1. Review Test 2 BSAD 30 Dave Novak Source: Anderson et al., 2015 Quantitative Methods for Business 13 th edition – some slides are directly from J. Loucks © 2013 Cengage Learning 1

2. Chapter 6 You should be able to calculate all four basic measures of forecast accuracy (MFE, MAE, MSE, and MAPE) You should be able to make a forecast for any time period using any of the five forecasting methods we discussed (naïve, moving average, weighted moving average, exponential smoothing, linear trend 2

3. Using linear trend Seasonal pattern with trend The time series (the data we are looking at) includes both a seasonal effect AND a positive or negative trend over time We will have seasonal variables AND a time variable in our regression model 3

4. TV sales example 4 Assume that we have collected quarterly data on the number of TVs sold by a particular retailer over the past four years

5. TV sales example 5 Average sales for each quarter for the past four years

6. TV sales example 6 Year 1Year 2Year 3Year 4

7. Seasonal pattern with trend We have a positive trend in sales over time We have seasonal variation in sales that appears to repeat every year Requires the use of (k – 1) dummy variables 7

8. Seasonal pattern with trend General form of equation: 8 We can estimate the regression function coefficients b 0, b 1, b 2, b 3, b 4 using linear regression

9. Seasonal pattern with trend 9 Dummy variables capture seasonal effects Quarter #2 of year #4 = Time period 14 Quarter #3 of year #2 = Time period 7

10. Seasonal pattern with trend 10

11. Seasonal pattern with trend How much of the sales variability is explained by the linear regression model? 11

12. Seasonal pattern with trend In this model, Qtr4 is our baseline for comparison (we have no Qtr4 dummy). How many more / fewer TVs do you expect to sell in Qtr2 compared to Qtr4? 12

13. Seasonal pattern with trend How many more / fewer TVs do we expect to sell each quarter? 13

14. Seasonal pattern with trend Using the linear trend, forecast sales for time period 11 (Year 3, Quarter 3) 14

15. Seasonal pattern with trend Using the linear trend, forecast sales for time period 18 (Year 5, Quarter 2) 15

16. Chapter 7 and 8 You should be able to formulate an LP from a word problem You should be able to solve an LP graphically You should be able to calculate slack and surplus You should be able to interpret the Answer and Sensitivity Reports 16

17. 8-19 17 CategoryProduct 1Product 2Product 3 Profit/unit$31$60$16 Machine 1 time/unit 0.51.5 Machine 2 time/unit 11.51 Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 120 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 55% of the units produced and that product 3 must account for at least 25% of the units produced.

18. 8-19 18 Formulate the problem

19. 8-19 19 Write the Standard Form of the LP

20. 8-19 20 Answer Report

21. 8-19 21 Solve for S1 and S4

22. 8-19 22 Sensitivity Report

23. 8-19 23 How many units of each product should be produced to maximize the total profit contribution? If required, round your answers to the nearest integer. What is the projected weekly profit associated with your solution?

24. 8-19 24 How many hours of production time will be scheduled on each machine? If required, round your answers to two decimal places. What is the value of one additional hour of labor? If required, round your answers to two decimal places.

25. 8-19 25 Assume that labor capacity can be increased to 130 hours. Develop the optimal product mix, assuming that the extra hours are made available? If required, round your answers to the nearest integer. Would you be interested in using the 10 additional hours of labor?

26. 8-19 26 If labor hours decrease by 10, what is the impact on the optimal solution mix and the total profit?

27. 8-19 27 If the profit you receive per unit of product #1 were to increase by $10, what is the optimal solution mix and profit maximizing solution? If the profit you receive per unit of product #1 were to decrease by $5, what is the optimal solution mix and profit maximizing solution?

28. 8-19 28 Interpret the Shadow Price associated with constraint #1