4 Forecasting Demand PowerPoint presentation to accompany Heizer and Render Operations Management, 10e, Global Edition Principles of Operations Management, 8e, Global Edition PowerPoint slides by Jeff Heyl © 2011 Pearson Education

Chapter Outline What Is Forecasting? Forecasting definition The differences between forecasting & prediction Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts The Strategic Importance of Forecasting Seven Steps in the Forecasting System Forecasting Approaches Qualitative approach Quantitative approach © 2011 Pearson Education

Outline – Continued Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclical Variations in Data © 2011 Pearson Education

Associative Forecasting Methods: Regression and Correlation Analysis Monitoring and Controlling Forecasts Adaptive Smoothing Focus Forecasting Forecasting in the Service Sector © 2011 Pearson Education

?? What is Forecasting? Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities ?? © 2011 Pearson Education

Forecasting definition Forecasting is defined as a planning tool that helps management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends There is a dereferences between forecasting and prediction © 2011 Pearson Education

The Differences Between Forecasting & Prediction Prediction involves judgment in management after taking all available information into account. Forecasting involves the projection of the past into the future Prediction involves the anticipated change into the future. It may include even new factors that may affect future demand Forecast involves estimating the level of demand of a product on the basis of factors that generated the demand in the past Prediction is more intuitive Forecasting is more scientific © 2011 Pearson Education

It is more governed by personal bias and preferences. It is relatively free from personal bias. It is more subjective It is more objective Prediction does not contain error analysis Error analysis is possible © 2011 Pearson Education

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 1 year to 3 years Sales and production planning, budgeting Long-range forecast 3+ years New product planning, facility location, research and development © 2011 Pearson Education

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 © 2011 Pearson Education

Product Life Cycle Introduction Growth Maturity Decline Forecasting Time Horizon Long run forecasting + 3 years Medium forecasting 1 year – 3 years Short run forecasting Up to 1 year Internet search engines Sales Drive-through restaurants CD-ROMs Analog TVs iPods Boeing 787 LCD & plasma TVs Twitter Avatars Xbox 360 Figure 2.5 © 2011 Pearson Education

Types of Forecasts Economic forecasts Technological forecasts Address business cycle – inflation rate, money supply, dollar price, etc. Technological forecasts Predict rate of technological progress Impacts development of new products Demand forecasts Predict sales of existing products and services © 2011 Pearson Education

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 © 2011 Pearson Education

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 © 2011 Pearson Education

The Realities! Forecasts are seldom perfect Most techniques assume an underlying stability in the system The aggregated forecasts are more accurate than individual forecasts © 2011 Pearson Education

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 © 2011 Pearson Education

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 © 2011 Pearson Education

Overview of Qualitative Methods Sales force composite Delphi method Consumer Market Survey © 2011 Pearson Education

Sales Force Composite Each salesperson projects his or her sales Combined at district and national levels Salesperson know customers’ wants Tends to be overly optimistic © 2011 Pearson Education

Delphi Method Iterative group process, continues until agreement is reached 3 types of participants Decision makers Staff Respondents Decision Makers (Evaluate responses and make decisions) Staff (Administering survey) Respondents (People who can make valuable judgments) © 2011 Pearson Education

Consumer Market Survey Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer © 2011 Pearson Education

Overview of Quantitative Approaches Naive approach Simple average Moving averages Exponential smoothing Trend projection Linear regression time-series models associative model © 2011 Pearson Education

Time Series Forecasting Forecast based only on past values, no other variables important Assumes that factors influencing past and present will continue influence in future © 2011 Pearson Education

Time Series Components Trend Cyclical Seasonal Random © 2011 Pearson Education

COMPONENTS OF TIME SERIES DEMAND .1 average: the mean of the observations over time 2. trend: a gradual increase or decrease in the average over time 3. seasonal influence: predictable short-term cycling behavior due to time of day, week, month, season, year, etc. 4. cyclical movement: unpredictable long-term cycling behavior due to business cycle or product/service life cycle 5. random error: remaining variation that cannot be explained by the other four components © 2011 Pearson Education

Average demand over 4 years Components of Demand Trend component Demand for product or service | | | | 1 2 3 4 Time (years) Seasonal peaks Actual demand line Average demand over 4 years Random variation Figure 4.1 © 2011 Pearson Education

Trend Component Persistent, overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration © 2011 Pearson Education

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 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52 © 2011 Pearson Education

Cyclical Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships 0 5 10 15 20 © 2011 Pearson Education

Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and non- repeating M T W T F © 2011 Pearson Education

Naive Approach It is assume that demand in next period is the same as demand in most recent period e.g., If January sales were 68 units , then February sales will be 68 This simple way is the most cost- effective and efficient forecasting model It can be a good starting point © 2011 Pearson Education

Naive approach Suppose the demand for York factory last year was 1000 cars According to the naive approach the demand of the next year is 1000 car © 2011 Pearson Education

Simple Average Method It is assume that demand in the next period is the mean of the actual demand in last periods © 2011 Pearson Education

Simple average example A XYZ television supplier found a demand of 200 sets in July, 225 sets in August & 245 sets in September. Find the demand forecast for the month of October using simple average method. F = D1+D2+D3/3= 200+225+245/3=223.3 224 units © 2011 Pearson Education

Moving Average Method MA 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 © 2011 Pearson Education

Moving Average Method example Donna’s garden supply wants a 3 – month moving average forecast including a forecast for next January, for shed sales © 2011 Pearson Education

Moving Average Example January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Month Shed Sales Moving Average 10 12 13 (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 © 2011 Pearson Education

Graph of Moving Average Moving Average Forecast | | | | | | | | | | | | J F M A M J J A S O N D Shed Sales 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales © 2011 Pearson Education

Weighted Moving Average Used when some trend might be present Older data usually less important Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights © 2011 Pearson Education

Weighted Moving Average example Donna’s garden supply wants to forecast shed sales by weighted the past 3 months ,with more weight given to recent data to make them more significant © 2011 Pearson Education

Weighted Moving Average Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights Weighted Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Weighted Month Shed Sales Moving Average 10 12 13 [(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 © 2011 Pearson Education

Moving Average And Weighted Moving Average 30 – 25 – 20 – 15 – 10 – 5 – Sales demand | | | | | | | | | | | | J F M A M J J A S O N D Actual sales Moving average Figure 4.2 © 2011 Pearson Education

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 © 2011 Pearson Education

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 © 2011 Pearson Education

Exponential Smoothing New forecast = Last period’s forecast + a (Last period’s actual demand – Last period’s forecast) Ft = Ft – 1 + a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0 ≤ a ≤ 1) © 2011 Pearson Education

Exponential Smoothing Example In January , a car dealer predicted February demand for 142 ford mustangs , Actual Febrruary demand = 153 autos, using a Smoothing constant a = .20 , the dealer wants to forecast march demand using the exponential smoothing model © 2011 Pearson Education

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) © 2011 Pearson Education

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars © 2011 Pearson Education

Effect of Smoothing Constants Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (a) a(1 - a) a(1 - a)2 a(1 - a)3 a(1 - a)4 a = .1 .1 .09 .081 .073 .066 a = .5 .5 .25 .125 .063 .031 © 2011 Pearson Education

Impact of Different  Actual demand a = .5 a = .1 225 – 200 – 175 – 225 – 200 – 175 – 150 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Demand Actual demand a = .5 a = .1 © 2011 Pearson Education

Impact of Different  225 – 200 – 175 – 150 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Demand Chose high values of  when underlying average is likely to change Choose low values of  when underlying average is stable Actual demand a = .5 a = .1 © 2011 Pearson Education

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 © 2011 Pearson Education

Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors)2 n © 2011 Pearson Education

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 5.00 175 5.00 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 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 © 2011 Pearson Education

Comparison of Forecast Error MAD = ∑ |deviations| n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 = 82.45/8 = 10.31 For a = .10 1 180 175 5.00 175 5.00 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 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 = 98.62/8 = 12.33 For a = .50 © 2011 Pearson Education

Comparison of Forecast Error MSE = ∑ (forecast errors)2 n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 = 1,526.54/8 = 190.82 For a = .10 1 180 175 5.00 175 5.00 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 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 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 = 1,561.91/8 = 195.24 For a = .50 © 2011 Pearson Education

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 5.00 175 5.00 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 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 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 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FITt) = trend Exponentially Exponentially smoothed (Ft) + smoothed (Tt) forecast trend © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Ft = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1) Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1 Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt = Ft + Tt © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Table 4.1 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 1: Forecast for Month 2 F2 = aA1 + (1 - a)(F1 + T1) F2 = (.2)(12) + (1 - .2)(11 + 2) = 2.4 + 10.4 = 12.8 units Table 4.1 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 2: Trend for Month 2 T2 = b(F2 - F1) + (1 - b)T1 T2 = (.4)(12.8 - 11) + (1 - .4)(2) = .72 + 1.2 = 1.92 units Table 4.1 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 3: Calculate FIT for Month 2 FIT2 = F2 + T2 FIT2 = 12.8 + 1.92 = 14.72 units Table 4.1 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 14.72 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 15.18 2.10 17.28 17.82 2.32 20.14 19.91 2.23 22.14 22.51 2.38 24.89 24.11 2.07 26.18 27.14 2.45 29.59 29.28 2.32 31.60 32.48 2.68 35.16 Table 4.1 © 2011 Pearson Education

Exponential Smoothing with Trend Adjustment Example | | | | | | | | | 1 2 3 4 5 6 7 8 9 Time (month) Product demand 35 – 30 – 25 – 20 – 15 – 10 – 5 – 0 – Actual demand (At) Forecast including trend (FITt) with  = .2 and  = .4 Figure 4.3 © 2011 Pearson Education

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 ^ © 2011 Pearson Education

Least Squares Method Equations to calculate the regression variables y = a + bx ^ b = Sxy - nxy Sx2 - nx2 a = y - bx © 2011 Pearson Education

Least Squares Example Time Electrical Power Year Period (x) Demand (y) x2 xy 2003 1 74 1 74 2004 2 79 4 158 2005 3 80 9 240 2006 4 90 16 360 2007 5 105 25 525 2008 6 142 36 852 2009 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 b = = = 10.54 ∑xy - nxy ∑x2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 © 2011 Pearson Education

Least Squares Example The trend line is y = 56.70 + 10.54x ^ Time Electrical Power Year Period (x) Demand x2 xy 2003 1 74 1 74 2004 2 79 4 158 2005 3 80 9 240 2006 4 90 16 360 2007 5 105 25 525 2008 6 142 36 852 2009 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 The trend line is y = 56.70 + 10.54x ^ b = = = 10.54 ∑xy - nxy ∑x2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 © 2011 Pearson Education

Least Squares Requirements We always plot the data to insure a linear relationship We do not predict time periods far beyond the database Deviations around the least squares line are assumed to be random © 2011 Pearson Education

Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand © 2011 Pearson Education

Seasonal Variations In Data Steps in the process: Find average historical demand for each season Compute the average demand over all seasons Compute a seasonal index for each season Estimate next year’s total demand Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season © 2011 Pearson Education

Seasonal Index Example Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 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 Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index © 2011 Pearson Education

Seasonal Index Example Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 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 Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index 0.957 Seasonal index = Average 2007-2009 monthly demand Average monthly demand = 90/94 = .957 © 2011 Pearson Education

Seasonal Index Example Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851 Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index © 2011 Pearson Education

Seasonal Index Example Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851 Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index Forecast for 2010 Expected annual demand = 1,200 Jan x .957 = 96 1,200 12 Feb x .851 = 85 1,200 12 © 2011 Pearson Education

Seasonal Index Example 2010 Forecast 2009 Demand 2008 Demand 2007 Demand 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – | | | | | | | | | | | | J F M A M J J A S O N D Time Demand © 2011 Pearson Education

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 © 2011 Pearson Education

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 ^ © 2011 Pearson Education

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 +1 © 2011 Pearson Education

Correlation Coefficient nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] © 2011 Pearson Education

Correlation Coefficient y x (a) Perfect positive correlation: r = +1 y x (b) Positive correlation: 0 < r < 1 Correlation Coefficient r = nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] y x (c) No correlation: r = 0 y x (d) Perfect negative correlation: r = -1 © 2011 Pearson Education

Correlation Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret For example if: r = .901 r2 = .81 © 2011 Pearson Education

(positive +)or( negative (-) R ---------- to what extent there is a correlation relationship between two variables (-1 to 1) (positive +)or( negative (-) (strong more than .5) or( weak less than .5 ) R2 ----------- to what extent the change in one variable can be explained by the other variables % © 2011 Pearson Education

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 + b1x1 + b2x2 … ^ Computationally, this is quite complex and generally done on the computer © 2011 Pearson Education

Multiple Regression Analysis In the Nodel example, including interest rates in the model gives the new equation: y = 1.80 + .30x1 - 5.0x2 ^ 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 © 2011 Pearson Education

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 © 2011 Pearson Education

Monitoring and Controlling Forecasts Tracking signal Cumulative error MAD = Tracking signal = ∑(Actual demand in period i - Forecast demand in period i) (∑|Actual - Forecast|/n) © 2011 Pearson Education

Tracking Signal Signal exceeding limit Tracking signal + 0 MADs – Upper control limit Lower control limit Time Acceptable range © 2011 Pearson Education

Tracking Signal Example Cumulative Absolute Absolute Actual Forecast Cumm Forecast Forecast Qtr Demand Demand Error Error Error Error MAD 1 90 100 -10 -10 10 10 10.0 2 95 100 -5 -15 5 15 7.5 3 115 100 +15 0 15 30 10.0 4 100 110 -10 -10 10 40 10.0 5 125 110 +15 +5 15 55 11.0 6 140 110 +30 +35 30 85 14.2 © 2011 Pearson Education

Tracking Signal Example Cumulative Absolute Absolute Actual Forecast Cumm Forecast Forecast Qtr Demand Demand Error Error Error Error MAD 1 90 100 -10 -10 10 10 10.0 2 95 100 -5 -15 5 15 7.5 3 115 100 +15 0 15 30 10.0 4 100 110 -10 -10 10 40 10.0 5 125 110 +15 +5 15 55 11.0 6 140 110 +30 +35 30 85 14.2 Tracking Signal (Cumm Error/MAD) -10/10 = -1 -15/7.5 = -2 0/10 = 0 +5/11 = +0.5 +35/14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits © 2011 Pearson Education

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 © 2011 Pearson Education

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 © 2011 Pearson Education

Fast Food Restaurant Forecast 20% – 15% – 10% – 5% – 11-12 1-2 3-4 5-6 7-8 9-10 12-1 2-3 4-5 6-7 8-9 10-11 (Lunchtime) (Dinnertime) Hour of day Percentage of sales Figure 4.12 © 2011 Pearson Education

FedEx Call Center Forecast 12% – 10% – 8% – 6% – 4% – 2% – 0% – Hour of day A.M. P.M. 2 4 6 8 10 12 Figure 4.12 © 2011 Pearson Education