Problem 4.1, HR7E Forecasting R. Saltzman. b) Forecast for Oct. 12 using 3-week weighted moving average with weights.1,.3,.6: 372.

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1 Problem 4.1, HR7E Forecasting R. Saltzman Part c Week Pints ES Forecast Aug Sept Sept Sept Sept Oct Oct. 12? a) Forecast for Oct. 12 using 3-week moving average: b) Forecast for Oct. 12 using 3-week weighted moving average with weights.1,.3,.6: c) Forecast for Oct. 12 with ES using F(Aug. 31) = 360 and alpha = 0.2. See table above.

2 Problem 4.2, HR7E Forecasting R. Saltzman Year Demand 3-yr MA 3-yr wtd MA a) Plot the data. Any trend, cycles, or random variations? Demand Actual vs Forecasted Demand Demand 3-yr MA 3-yr wtd MA Year No trend No cycles Random variation b) Use a 3-year moving average: see table & plot c) Use a 3-year weighted moving average: see table & plot d) Which seem to give better results? 3-yr MA

3 Problem 4.4, HR7E Forecasting R. Saltzman ES Month Checks Forecast June July August a) Forecast for July, using alpha = 0.2 see table b) Forecast for August if actual demand in July was 45 see table c) Why might this be an inappropriate method? could be missing trend or seasonality but need more data to tell.

4 Problem 4.5, HR7E Forecasting R. Saltzman Part a Part b Part c Part c Part d (FYI) Year Mileage 2-yr MA Abs. Error Wtd. MA Abs. Error ES with α = 0.5 Abs. Error MAD -->

5 Problem 4.10, HR7E Forecasting R. Saltzman part a part b Year Registration 3-yr MA 3-yr wtd MA a) Develop 3-year MA forecasts see table b) Forecast using weighted MA, with weights of 1, 1, 2 (most recent) => 0.25, 0.25, 0.50 see table c) Graph the data. Which seems better? Very close; perhaps Wtd. MA is better. Actual vs Forecasted Demand 20 Demand Registration 3-yr MA 3-yr wtd MA Year

6 Problem 4.11, HR7E Forecasting R. Saltzman Actual Forecasts Year Registration ES with alpha = (assumed value)

7 Problem 4.12, HR7E Forecasting R. Saltzman Absolute Errors Year Registration 3-yr MA 3-yr wtd MA ES w/ alpha = yr MA 3-yr wtd MA ES with alpha = Using the MAD criterion, which method works be MAD Best

8 Problems 4.13 & 4.14, HR7E Forecasting R. Saltzman Absolute Errors ES (0.6) ES (0.9) 3-Yr. MA Trend Proj ES (0.6) ES (0.9) 3-Yr. MA Trend Proj Year Transplants FC FC FC FC Et Et Et Et Using the MAD criterion, which method works best? MAD Best intercept slope Trend Projection

9 Problems 4.15 & 4.16, HR7E Forecasting R. Saltzman See Solved Problem 4.1 on p Use a 3-year MA and trend projection to forecast sales. Absolute Errors 3-Yr. MA Trend Proj 3-Yr. MA Trend Proj Year Sales FC FC Et Et Using MAD criterion, which is better? better intercept slope Trend Projection

10 Problem 4.23, HR7E Forecasting R. Saltzman Absolute Errors Absolute % Errors Mgmt's Naïve Mgmt's Naïve Mgmt's Naïve Month Sales Forecast Forecast Forecast Forecast Forecast Forecast Feb 83 March % 17.8% April % 5.2% May % 7.9% June % 17.6% July? a) Compute MAD & MAPE for management's technique MAD = 14.5 MAPE = 15.3% b) Do management's results outperform a naïve forecast? NO! MAD = for naïve MAPE = 12.1% method c) Based on lower forecast error, Naïve method appears to be better.

11 Problem 4.24, HR7E Forecasting R. Saltzman 12 y x Demand for Green Shades Bass Drums TV appearances Bass Drum Demand TV Appearances a) Graph Data is relationship linear? b) Least squares method: intercept = 1 So, yhat = 1 + 1x slope = 1 c) If x = 9 TV appearances, yhat = 1 + 9(1) = 10 bass drums demanded

12 Problem 4.26, HR7E Forecasting R. Saltzman Sales of Radial Tires Forecasted Quarter Year 1 Year 2 Seasonal Index Sales Year 3 Fall Winter Spring Summer Year Total Average Sales 250 per quarter Year 3 Projected Sales 1200 Average Sales 300 per quarter

13 Problem 4.28, HR7E Forecasting R. Saltzman Attendance at Vacation World Season Quarter Average Seasonal Index Winter Spring Summer Fall Overall Ave/quarter

14 Problem 4.32, HR7E Forecasting R. Saltzman x y Week #Guests Bar Sales a) Perform linear regression intercept a = 50 slope b = 18 So, Bar Sales = *(#Guests) b) Forecast bar sales if # Guests =

15 Problem 4.36, HR7E Forecasting R. Saltzman Multiple regression equation, with correlation = 0.68 Travel Cost = *X *X2, where X1 = days on the road X2 = distance travelled in miles a) For a 300 mile trip (X2) that lasted 5 days (X1), what is expected travel cost? $ b) Tomlinson requested $685. What should the accountant do? Since the request is so much higher than the expected amount, the accountant should get more information from Tomlinson to justify his requests. c) Should any other variables be included in the regression equation? Since r = 0.68 only, perhaps add variables regarding the number of meals eaten out, the relative cost of the cities visited, and size of car rented, etc. Including data on these variables might increase r and r-squared.

16 Problem 4.38, HR7E Forecasting R. Saltzman y x Sales Tax Collected New Car Registrations a) Find the regression equation: intercept a = slope b = So, Sales Tax Collected = *New Car Reg. b) Forecast Sales Tax Collected if New Car Reg. = Thousand Million $ c) Find the coefficients of correlation r = and determination r 2 = 0.934