Final Requirement in OR

The Americo Oil Company is considering making a bid for a shale oil development contract to be awarded by the federal government. The company has decided to bid $110 million. The company estimates that it has a 60% chance of winning the contract with this bid. If the firm wins the contract, it can choose one of the three methods for getting the oil from the shale. It can develop a new method for oil extraction, use an existing (inefficient) process, or subcontract the processing to a number of smaller companies once the shale has been excavated. The results from these alternatives are given as follows.

In millions The cost of preparing the contract/bid proposal is $2 million. If the company does not make a bid, it will invest in an alternative venture with a guaranteed profit of $30 million. Construct a sequential decision tree for this decision situation and determine whether the company should make a bid.

Chapter 10

2. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customers will buy their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the past 8 months:

Demand for Soft Shag Month Carpet (1,000 yd.) 1 8 2 12 3 7 4 9 5 15 6 11 7 10 8 12

a. Compute a 3-month moving average forecast for months 4 through 9.

b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55, 0.33, and 0.12 to the months in sequence, starting with the most recent month.

c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate? 6. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:

Month Gasoline Demanded (gal.) October 800 November 725 December 630 January 500 February 645 March 690 April 730 May 810 June 1,200 July 980

a. Compute an exponentially smoothed forecast, using an α value of 0.30.

b. Compute the MAPD.

10-29 Infoworks is a large computer discount store that sells computers and ancillary equipment and software in the town where State University is located. Infoworks has collected historical data on computer sales and printer sales for the past 10 years, as follows:

Year Personal Computers Sales Printers Sold 1 1,045 326 2 1,610 510 3 860 296 4 1,211 478 5 975 305 6 1,117 506 7 1,066 612 8 1,310 560 9 1,517 590 10 1,246 676

1. Develop a linear trend line forecast to forecast printer demand in year 11. 2. Develop a linear regression model relating printer sales to computer sales in order to forecast printer demand in year 11 if 1,300 computers are sold. 3. Compare the forecasts developed in (a) and (b) and indicate which one appears to be more accurate. 10-31 Arrow Air is a regional East Coast airline that has collected data for the percentage available seats occupied on its fliughts for four quarters-(1) January-March, (2) April-June, (3)July-September, and (4) October-December-for the past 5 years Arrow Air also has collected data for the average percentage fare discount for each of these quarters, as follows

a. Develop a seasonally adjusted forecast model for seat occupancy. Forecast seat occupancy for year 6 by using a linear trend line forecast estimate for seat occupancy in year 6. b. Develop linear regression models relating seat occupancy to discount fares in order to forecast set occupancy for each quarter in year 6. Assume a fare discount of 20% for quarter 1, 36% for quarter 2, 25% for quarter 2, and 30% for quarter 4. c. Compare the forecasts developed in (a) and (b) and indicate which on e appears to be the best.

Sunshine House received a contract this year as a supplier of Girl Scout cookies. Sunshine currently has five production lines, each of which will be dedicated to a particular kind of cookie. The production lines differ by sophistication of machines, site, and experience of personnel. Given the following estimates of processing times (in hours), assign cookies to lines so that the order can be completed as soon as possible: Production Line

Cookies 1 2 3 4 5

Chocolate Mint 30 18 26 17 15

Peanut Butter 23 22 32 25 30

Shortbread 17 31 24 22 29

Fudge Delight 28 19 13 18 23

Macaroons 23 14 16 20 27