Accurate forecasting is a crucial part of quality management because it lowers costs so companies can be competitive enables companies to produce better goods and services allows companies to provide products and services when they are demanded provides companies more flexibility in their production processes Question 21 pts The ______________ effect is caused in part by distortion in product demand information caused by inaccurate forecasts. regression butterfly bullwhip causal Question 31 pts A forecast where the current period’s demand is used as the next period’s forecast is known as a moving average forecast naive forecast weighted moving average forecast Delphi method Question 41 pts In an exponential smoothing forecast, the closer the smoothing constant, α, is to 1.0 the greater the reaction to the most recent demand greater the dampening, or smoothing, effect more accurate the forecast less accurate the forecast Question 51 pts The adjusted exponential smoothing forecast consists of the exponential smoothing forecast with an adjustment for cycles seasonal patterns random variations trend Question 61 pts An oscillating movement in demand that occurs repetitively over the short-run is referred to as a seasonal pattern cycle trend time series forecast Question 71 pts Which of the following is generally true about short-term forecasting? The most common models are qualitative. Many companies are shifting from long-term to short-term forecasts for strategic planning. Time-series methods are common forecasting methods used in the short-term. Short-term forecasts are often used to help design supply chains. Question 81 pts If a company’s product demand is 100 units in month 1, 75 units in month 2, 110 units in month 3 and 50 units in month 4, its 4-month moving average prediction for month 5 is 103.35 50 71.25 83.75 Question 91 pts A mathematical technique for forecasting that relates a dependent variable to an independent variable is correlation analysis exponential smoothing linear regression weighted moving average Question 101 pts All of the following are true about time-series and causal modeling EXCEPT Time-series techniques assume that what has occurred in the past will continue to occur in the future. Causal forecasting methods attempt to develop a mathematical relationship between demand and factors that cause demand to behave the way it does. A causal forecasting method in which time is used as the independent variable is considered a form of time-series modeling. Causal forecasting methods are based on judgment, opinion, past experience, or best guesses. Chapter 12 Forecasting Russell and Taylor Operations and Supply Chain Management, 9th Edition Lecture Outline • Strategic Role of Forecasting in Supply Chain Management • Components of Forecasting Demand • Time Series Methods • Forecast Accuracy • Time Series Forecasting Using Excel • Regression Methods Learning Objectives • Discuss the strategic role of forecasting in supply chain management • Describe the forecasting process and identify the components of forecasting demand • Forecast demand using various time series models, including exponential smoothing, and trend and seasonal adjustments • Discuss and calculate various methods for evaluating forecast accuracy • Use Excel to create various forecast models • Develop forecasting models with linear and multiple regression analysis Forecasting • Predicting the future • Qualitative forecast methods • subjective • Quantitative forecast methods • based on mathematical formulas Important Principles • Decisions are made under uncertainty • Good forecasts reduce uncertainty • Forecasts are part of ops decision making • Inventory control • Capacity and facility location • Manpower requirements • Forecasts are always wrong! • Based on past information, guesses about the future Strategic Role of Forecasting in Supply Chain Management • Accurate forecasting determines inventory levels in the supply chain • Continuous replenishment • • • • supplier & customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery • Variations of continuous replenishment • • • • quick response JIT (just-in-time) VMI (vendor-managed inventory) stockless inventory The Effect of Inaccurate Forecasting Forecasting • Quality Management • Accurately forecasting customer demand is a key to providing good quality service • Strategic Planning • Successful strategic planning requires accurate forecasts of future products and markets Components of Forecasting Demand • • • • • Time frame Demand behavior Causes of behavior (Data availability) (Forecasting budget and available expertise) • (Consequence of a bad forecast) Time Frame • Indicates how far into the future is forecast • Short- to mid-range forecast • typically encompasses the immediate future • daily up to two years • more data required for accuracy • Long-range forecast • usually encompasses a period of time longer than two years • less data, more subject area knowledge Demand Behavior • Trend • a gradual, long-term up or down movement of demand • Random variations • movements in demand that do not follow a pattern • Seasonal pattern • an up-and-down repetitive movement in demand occurring periodically (e.g., weeks, months, qtrs • Cycle • an up-and-down repetitive movement in demand • usually longer in nature, e.g., recession Forms of Forecast Movement Forecasting Methods • Time series • statistical techniques that use historical demand data to predict future demand • Regression methods • attempt to develop a mathematical relationship between demand and factors that cause its behavior • Qualitative • use management judgment, expertise, and opinion to predict future demand Qualitative Methods • Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts • Delphi method • involves soliciting forecasts about technological advances from experts Forecasting Process 1. Identify the purpose of forecast 2. Collect historical data 3. Plot data and identify patterns 6. Check forecast accuracy with one or more measures 5. Develop/compute forecast for period of historical data 4. Select a forecast model that seems appropriate for data 7. Is accuracy of forecast acceptable? No 8b. Select new forecast model or adjust parameters of existing model Yes 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy Time Series • Assume that what has occurred in the past will continue to occur in the future • Relate the forecast to only one factor - time • Include • • • • naïve forecast moving average exponential smoothing linear trend line Moving Average • Naive forecast • demand in current period is used as next period’s forecast • Simple moving average • uses average demand for a fixed sequence of periods • good for stable demand with no pronounced behavioral patterns • Weighted moving average • weights are assigned to data from past periods Moving Average: Naïve Approach MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - FORECAST Moving Average: Naïve Approach MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - FORECAST 120 90 100 75 110 50 75 130 110 90 Simple Moving Average n Di  i=1 MAn = n where n = number of periods in the moving average Di = demand in period i 3-month Simple Moving Average MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - MOVING AVERAGE 3 Di  i=1 MA3 = 3 3-month Simple Moving Average MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - MOVING AVERAGE – – – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 110.0 3 Di  i=1 MA3 = = 3 90 + 110 + 130 3 = 110 orders for Nov 5-month Simple Moving Average MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - MOVING AVERAGE 5 Di  i=1 MA5 = 5 5-month Simple Moving Average MONTH Jan Feb Mar Apr May June July Aug Sept Oct Nov ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 - MOVING AVERAGE – – – – – 99.0 85.0 82.0 88.0 95.0 91.0 5 Di  i=1 MA5 = = 5 90 + 110 + 130+75+50 5 = 91 orders for Nov Smoothing Effects Weighted Moving Average • Adjusts moving average method to more closely reflect data fluctuations n WMAn =  Wi Di i=1 where Wi = the weight for period i, between 0 and 100 percent  Wi = 1.00 Weighted Moving Average Example MONTH August September October WEIGHT DATA 17% 33% 50% 130 110 90 3 November Forecast WMA3 = Wi Di  i=1 Weighted Moving Average Example MONTH August September October WEIGHT DATA 17% 33% 50% 130 110 90 3 November Forecast WMA3 = Wi Di  i=1 = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders Exponential Smoothing • Averaging method • Weights most recent data more strongly ▪ Parameter, a, determines level of smoothing and speed of reaction to differences between forecasts and actual occurrences ▪Small values lessen the effects of random changes ▪Larger values keep up with rapid change • Reacts more to recent changes • Widely used, accurate method • “Adaptive” forecasting involves changing a over time to increase accuracy Exponential Smoothing Ft +1 = a Dt + (1 - a)Ft where: Ft +1 = forecast for next period Dt = actual demand for present period Ft = previously determined forecast for present period a= weighting factor, smoothing constant Effect of Smoothing Constant 0.0  a  1.0 If a = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft If a = 0, then Ft +1 = 0 Dt + 1 Ft = Ft Forecast does not reflect recent data If a = 1, then Ft +1 = 1 Dt + 0 Ft = Dt Forecast based only on most recent data Exponential Smoothing (α=0.30) PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 MONTH Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec DEMAND 37 40 41 37 45 50 43 47 56 52 55 54 F2 = aD1 + (1 - a)F1 F3 = aD2 + (1 - a)F2 F13 = aD12 + (1 - a)F12 Exponential Smoothing (α=0.30) PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 MONTH Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec DEMAND 37 40 41 37 45 50 43 47 56 52 55 54 F2 = aD1 + (1 - a)F1 = (0.30)(37) + (0.70)(37) = 37 F3 = aD2 + (1 - a)F2 = (0.30)(40) + (0.70)(37) = 37.9 F13 = aD12 + (1 - a)F12 = (0.30)(54) + (0.70)(50.84) = 51.79 Exponential Smoothing PERIOD MONTH DEMAND 1 2 3 4 5 6 7 8 9 10 11 12 13 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 37 40 41 37 45 50 43 47 56 52 55 54 – FORECAST, Ft + 1 (a = 0.3) (a = 0.5) – – Exponential Smoothing PERIOD MONTH DEMAND 1 2 3 4 5 6 7 8 9 10 11 12 13 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 37 40 41 37 45 50 43 47 56 52 55 54 – FORECAST, Ft + 1 (a = 0.3) (a = 0.5) – 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 51.79 – 37.00 38.50 39.75 38.37 41.68 45.84 44.42 45.71 50.85 51.42 53.21 53.61 Exponential Smoothing Adjusted Exponential Smoothing AFt +1 = Ft +1 + Tt +1 where T = an exponentially smoothed trend factor Tt +1 = (Ft +1 - Ft) + (1 - ) Tt where Tt = the last period trend factor  = a smoothing constant for trend 0≤≤1 Adjusted Exponential Smoothing (β=0.30) PERIOD MONTH DEMAND 1 2 3 4 5 6 7 8 9 10 11 12 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 37 40 41 37 45 50 43 47 56 52 55 54 T3 = (F3 - F2) + (1 - ) T2 AF3 = F3 + T3 T13 = (F13 - F12) + (1 - ) T12 AF13 = F13 + T13 = Adjusted Exponential Smoothing (β=0.30) PERIOD MONTH DEMAND 1 2 3 4 5 6 7 8 9 10 11 12 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 37 40 41 37 45 50 43 47 56 52 55 54 T3 = (F3 - F2) + (1 - ) T2 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45 AF3 = F3 + T3 = 38.5 + 0.45 = 38.95 T13 = (F13 - F12) + (1 - ) T12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36 AF13 = F13 + T13 = 53.61 + 1.36 = 54.97 Adjusted Exponential Smoothing PERIOD MONTH DEMAND 1 2 3 4 5 6 7 8 9 10 11 12 13 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 37 40 41 37 45 50 43 47 56 52 55 54 – FORECAST Ft +1 TREND Tt +1 ADJUSTED FORECAST AFt +1 Adjusted Exponential Smoothing PERIOD MONTH DEMAND FORECAST Ft +1 1 2 3 4 5 6 7 8 9 10 11 12 13 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 37 40 41 37 45 50 43 47 56 52 55 54 – 37.00 37.00 38.50 39.75 38.37 38.37 45.84 44.42 45.71 50.85 51.42 53.21 53.61 TREND Tt +1 ADJUSTED FORECAST AFt +1 – 0.00 0.45 0.69 0.07 0.07 1.97 0.95 1.05 2.28 1.76 1.77 1.36 – 37.00 38.95 40.44 38.44 38.44 47.82 45.37 46.76 58.13 53.19 54.98 54.96 Adjusted Exponential Smoothing Forecasts Linear Trend Line y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x  xy - nxy b =  x2 - nx2 a = y-bx where n = number of periods x x = = mean of the x values n y y = n = mean of the y values Least Squares Example x(PERIOD) 1 2 3 4 5 6 7 8 9 10 11 12 y(DEMAND) 73 40 41 37 45 50 43 47 56 52 55 54 xy x2 Least Squares Example x(PERIOD) y(DEMAND) xy x2 1 2 3 4 5 6 7 8 9 10 11 12 73 40 41 37 45 50 43 47 56 52 55 54 37 80 123 148 225 300 301 376 504 520 605 648 1 4 9 16 25 36 49 64 81 100 121 144 78 557 3867 650 Least Squares Example x = y = b = xy - nxy = x2 - nx2 a = y - bx Least Squares Example x = 78 = 6.5 12 y = 557 = 46.42 12 b = xy - nxy = x2 - nx2 3867 - (12)(6.5)(46.42) =1.72 650 - 12(6.5)2 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 Linear trend line y = 35.2 + 1.72x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units Seasonal Adjustments ▪ Repetitive increase/ decrease in demand ▪ Use seasonal factor to adjust forecast Seasonal factor = Si = Di D Seasonal Adjustment YEAR 2002 2003 2004 DEMAND (1000’S PER QUARTER) 1 2 3 4 Total 12.6 14.1 15.3 8.6 10.3 10.6 6.3 7.5 8.1 17.5 18.2 19.6 D1 S1 = = D D3 S3 = = D D2 S2 = = D D4 S4 = = D Seasonal Adjustment YEAR 2002 2003 2004 Total DEMAND (1000’S PER QUARTER) 1 2 3 4 Total 12.6 14.1 15.3 42.0 8.6 10.3 10.6 29.5 6.3 7.5 8.1 21.9 17.5 18.2 19.6 55.3 45.0 50.1 53.6 148.7 D1 42.0 S1 = = = 0.28 D 148.7 D3 21.9 S3 = = = 0.15 D 148.7 D2 29.5 S2 = = = 0.20 D 148.7 D4 55.3 S4 = = = 0.37 D 148.7 Seasonal Adjustment For 2005 y= SF1 = (S1) (F5) = SF2 = (S2) (F5) = SF3 = (S3) (F5) = SF4 = (S4) (F5) = Seasonal Adjustment For 2005 y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17 SF1 = (S1) (F5) = (0.28)(58.17) = 16.28 SF2 = (S2) (F5) = (0.20)(58.17) = 11.63 SF3 = (S3) (F5) = (0.15)(58.17) = 8.73 SF4 = (S4) (F5) = (0.37)(58.17) = 21.53 Using Seasonal Indices • Many ways to model seasonality • Don’t forget to check accuracy of this forecast against historical data, as for any other forecast! • Note: text doesn’t calculate entire forecast for this method and check accuracy Forecast Accuracy • Forecast error • difference between forecast and actual demand • MAD • mean absolute deviation • MAPD • mean absolute percent deviation • Cumulative error • Average error or bias Mean Absolute Deviation (MAD)  Dt - Ft  MAD = n where t = period number Dt = demand in period t Ft = forecast for period t n = total number of periods   = absolute value MAD Example PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 DEMAND, Dt Ft (a =0.3) 37 40 41 37 45 50 43 47 56 52 55 54 37.00 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 (Dt - Ft) – |Dt - Ft| – MAD Example PERIOD 1 2 3 4 5 6 7 8 9 10 11 12 DEMAND, Dt Ft (a =0.3) (Dt - Ft) |Dt - Ft| 37 40 41 37 45 50 43 47 56 52 55 54 37.00 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 – 3.00 3.10 -1.83 6.72 9.69 -0.20 3.86 11.70 4.19 5.94 3.15 – 3.00 3.10 1.83 6.72 9.69 0.20 3.86 11.70 4.19 5.94 3.15 49.31 53.39 557 MAD Calculation  Dt - Ft  MAD = n MAD Calculation  Dt - Ft  MAD = n 53.39 = 11 = 4.85 Other Accuracy Measures Mean absolute percent deviation (MAPD) |Dt - Ft| MAPD = Dt Cumulative error E = et Average error et E= n Comparison of Forecasts FORECAST MAD MAPD E (E) Exponential smoothing (a = 0.30) Exponential smoothing (a = 0.50) Adjusted exponential smoothing (a = 0.50,  = 0.30) Linear trend line 4.85 4.04 3.81 9.6% 8.5% 7.5% 49.31 33.21 21.14 4.48 3.02 1.92 2.29 4.9% – – Forecast Control • Tracking signal • monitors the forecast to see if it is biased high or low • 1 MAD ≈ 0.8 б • Control limits of 2 to 5 MADs are used most frequently Tracking signal = (Dt - Ft) E = MAD MAD Tracking Signal Values PERIOD DEMAND Dt FORECAST, Ft 1 2 3 4 5 6 7 8 9 10 11 12 37 40 41 37 45 50 43 47 56 52 55 54 37.00 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 ERROR Dt - Ft – 3.00 3.10 -1.83 6.72 9.69 -0.20 3.86 11.70 4.19 5.94 3.15 E = (Dt - Ft) MAD – 3.00 6.10 4.27 10.99 20.68 20.48 24.34 36.04 40.23 46.17 49.32 – 3.00 3.05 2.64 3.66 4.87 4.09 4.06 5.01 4.92 5.02 4.85 Tracking Signal Values PERIOD DEMAND Dt FORECAST, Ft 1 2 3 4 5 6 7 8 9 10 11 12 37 40 41 37 45 50 43 47 56 52 55 54 37.00 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 TS3 = ERROR Dt - Ft – 3.00 3.10 -1.83 6.72 9.69 -0.20 3.86 11.70 4.19 5.94 3.15 E = (Dt - Ft) MAD – 3.00 6.10 4.27 10.99 20.68 20.48 24.34 36.04 40.23 46.17 49.32 – 3.00 3.05 2.64 3.66 4.87 4.09 4.06 5.01 4.92 5.02 4.85 6.10 = 2.00 3.05 TRACKING SIGNAL – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17 Tracking Signal Plot Statistical Control Charts ▪ Using  we can calculate statistical control limits for the forecast error ▪ Control limits are typically set at  3 = (Dt - Ft)2 n-1 ▪Mean squared error (MSE) ▪Average of squared forecast errors Statistical Control Charts Time Series Forecasting Using Excel • Excel can be used to develop forecasts: • • • • Moving average Exponential smoothing Adjusted exponential smoothing Linear trend line Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts =B5*(C11-C10)+ (1-B5)*D10 =C10+D10 =ABS(B10-E10) =SUM(F10:F20) =G22/11 Demand and Exponentially Smoothed Forecast Data Analysis Option Forecasting With Seasonal Adjustment Regression Methods • Linear regression • mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation • Correlation • a measure of the strength of the relationship between independent and dependent variables Linear Regression y = a + bx a = y-bx  xy - nxy b =  x2 - nx2 where a = intercept b = slope of the line x x = = mean of the x data n y y = n = mean of the y data Linear Regression Example x (WINS) y (ATTENDANCE) 4 6 6 8 6 7 5 7 36.3 40.1 41.2 53.0 44.0 45.6 39.0 47.5 xy x2 Linear Regression Example x (WINS) y (ATTENDANCE) xy x2 4 6 6 8 6 7 5 7 36.3 40.1 41.2 53.0 44.0 45.6 39.0 47.5 145.2 240.6 247.2 424.0 264.0 319.2 195.0 332.5 16 36 36 64 36 49 25 49 49 346.7 2167.7 311 Linear Regression Example x= y= xy - nxy2 b= x2 - nx2 a = y - bx Linear Regression Example 49 = 6.125 8 346.9 y= = 43.36 8 x= xy - nxy2 b= x2 - nx2 (2,167.7) - (8)(6.125)(43.36) = (311) - (8)(6.125)2 = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 Linear Regression Example 60,000 – Attendance, y 50,000 – 40,000 – 30,000 – Linear regression line, y = 18.46 + 4.06x 20,000 – Attendance forecast for 7 wins y = 18.46 + 4.06(7) = 46.88, or 46,880 10,000 – | 0 | 1 | 2 | 3 | 4 | 5 Wins, x | 6 | 7 | 8 | 9 | 10 Correlation and Coefficient of Determination • Correlation, r • Measure of strength of relationship • Varies between -1.00 and +1.00 • Coefficient of determination, r2 • Percentage of variation in dependent variable resulting from changes in the independent variable Computing Correlation r= n xy -  x y [n x2 - ( x)2] [n y2 - ( y)2] Computing Correlation r= n xy -  x y [n x2 - ( x)2] [n y2 - ( y)2] (8)(2,167.7) - (49)(346.9) r= [(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2] r = 0.947 Coefficient of determination r2 = (0.947)2 = 0.897 Regression Analysis With Excel =INTERCEPT(B5:B12,A5:A12) =SUM(B5:B12) =CORREL(B5:B12,A5:A12) Regression Analysis with Excel Regression Analysis With Excel Multiple Regression Study the relationship of demand to two or more independent variables y = 0 + 1x1 + 2x2 … + kxk where 0 = the intercept 1, … , k = parameters for the independent variables x1, … , xk = independent variables Multiple Regression With Excel r2, the coefficient of determination Regression equation coefficients for x1 and x2 Multiple Regression Example y = 19,094.42 + 3560.99 x1 + .0368 x2 Attendance for 7 wins and $60,000 promotion y= Multiple Regression Example y = 19,094.42 + 3560.99 x1 + .0368 x2 Attendance for 7 wins and $60,000 promotion y = 19,094.42 + 3560.99 (7) + .0368 (60,000) = 46,229.35 Basic Forecasting Process in Excel • Plot data to detect general behavior • Be aware of outliers • Try simple models -- MA, WMA, ES, LR • Check accuracy • Increase complexity of model using seasonality, etc., if desired • Check accuracy • Choose best model to forecast future Notes on Forecasting in Excel • Don’t do linear regression equations! • SLOPE and INTERCEPT functions • Optional: use Solver to determine optimal smoothing constants and weights • minimize MAD or other accuracy measure
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