Report

Chapter 3 Forecasting Forecasting Demand Why is demand forecasting important? What is bad about poor forecasting? What do these organizations forecast: • Sony (consumer products division) • Foley’s • Dallas Area Rapid Transit (DART) • UTA Questions in Demand Forecasting For a particular product or service: • What exactly is to be forecasted? • What will the forecasts be used for? • What forecasting period is most useful? • What time horizon in the future is to be forecasted? • How many periods of past data should be used? • What patterns would you expect to see? • How do you select a forecasting model? Demand Management Recognizing and planning for all sources of demand Can demand be controlled or influenced? • appointment schedules – doctor’s office – attorney – SAM telephone registration • sales promotions – – – – restaurant discounts before 6pm video rental store discounts on Tuesdays golf course discounts if you start playing after 4pm theater matinee movie discounts Qualitative vs. Quantitative Forecasting Methods Some Qualitative Methods: • Experienced guess/judgement • Consensus of committee • Survey of sales force • Survey of all customers • Historical analogy – new products • Market research – survey a sample of customers – test market a product Steps for Quantitative Forecasting Methods 1. 2. 3. 4. Collect past data—usually the more the better Identify patterns in past data Select one or more appropriate forecasting methods Forecast part of past data with each method – – 5. Determine best parameters for each method Compare forecasts with actual data Select method that had smallest forecasting errors on past data Forecast future time periods Determine prediction interval (forecast range) Monitor forecasting accuracy over time 6. 7. 8. – Tracking signal Types of Quantitative Forecasting Methods Pattern Projection – time series regression – trend or seasonal models Data Smoothing – moving average – exponential smoothing Causal – multiple regression Data Pattern Components Time Time LEVEL Time TREND SEASONALITY 1986 Sales 1980 Sales Time CYCLICALITY Dec Sales Dec Sales Dec Sales Time NOISE Identifying Data Patterns for Time Series Always Plot Data First – After plotting data, patterns are often obvious. Average or level – Use mean of all data Trend – Use time series regression – slope is trend – time period is independent variable Seasonality – Deseasonalize the data Cyclicality – Similar to deseasonalizing Random noise – No pattern – try to eliminate in forecasts Forecast Accuracy E t forecast error for period t E t D t Ft D t or At actual demand for period t Ft forecast for period t n Mean Absolute Deviation MAD Et t 1 n Forecast Accuracy Mean Squared Error n E t t 1 MSE n Mean Error (Bias) n ME E t 1 n t 2 Forecast Accuracy Example Period 1 2 3 4 5 6 At 32 28 31 34 34 36 Ft 30 31 33 35 33 34 Totals: Et |Et| (Et)2 Forecast Accuracy Example Bias = MAD = MSE = Quantity of Electric Irons Shipped by U.S. Mfgs. 14 12 8 6 4 2 88 19 87 19 86 19 85 19 84 19 83 19 82 19 81 19 80 19 79 0 19 million units 10 Electric Irons Example -- Data Year 1979 1980 1981 1982 1983 Qty 12.079 11.478 11.013 6.616 7.279 10-year average = Last-7-year average = Year 1984 1985 1986 1987 1988 Qty 7.843 6.834 7.660 5.918 7.115 Do time series regression analysis Y = a + bX Y = dependent variable (actual sales) X = independent variable (time period in this case) a = y-intercept (value of Y when X=0) b = slope or trend b N XY N X 2 X Y X 2 a Y where N = number of periods of data N b X N Electric Irons Example X 4 5 6 7 8 9 10 == 49 Y 6.616 7.279 7.843 6.834 7.660 5.918 7.115 ===== 49.265 X2 16 25 : : : : : === 371 XY 26.46 36.40 : : : : : ===== 343.45 b= a= Y= Y11 = Y12 = 19 88 Su m Fa ll W in Fa ll Sp Win 19 91 Su m Fa ll W Sp in 19 90 Su m Fa ll Sp Win 19 89 Su m Sp Number of Trucks Leased Moving Company Sales 250 200 150 100 50 0 Overlay the Years Number of Trucks Leased 250 1988 1989 1990 1991 200 150 100 50 0 Spring Summer Fall Winter Seasonality and Trend Patterns (Seasonalized Regression) Steps: 1. Deseasonalize the data to remove seasonality – divide by seasonal index (SI) 2. Use regression to model trend 3. Make initial forecasts to project trend 4. Seasonalize the forecast – multiply by SI Moving Company Example 1988 1989 1990 1991 Total: Avg: SI: Spring Summer Fall Winter 90 160 70 120 Overall Avg. 130 200 90 100 2020/16 80 170 130 140 = 126.25 130 210 80 120 430 740 370 480 107.5 185 92.5 120 Deseasonalize the Data 1988 1989 1990 1991 * Spring Summer Fall 105.7* 109.2 95.5 152.7 136.5 122.8 94.0 116.0+ 177.4 152.7 143.3 109.2 Winter 126.3 105.2 147.3 126.3 Spring 1988: 90/.851 = 105.7 + Summer 1990: 170/1.465 = 116.0 Perform Time Series Regression X 1 2 3 4 : 16 === 136 Y X2 XY 105.7 1 105.7 109.2 4 218.4 95.5 9 286.6 : : : : : : 126.3 256 2020.0 ====== ===== ======= 2,020.0 1,496 17,773.5 Totals b N XY b= a= Y= N X 2 X Y X 2 a Y N b X N Make initial forecasts: Y17 = Y18 = Y19 = Y20 = Make final forecasts: (Seasonalize F17 = F18 = F19 = F20 = F = Y x SI) Gasoline Service Station Monthly Sales 13 12 billion $ 11 10 9 8 7 6 0 6 12 18 24 30 36 42 month 48 54 60 66 72 78 Gasoline Service Station Monthly Sales 13 1985 1986 1987 1988 1989 1990 12 billion $ 11 10 9 8 7 6 Jan Feb Mar Apr May Jun Jul month Aug Sep Oct Nov Dec Deseasonalized Sales 13 12 billion $ 11 10 9 8 7 6 0 6 12 18 24 30 36 42 month 48 54 60 66 72 78 Regression Line 13 12 billion $ 11 10 9 8 7 6 0 6 12 18 24 30 36 42 month 48 54 60 66 72 78 Final Forecasts 13 12 billion $ 11 10 9 8 7 6 0 6 12 18 24 30 36 42 month 48 54 60 66 72 78 Actual Sales Past Sales Forecasts Actuals 13 12 billion $ 11 10 9 8 7 6 0 6 12 18 24 30 36 42 month 48 54 60 66 72 78 Forecast Ranging Forecasts are rarely perfect! A forecast range reflects the degree of confidence that you have in your forecasts. Forecast ranging allows you to estimate a prediction interval for actual demand “There is a ___% probability that actual demand will be within the upper and lower limits of the forecast range.” Standard Error of the Forecast (a measure of dispersion of the forecast errors) s yx y a y b xy 2 n2 Upper Limit = Fi + t(syx) Lower Limit = Fi - t(syx) Need desired level of significance (α) and degrees of freedom (df) to look up t in table Forecast Confidence Intervals (Forecast Ranging) (1 – α) α/2 α/2 t(Syx) Lower Limit Ft Upper Limit Actual Sales in Future t-statistic and degrees of freedom For a confidence interval of 95%,α = .05 (.025 in each tail), and df=16 From table, t = Why does df = n-2 for simple regression? If the forecast was from a multiple regression model with 3 independent variables, what would be the degrees of freedom? df = n - __ Example: Judy manages a large used car dealership that has experienced a steady growth in sales during the last few years. Using time series regression and sales data for the last 20 quarters, Judy obtained a forecast of 800 car sales for next quarter. With her model and the past data the standard error of the forecast was 50 cars. What are the limits for a 95% forecast range? for an 80% forecast range? Example: A manager’s forecast of next month’s sales of product Q was 1500 units using time series regression based on the last 24 months of sales, which had a standard forecast error of 29 units. Her boss asked how sure she was that actual sales would be within 50 units of her forecast. Short Range Forecasting • A few days to a few months • Assumes there are no patterns in the data • Random noise has a greater impact in the short term • These approaches try to eliminate some of the random noise • Random walk, moving average, weighted moving average, exponential smoothing Random Walk The next forecast is equal to the last period’s actual value Period 1 2 3 4 Sales 21 30 27 ? Forecast Moving Average Method The next forecast is equal to an average of the last AP periods of actual data Period 1 2 3 4 5 Sales 21 28 35 30 ? AP=4 AP=3 AP=2 Impulse Response – how fast the forecasts react to changes in the data The higher the value of AP, the less the forecast will react to changes in the data, so the lower the impulse response is. Noise Dampening – how much the forecasts are smoothed Noise dampening is the opposite of impulse response. A moving average model with AP=1 has high impulse response and low noise dampening characteristics. Weighted Moving Average method Like the moving average method except that each of the AP periods can have a different weight Period 1 2 3 4 5 Actual Sales 21 28 35 30 ? AP=4 Weight .1 .15 .25 .5 Usually the recent periods have more weight Exponential Smoothing Most common short-term quantitative forecasting method (especially for forecasting inventory levels) Why? – surprisingly accurate – easy to understand – simple to use – very little data is stored Need 3 pieces of data to make forecast 1. most recent forecast 2. actual sales for that period 3. smoothing constant (α) Exponential Smoothing method – gives a different weight to each period Ft = Ft-1 + α(At-1 – Ft-1) α is the smoothing parameter and is between 0 and 1 Interpretation: the next forecast equals last period’s forecast plus a percentage of last period’s forecasting error. Alternative formula: Ft = αAt-1 + (1 - α)Ft-1 (rearranging terms) Example: assume α = 0.3 We must assume a forecast for an earlier period Period 1 2 3 4 5 6 Sales 21 24 23 19 22 ? Forecast Find best value for α by trial and error The larger α is, the more weight that is placed on the more recent periods’ actual values, so the higher the impulse and the lower the noise dampening. Tracking Signal After a forecasting method has been selected, tracking signal is used to monitor accuracy of the method as time passes Particularly good at identifying underforecasting or overforecasting trends Tracking Signal = Sum of Errors (E t ) MAD Ideal value for tracking signal is ___ Guidelines would be used if the value exceeds specified limits Example: Suppose exponential smoothing is used (α = .2) If |TS| < 2.3 then do not change α If |TS| > 2.3 then increase α by .1 If |TS| > 3.0 then increase α by .3 If |TS| > 3.6 then increase α by .5 After tracking signal goes back down, restore original value of α or calculate new α Double Exponential Smoothing (Exponential Smoothing with Trend) Two smoothing constants are used: α smoothes out random variations β smoothes out trends An alternative to time series regression Especially useful if there is much random variation Winter’s Exponential Smoothing Accounts for trend and seasonality Three smoothing constants are used α smoothes out random variations β smoothes out trends γ smoothes out seasonality There are many other variations of exponential smoothing Box-Jenkins Forecasting Approach Relatively accurate, but complex and time consuming to use Needs at least 60 points Good choice if there are not many time series to forecast, and accuracy is very important Works best when random variation is a small component Example: monthly automobile registrations in U.S. Forecast = Dt + Dt-11 – Dt-12 – 0.21Et – 0.21Et-1 – 0.85Et-11 + 0.18Et-12 + 0.22Et-13 where Dt = Actual demand for time period t Et = Error term for time period t Focus Forecasting (Forecasting Simulation) Bernard Smith at American Hardware Supply developed this method to make forecasts for 100,000 items Based on 2 principles: – sophisticated methods don’t always work better – no single method works best for all items Buyers tended not to use the previous exponential smoothing model because they did not trust or understand it. Instead, they were making up their own simple rule-of-thumb approaches. Smith selected 7 forecasting methods to use, such as 1. sales = last month’s sales plus a percentage 2. sales = sales for same month last year plus a % 3. 2-month moving average 4. exponential smoothing etc. (most were relatively simple) All methods were used to forecast each product. Whichever method worked best for the previous month, that method was used to forecast the next month. Approach worked very well, and people understood and used it. Smith wrote a popular book describing his approach and success. Multiple Regression Forecasting Sales = f($advertising, #salespeople, $price) Sales Adv People Price 5200 350 18 53 5600 520 18 52 5100 400 15 54 3800 320 13 64 5200 410 16 51 4900 290 17 60 5200 390 17 54 5400 470 20 55 4700 450 14 61 5000 500 15 58 5100 470 18 60 SUMMARY OUTPUT Regression Statistics Multiple R 0.952 R Square 0.907 Adjusted R Square 0.867 Standard Error 170.988 Observations 11 ANOVA df SS MS F Significance F Regression 3 1991704.974 663901.7 Residual 7 204658.662 29236.95 10 2196363.636 Coefficients Standard Error 5839.347 1236.003 4.724 0.002 1.742 0.765 2.277 0.057 People 100.207 30.723 3.262 0.014 Price -56.478 14.999 -3.765 0.007 Total Intercept Adv t Stat 22.708 P-value 0.00055 Multiple Regression Example Suppose the manager wants to forecast sales if $430 in advertising, 19 salespeople, and a price of $64 per unit are planned. Coefficients Intercept Adv 5839.347 1.742 People 100.207 Price -56.478 Forecasting equation: Sales = 5839.347 + 1.742(adv) + 100.207(people) – 56.478(price) Sales = Sales =