# Problem 1. stocking textbooks for INEN455 rne past, they have just ordered 50

Problem 1. stocking textbooks for INEN455 rne past, they have just ordered 50 textbooks. The data for sales of the textbook for the past semesters is listed in the table below. A graph of the sales data is also presented (Figure 1). The bookstore manager has decided to ask students from the IF forecasting techniques that will drive their future ordering decisions. The campus bookstore is trying to develop a better method for re manager has decided to ask students from the IE department to help them use Sales 20 25 30 10 15 40 30 Sales 20 10 Period Semester Fall 10 Spring 1l Fall 11 Spring 12 Series Linear (Series 1 ) Period (10 points) a) Which forecasting method(s) would you suggest based on the graph and why? b) Suppose that 2 period moving averages are used to forecast sales. Determine the (10 points) one-step ahead forecasts for periods 3 through 6 and place your response in column ofthe table below. Be sure to place your answer in the correct location in the table c Suppose that exponential smoothing was used to forecast sales. Determine the one- (20 points) step ahead forecasts for periods 2 through 6 using an alpha of 0.3. Place the result in the column (e) of the table below. Assume the forecast in period 1 is the same as the sales for period 1. Calculate the forecast error (absolute value of the error) for periods 3-5 for both the moving average and exponential smoothing forecasts and place the result in columns F and G, respectively. Using this information compute the MAD and MSE. What can you conclude about the two forecasting methods based on the MAD and MSE? d) (20 points)

A.

As the trend is linear and decreasing either Moving average or exponential smoothening or smoothening with trend should be used.

B.

 A B C D F Period Sem Sales MA(2) Error MA(2) AD 1 Fall 10 20 2 Spring 11 25 3 Fall 11 30 22.5 7.5 7.5 4 Spring 12 10 27.5 -17.5 17.5 5 Fall 12 15 20 -5 5 6 Spring 13 12.5 10 MAD

C.

 a = 0.3 Period Sem Sales Forecast Error ES AD SE 1 Fall 10 20 20.00 2 Spring 11 25 20.00 3 Fall 11 30 21.50 8.5 8.50 72.25 4 Spring 12 10 24.05 -14.05 14.05 197.40 5 Fall 12 15 19.84 -4.835 4.84 23.38 6 Spring 13 18.38 9.13 97.68 MAD MSE

D.

 A B C D E F G Period Sem Sales MA(2) ES Error MA(2) Error ES 1 Fall 10 20 20.00 2 Spring 11 25 20.00 3 Fall 11 30 22.5 21.50 7.5 8.5 4 Spring 12 10 27.5 24.05 -17.5 -14.05 5 Fall 12 15 20 19.84 -5 -4.835 6 Spring 13 12.5 18.38

So comparing:

 A B C D F Period Sem Sales MA(2) Error MA(2) AD SE 1 Fall 10 20 2 Spring 11 25 3 Fall 11 30 22.5 7.5 7.5 56.25 4 Spring 12 10 27.5 -17.5 17.5 306.25 5 Fall 12 15 20 -5 5 25.00 6 Spring 13 12.5 10 129.17 MAD MSE a = 0.3 Period Sem Sales Forecast Error ES AD SE 1 Fall 10 20 20.00 2 Spring 11 25 20.00 3 Fall 11 30 21.50 8.5 8.50 72.25 4 Spring 12 10 24.05 -14.05 14.05 197.40 5 Fall 12 15 19.84 -4.835 4.84 23.38 6 Spring 13 18.38 9.13 97.68 MAD MSE

ES is the better ooption as MAD and MSE both are better.

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