Roberta Russell & Bernard W. Taylor, III Chapter 11 Forecasting Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III

Forecasting Predicting the Future Qualitative forecast methods subjective Quantitative forecast methods based on mathematical formulas

Forecasting and Supply Chain Management Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Continuous replenishment supplier and 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

Forecasting and TQM Accurate forecasting customer demand is a key to providing good quality service Continuous replenishment and JIT complement TQM eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM smoothes process flow with no defective items meets expectations about on-time delivery, which is perceived as good-quality service

Types of Forecasting Methods Depend on time frame demand behavior causes of behavior

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 Long-range forecast usually encompasses a period of time longer than two years

Demand Behavior Trend Random variations Cycle Seasonal pattern a gradual, long-term up or down movement of demand Random variations movements in demand that do not follow a pattern Cycle an up-and-down repetitive movement in demand Seasonal pattern an up-and-down repetitive movement in demand occurring periodically

Forms of Forecast Movement Time (a) Trend (d) Trend with seasonal pattern (c) Seasonal pattern (b) Cycle Demand Random movement

Forecasting Methods Qualitative Time series Regression methods use management judgment, expertise, and opinion to predict future demand 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 Methods Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts Delphi method involves soliciting forecasts about technological advances from experts

Is accuracy of forecast acceptable? 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 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8a. Forecast over planning horizon

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 moving average exponential smoothing linear trend line

Moving Average Naive forecast Simple moving average demand the current period is used as next period’s forecast Simple moving average stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data

Moving Average: Naïve Approach Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 ORDERS MONTH PER MONTH - 120 90 100 75 110 50 130 Nov - FORECAST

n = number of periods in the moving average Simple Moving Average MAn = n i = 1  Di where n = number of periods in the moving average Di = demand in period i

3-month Simple Moving Average MA3 = 3 i = 1  Di = 90 + 110 + 130 = 110 orders for Nov Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MOVING AVERAGE

5-month Simple Moving Average Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE MA5 = 5 i = 1  Di = 90 + 110 + 130+75+50 = 91 orders for Nov

Smoothing Effects 150 – 125 – 100 – 5-month 75 – 50 – 25 – 0 – Orders | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Actual Orders Month 5-month 3-month

Weighted Moving Average WMAn = i = 1  Wi Di where Wi = the weight for period i, between 0 and 100 percent  Wi = 1.00 Adjusts moving average method to more closely reflect data fluctuations

Weighted Moving Average Example MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 WMA3 = 3 i = 1  Wi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders November Forecast

Exponential Smoothing Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method

Exponential Smoothing (cont.) Ft +1 = Dt + (1 - )Ft where: Ft +1 = forecast for next period Dt = actual demand for present period Ft = previously determined forecast for present period = weighting factor, smoothing constant

Effect of Smoothing Constant 0.0  1.0 If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft If = 0, then Ft +1 = 0Dt + 1 Ft 0 = Ft Forecast does not reflect recent data If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data

Exponential Smoothing (α=0.10) PERIOD MONTH DEMAND 1 Jan 120 2 Feb 90 3 Mar 100 4 Apr 75 5 May 110 6 Jun 50 7 Jul 75 8 Aug 130 9 Sep 110 10 Oct 90 F2 = D1 + (1 - )F1 = (0.10)(120) + (0.90)(120) = 120 F3 = D2 + (1 - )F2 = (0.10)(90) + (0.90)(120) = 117 F11 = D10 + (1 - )F10 = (0.10)(90) + (0.90)(105.34) = 103.81

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  n MAD = where t = period number Dt = demand in period t Ft = forecast for period t n = total number of periods  = absolute value

Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD = |Dt - Ft| Dt Cumulative error E = et Average error E = et n

Regression Methods Linear regression Correlation a 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 - b x b = xy - nxy x2 - nx2 where a = intercept b = slope of the line x = = mean of the x data y = = mean of the y data xy - nxy x2 - nx2 x n y

Linear Regression Example x y (WINS) (ATTENDANCE) xy x2 4 36.3 145.2 16 6 40.1 240.6 36 6 41.2 247.2 36 8 53.0 424.0 64 6 44.0 264.0 36 7 45.6 319.2 49 5 39.0 195.0 25 7 47.5 332.5 49 49 346.7 2167.7 311

Linear Regression Example (cont.) y = = 43.36 b = = = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 346.9 xy - nxy2 x2 - nx2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125)2

Linear Regression Example (cont.) y = 18.46 + 4.06x y = 18.46 + 4.06(7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 60,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = 18.46 + 4.06x Wins, x Attendance, y

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 n xy -  x y [n x2 - ( x)2] [n y2 - ( y)2] r = Coefficient of determination r2 = (0.947)2 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2] r = 0.947