4 Forecasting PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl 03: CH4 - Forecasting (MGMT3102: Fall13)

Outline What Is Forecasting? Forecasting Approaches Forecasting Time Horizons Forecasting Approaches Overview of Qualitative Methods and Quantitative Methods Time-Series Forecasting Decomposition of a Time Series Naive Approach Time-Series Forecasting (cont.) Moving Averages Exponential Smoothing(with trend) Associative Forecasting Methods: Regression and Correlation Using Regression Analysis for Forecasting Correlation Coefficients for Regression Lines Multiple-Regression Analysis 03: CH4 - Forecasting (MGMT3102: Fall13)

Learning Objectives When you complete this chapter you should be able to : 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, and exponential smoothing Compute measures of forecast accuracy 03: CH4 - Forecasting (MGMT3102: Fall13)

Forecasting at Disney World Revenues are derived from people Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted Model includes gross domestic product, cross-exchange rates, arrivals into the USA Survey 1 million park guests, employees, and travel professionals each year Inputs are airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world Revenues are derived from people – how many visitors and how they spend their money Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world 03: CH4 - Forecasting (MGMT3102: Fall13)

Why Forecast? What are we trying to Forecast? A very well known attribute of a forecast is that they are always wrong. For example, Snackwell Cookies (1993), But . . . L. L. Bean Taco Bell AMR Characteristics of Forecasts A forecast is more than a single number Aggregate forecasts are better The further in the future, the more inaccuracy Forecasts only predict from past events OOPS! Snack well Cookies - misforecasted demand for Fat-free Devil’s Food Cookies L. L. Bean -> (Time Series Forecasting) - Forecasts to set labor capacity saved $300,000 per year Taco Bell -> (Six Week Moving Average) – Staffing savings of $16.4 million American Airline -> (Linear Regression) – Repairable parts – decreased inventory and increased availability saved $1 million/year 03: CH4 - Forecasting (MGMT3102: Fall13)

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 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 03: CH4 - Forecasting (MGMT3102: Fall13)

Forecasting Approaches Qualitative Methods Used when situation is vague and little data exist Involves intuition, experience Quantitative Methods Used when situation is ‘stable’ - historical data exist Involves mathematical techniques Qualitative Methods Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet 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 03: CH4 - Forecasting (MGMT3102: Fall13)

Overview of Qualitative Methods Jury of executive opinion Pool opinions of high-level experts Delphi method Sales force composite Aggregated estimates from salespersons Consumer Market Survey 03: CH4 - Forecasting (MGMT3102: Fall13)

Delphi Method Iterative group process, continues until consensus 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) 03: CH4 - Forecasting (MGMT3102: Fall13)

Overview of Quantitative Approaches Naive approach Moving averages Exponential smoothing Trend projection Linear regression time-series models associative model 03: CH4 - Forecasting (MGMT3102: Fall13)

Time Series Forecasting Set of evenly spaced numerical data Forecast based only on past values, no other variables important Components of a Time Series: Trend Seasonal Cyclical Random Forecast based only on past values, Assumes that factors influencing past and present will continue influence in future Trend Component Changes due to population, technology, age, culture, etc. Seasonal Component Occurs within a single year Cyclical Component Affected by business cycle, political, and economic factors Multiple years duration - causal or associative relationships Random Component Erratic, unsystematic, ‘residual’ fluctuations 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then February sales will be 68 Sometimes cost effective and efficient Can be good starting point 03: CH4 - Forecasting (MGMT3102: Fall13)

∑ demand in previous n periods Moving Average Method MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Moving average = ∑ demand in previous n periods n 03: CH4 - Forecasting (MGMT3102: Fall13)

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 (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3 10 12 13 (10 + 12 + 13)/3 = 11 2/3 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 [(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 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 03: CH4 - Forecasting (MGMT3102: Fall13)

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 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 Figure 4.2 03: CH4 - Forecasting (MGMT3102: Fall13)

Exponential Smoothing Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant () Ranges from 0 to 1 Less need for keeping past data 03: CH4 - Forecasting (MGMT3102: Fall13)

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) 03: CH4 - Forecasting (MGMT3102: Fall13)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 03: CH4 - Forecasting (MGMT3102: Fall13)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 Chose high values of  when underlying average is likely to change Choose low values of  when underlying average is stable 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

Common Measures of Error Mean Absolute Deviation (MAD) MAD= |Actual−Forecast| n Mean Squared Error (MSE) MSE= (Forecast Errors)𝟐 n Mean Absolute Percent Error (MAPE) MAPE= 𝒊=𝟏 𝒏 100|Actuali−Forecasti|/Actuali n 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

Comparison of Forecast Error MAPE = ∑100|deviationi|/actuali n i = 1 Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 = 44.75/8 = 5.59% 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 MSE 190.82 195.24 = 54.05/8 = 6.76% For a = .50 03: CH4 - Forecasting (MGMT3102: Fall13)

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 MAPE 5.59% 6.76% 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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, Inc. publishing as Prentice Hall 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 ^ 03: CH4 - Forecasting (MGMT3102: Fall13)

Actual observation (y-value) Least Squares Method Time period Values of Dependent Variable Deviation1 (error) Deviation5 Deviation7 Deviation2 Deviation6 Deviation4 Deviation3 Actual observation (y-value) Trend line, y = a + bx ^ Figure 4.4 03: CH4 - Forecasting (MGMT3102: Fall13)

Associative Forecasting Example Sales Area Payroll ($ millions), y ($ billions), x 2.0 1 3.0 3 2.5 4 2.0 2 3.5 7 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Sales Area payroll 03: CH4 - Forecasting (MGMT3102: Fall13)

Associative Forecasting Example y = 1.75 + .25x ^ Sales = 1.75 + .25(payroll) If payroll next year is estimated to be $6 billion, then: 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Nodel’s sales Area payroll 3.25 Sales = 1.75 + .25(6) Sales = $3,250,000 03: CH4 - Forecasting (MGMT3102: Fall13)

Correlation How strong is the linear relationship between the variables? Coefficient of correlation r measures degree of association Values range from -1 to +1 Coefficient of Determination r2 the % change in y predicted by the change in x Values range from 0 to 1 For example, when r = .901 r2 = .81 Correlation does not necessarily imply causality! 03: CH4 - Forecasting (MGMT3102: Fall13)

Correlation Coefficient y x (a) Perfect positive correlation: r = +1 y x (b) Positive correlation: 0 < r < 1 y x (c) No correlation: r = 0 y x (d) Perfect negative correlation: r = -1 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

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 03: CH4 - Forecasting (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average. Week Auto Sales 1 8 2 10 3 9 4 11 5 6 13 7 - Week Auto Sales Three-Week Moving Average 1 8   2 10 3 9 4 11 (8 + 9 + 10) / 3 = 9 5 (10 + 9 + 11) / 3 = 10 6 13 (9 + 11 + 10) / 3 = 10 7 - (11 + 10 + 13) / 3 = 11 1/3 03: CH4 - Forecasting (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems Carmen’s decides to forecast auto sales by weighting the three weeks as follows: Weights Applied Period 3 Last week 2 Two weeks ago 1 Three weeks ago 6 Total Week Auto Sales Three-Week Moving Average 1 8   2 10 3 9 4 11 [(3*9) + (2*10) + (1*8)] / 6 = 9 1/6 5 [(3*11) + (2*9) + (1*10)] / 6 = 10 1/6 6 13 [(3*10) + (2*11) + (1*9)] / 6 = 10 1/6 7 - [(3*13) + (2*10) + (1*11)] / 6 = 11 2/3 03: CH4 - Forecasting (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems A firm uses simple exponential smoothing with α=0.1 to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8. 03: CH4 - Forecasting (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems Exponential smoothing is used to forecast automobile battery sales. Two value of α are examined α = 0.8 and α=0.5. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below: Month Actual Battery Sales Forecast January 20 22 February 21   March 15 April 14 May 13 June 16 On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a = 0.5 because it has a smaller MAD. Month Actual Battery Sales Rounded Forecast with  =0.8 Absolute Deviation with  =0.8 Rounded Forecast with  =0.5 Absolute Deviation with  =0.5 January 20 22 2.0 February 21 20.4 0.6 0.0 March 15 20.9 5.9 6.0 April 14 16.2 2.2 18 4.0 May 13 14.4 1.4 16 3.0 June 13.3 2.7 14.5 1.5    = 14.8  = 16.5 2.46 2.75 MSE 8.84 11.21 03: CH4 - Forecasting (MGMT3102: Fall13)