VVeek Day 7 Month Week 4 45 Month Day 28 31 Year Quarter 4 Year Month 12 Year Week 52 Cyclical Component Repeating up and down movements Affected by business cycle political and economic factors Multiple years duration Often causal or associative relationships Random Component p Erratic unsystematic residual fluctuations gt Due to random variatiOn or unforeseen events gt Short duration and nonrepeating Overview of Quantitative Approaches 1 Naive approach 2 Moving averages timeseries 3 Exponeptlal models smoothing 4 Trend proiection associative 5 LInear regressmn model Naive Approach p Assumes demand in next periOd is the same as demand in most recent period p eg If January sales were 68 then February sales will be 68 p Sometimes cost effective and efficient gt Can be gOOd starting point Moving Average Method V is a series Of arithmetic means gt Used if little or no trend gt Used often for smoothing p Provides overall impression of data over time Zdemand in previous n periods Movmg average 2 n Moving Average Example MONTH ACTUAL SHED SALES 3MONTH MOVING AVERAGE January 10 February 12 March 13 April 16 10121331123 May 19 12131631323 June 23 131619316 July 26 16 19 233 1913 August 30 19 23 263 22 23 September 28 23 26 303 26 13 October 18 29 30 283 28 November 16 30 28 183 25 13 December 14 28 18 163 20 23 Weighted Moving Average gt Used when some trend might be present gt Older data usually less important p Weights based on experience and intuition r nvgifmged 2Weight for period n Demand in period average ZWeights Weighted Moving Average MONTH ACTUAL SHED SALES 3MONTH WEIGHTED MOVING AVERAGE January 10 February 12 March 13 April 16 3x 13 2x 12 106 12 16 May 19 3x162x131261413 June 23 3x192x1613617 July 26 3 x 23 2 x 19 166 2012 August 30 3 x 26 2 x 23 196 23 56 September 28 3 x 30 2 x 26 236 27 12 October 18 3 x 28 2 x 30 266 28 13 November 16 3 x 18 2 x 28 306 23 13 December 14 3 x 16 2 x 18 286 18 23 Potential Problems With Moving Average p Increasing n smooths the forecast but makes it less sensitive to changes gt Does not forecast trends well gt Requires extensive historical data Exponential Smoothing p Form of weighted moving average gt Weights decline exponentially gt Most recent data weighted most p Requires smoothing constant a p Ranges from 0 to 1 p Subjectiver chosen p Involves little record keeping of past data Exponential Smoothing New forecast Last period s forecast aLast period s actual demand Last period s forecast choose high values of a when underlying avg is likely to change Ft Ft 1 At 1 39 t 1 where F new forecast previous period s forecast smoothing or weighting constant 0 S as 1 previous period s actual demand L Q L II II II Exponential Smoothing Example Predicted demand 142 Ford Mustangs Actual demand 153 Smoothing constant a 20 F1 142 2153142 1442 144 cars Effect of Smoothing Constants gt Smoothing constant generally 05 S as 50 gt As 0 increases older values become less significant WEIGHT ASSIGNED TO MOST 2ND MOST 339 MOST 4th MOST 5th MOST RECENT RECENT RECENT RECENT RECENT SMOOTHING PERIOD PERIOD PERIOD PERIOD PERIOD CONSTANT a a1 a a1 a2 a1 a3 a1 a4 a1 a 5 5 25 125 063 031 Demand 225 200 175 150 Impact of Different 0 Actual a demand 1 Quarter Choosing a 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 Common Measures of Error Mean Absolute Deviation MAD ZActual Forecast n MAD Determining the MAD ACTUAL TONNAGE FORECAST WITH QUARTER UNLOADED FORECAST WITH 0 10 a 50 1 180 175 175 2 168 17550 17500 10180 175 17750 3 159 17475 17550 10168 17550 17275 4 175 17318 17475 10159 17475 16588 5 190 173361731810175 17318 17044 8 205 17502 17338 10190 17336 18022 7 180 17802 17502 10205 17502 19281 8 182 17822 17802 10180 17802 18830 9 17859 17822 10182 17822 18415 Determining the MAD ACTUAL FORECAST ABSOLUTE ABSOLUTE DEVIATION FOR a 50 TONNAGE WITH QUARTER UNLOADED a 10 1 180 175 2 168 17550 3 159 17475 4 175 17318 5 190 17336 6 205 17502 7 180 17802 8 182 17822 Sum of absolute deviations ZDeviations MAD n FORECAST DEVIATION WITH FORa10 0550 500 175 750 17750 1575 17275 182 16588 1664 17044 2998 18022 198 19261 378 18630 8245 1031 500 950 1375 912 1956 2478 1261 430 9862 1233 Common Measures of Error Mean Squared Error MSE 2Forecast errors2 11 MSE Determining the MSE ACTUAL TONNAGE FORECAST FOR QUARTER UNLOADED a 10 ERROR2 1 180 175 52 25 2 188 17550 752 5625 3 159 17475 15752 24806 4 175 17318 1822 331 5 190 17336 18842 27889 6 205 17502 29982 89880 7 180 17802 1982 392 8 182 17822 3782 1429 Sum of errors squared 152652 2Forecast errors2 11 MSE 152652 8 1908 Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a 10 a 10 a 50 a 50 1 180 175 500 175 500 2 168 1755 750 17750 950 3 159 17475 1575 17275 1375 4 175 17318 182 16588 912 5 190 17336 1664 17044 1956 6 205 17502 2998 18022 2478 7 180 17802 198 19261 1261 8 182 17822 378 18630 430 8245 9862 goal is to have less deviation Forecast Error Example 1 Period Month Actual Forecast Er E 2 1 Jan 37 4O 3 9 2 Feb 40 39 1 1 3 Mar 41 39 2 4 4 Apr 38 4O 2 4 Totals 8 18 V n 4 MSE 18445 gtMAD 84 2 Forecast Error Example 2 Period Month Actual Forecast Et Et Et 2 1 Jan 37 42 5 5 25 2 Feb 40 37 3 3 9 3 Mar 41 42 1 1 1 4 Apr 38 43 5 5 25 Totals 14 60 gt n 4 gt MSE 60415 gt MAD 14435 Example 1 is a better method because MSE is lower 8 910111213141516 X rr T mcee Trend Projections Fitting a trend line to historical data points to project into the medium to longrange Linear trends can be found using the least squares technique A yabx where 339 computed value of the variable to be predicted dependent variable a yaxis intercept b slope of the regression line x the independent variable Values of Dependent Variable yvalues A Least Squares Method Actual observation yvalue Deviation3 lt J Deviation1 error Deviation2 l l Deviation7 Deviation6 Least squares method minimizes the sum of the squared errors deviations Trend line yA a bx 1 2 gt Figure 44 l l l l l 3 4 5 6 7 Time period Least Squares Method Equations to calculate the regression variables jabx Zxvn 2 2 2x nx azf bf b Least Squares Example Time Electrical Power Year Period x Demand x2 xy 2003 1 74 1 74 2004 2 79 4 1 58 2005 3 80 9 240 2006 4 90 1 6 360 2007 5 1 05 25 525 2008 6 142 36 852 2009 7 122 i9 E ZX 28 Zy 692 ZXZ 140 ny 3063 7 4 7 9886 b zxyniq39z 3063749886 39 2x24 39 140742 a 7 b 9886 10544 5670 2011 Pearson Education Inc publishing as Prentice Hall 1054 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 Least Squares Example Week Sales X Y X2 X Y 1 2300 1 2300 2 2400 4 4800 3 2300 9 6900 4 1 6 10000 Total 30 24000 25 x avg 2375y 3V9 Example cont Slope b ZXY nXY Z X2 an b 50 Intercept a I7 I9 2375 50 25 2250 Therefore E a 1 2250 50 t Forecasts Week 3 F3 2250 50 3 2400 Week 5 F5 2250 50 5 2500 55 12 3 4 5 6 7 8 910111213141516 X m T mcey 4 56 Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand Y o Is positive trend 0 o No evidence of seasonal variation 0 4 1234 X or Time Seasonal Variations In Data Steps in the process for monthly seasons 1 P39PP P Find average historical demand for each month Compute the average demand over all months Compute a seasonal index for each month Estimate next year s total demand Divide this estimate of total demand by the number of months then multiply it by the seasonal index for that month for avg monthly take total avg annual demand 12 easgnal Index Example ON FINAL AVERAGE AVERAGE YEARLY MONTH LY SEASONAL MONTH YEAR 1 YEAR 2 YEAR 3 DEMAND DEMAND INDEX Jan 80 85 105 90 Feb 70 85 85 80 Mar 80 93 82 85 Apr 90 95 115 100 May 113 125 131 123 June 110 115 120 115 July 100 102 113 105 Aug 88 102 11 o 100 Sept 85 90 95 90 Oct 77 78 85 80 NOV 75 82 83 80 Dec 82 78 8O 80 Total average annual demand 1128 94 112812 94 Seasonal Index Example Seasonal forecast for Year 4 Jan 1200 July 1200 x95796 x1117112 12 12 Feb 1 200 Aug 1 200 x851 85 x1064106 12 12 Mar 1200 Sept 1200 x 904 90 x 957 96 12 12 Apr 1 200 Oct 1 200 x1064106 x85185 12 12 May 1 200 Nov 1 200 x1309131 x85185 12 12 June 1200 Dec 1200 12 x1223122 12 x85185 Seasonal Index Example 140 130 120 110 1 OO 90 80 7O Demand Year 4 Forecast Year 3 Demand Year2 Demand Year1 Demand San Diego Hospital Trend Data Figure 46 D 55 9800 9745 e 9573 9515 9659 9702 7 g 9600 9530 9680 9724 9 66 as39 9594 9537 9000 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 7O 71 72 73 74 75 76 77 78 Month San Diego Hospital Seasonality Indices for Adult Inpatient Days at San Diego Hospital MONTH SEASONALITY INDEX MONTH SEASONALITY INDEX January 104 July 103 February 097 August 1 04 March 1 02 September 097 April 101 October 100 May 099 November 096 June 099 December 098 Seasonal index must equal 12 Seasonality factor number of periods Index for Inpatient Days San Diego Hospital Seasonal Indices Figure 47 106 1 4 104 104 O 103 102 100 098 096 097 097 094 192E Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 7O 71 72 73 74 75 76 77 78 Month 096 San Diego Hospital Period 67 68 69 70 71 72 Month Jan Feb Mar Apr May June Forecast with 9911 9265 9164 9691 9520 9542 Trend amp Seasonality Period 73 74 75 76 77 78 Month July Aug Sept Oct Nov Dec Forecast with 9949 10068 9411 9724 9355 9572 Trend amp Seasonality San Diego Hospital Combined Trend and Seasonal Forecast Figure 48 A 1 2 0 00 10068 10000 9911 9949 D gt 9764 cats 9800 9691 9724 6539 E 9 400 9520 9542 9411 9200 9255 9355 9oool I I I I I I I I I II Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month gt V V V V Forecasting Trend and Seasonality Decomposition Method Trend Component Linear trend line a Y intercept b slope abD Seasonal Component Seasonal lndices St seasonal index for time period t p number of periods in a year months quarters el C S1SzSpp Forecasting equation E a 192 x St o S gt 100 above trend line Y o Slt100 below trend line 39 Seasonal Index 101 084 095 120 39 I hOON l X or Time t period Example 1 Year Quarter Period Actual Forecast 2004 1 1 26 253 2 2 27 252 3 3 25 247 4 4 22 238 2005 1 5 36 345 2 6 34 333 3 7 33 323 4 8 36 303 Forecast Parameters a200b20 S1 115 82 105 83 095 84 085 E abtgtltSt Example 1 cont 4O 35 30 25 20 15 1O Demand Trend Line Forecast Example 2 Year Quarter Period Actual Forecast 2004 1 1 102 86 186 2 3 4 118 2005 120 107 187 hUJN OOOUlIgtUJN 126 Forecast Parameters a 118 b 25 81 090 82 075 83 140 84 095 E abtgtltSt Example 2 cont 200 150 100 50 Demand Trend Line Forecast 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 timeseries example Associative Forecasting Forecasting an outcome based on predictor variables using the least squares technique A y a bx where value of the dependent variable in our example sales a yaxis intercept b slope of the regression line the independent variable Associative Forecasting Exam ple 2 0 1 1 2 0 30 3 9 90 25 4 13 100 20 2 4 40 20 1 1 20 35 7 49 245 2y 150 Zx1 8 22 ny 515 XZEZLZ3 yZQZEZ25 6 6 6 6 ny nxT 51 5 6325 Z 25 15 23162 111752 80 632 a 12 52 25 253175 Associative Forecasting Example If payroll next year is estimated to be 6 million then Sales in billions 175 25 6 17515325 Sales 3250000000 Monitoring and Controlling Forecasts Tracking Signal p Measures how well the forecast is predicting actual values gt Ratio of cumulative not absolute valuef0recat errors to mean absolute deviation MAD gt Good tracking signal has low values gt If forecasts are continually high or low the forecast has a bias error Monitoring and Controlling Forecasts Tracking Cumulative error Signal MAD 2Actual demand in period i Forecast demand in period 2 ZActual Forecast 11 Tracking Signal Example ABSOLUTE CUM ABS TRACKING ACTUAL FORECAST CUM FORECAST FORECAST SIGNAL CUM QTR DEMAND DEMAND ERROR ERROR ERROR ERROR ERRORMAD 1 90 100 1 0 1 0 10 10 100 1010 1 2 95 100 5 15 5 15 75 1575 2 3 115 100 15 0 15 30 10 0100 4 100 110 10 10 10 40 10 1010 1 5 125 110 15 5 15 55 110 511 05 6 140 110 30 35 30 85 142 35142 25 ZForecast errors 35 At the end of quarter 6 MAD F142 n Cumulative error 2 35 2 25 M ADS Tracking signal MAD 14 2 Adaptive Smoothing gt It s possible to use the computer to continually monitor forecast error and adjust the values of the a and Bcoefficients used in exponential smoothing to continually minimize forecast error gt This technique is called adaptive smoothing Focus Forecasting p 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 gt Uses historical data to test multiple forecasting models for individual items gt Forecasting model with the lowest error used to forecast the next demand Forecasting in the Service Sector gt Presents unusual challenges gt Special need for short term records p Needs differ greatly as function Of industry and product gt Holidays and other calendar events gt Unusual events demand fluctuates

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