b. Rachel is considering leasing additional airplanes to achieve economies of scale. The leasing cost of each one again would be $30,000 per day. Perform what-if analysis to determine whether it would be worthwhile to have 5, 6, or 7 airplanes instead of 4. c. Now repeat part a under the more realistic assumption that there is a minimum turnaround time of 30 minutes on the ground for unloading and loading passengers between the arrival of a flight and the departure of the next flight by the same airplane. (Most airlines use a considerably longer turnaround time.) Does this change the number of flights that can be flown? d. Rachel now is considering having each of the four airplanes carry freight instead of flying empty if it flies overnight to another city. Instead of a cost of $5,000, this would result in net revenue of $5,000. Adapt the spreadsheet model used in part c to find the feasible combination of flights that maxi- mizes the total profit. Does this change the number of air- planes that fly overnight to another city? Case 6-3 Airline Scheduling Rachel Cook is very concerned. Until recently, she has always had the golden touch, having successfully launched two start- up companies that made her a very wealthy woman. However, the timing could not have been worse for her latest start-up- a regional airline called Northwest Commuter that operates on the west coast of the United States. All had been well at the beginning. Four airplanes had been leased and the com- pany had become fairly well established as a no-frills airline providing low-cost commuter flights between the west coast cities of Seattle, Portland, and San Francisco. Achieving fast turnaround times between flights had given Northwest Com- muter an important competitive advantage. Then the cost of jet fuel began spiraling upward and the company began going heavily into the red (like so many other airlines at the time). Although some of the flights were still profitable, others were losing a lot of money. Fortunately, jet fuel costs now are starting to come down, but it has become clear to Rachel that she needs to find new ways for Northwest Commuter to become a more efficient airline. In particular, she wants to start by dropping unprofitable flights and then identifying the most profitable combination of flights (including some new ones) for the coming year that could feasibly be flown by the four airplanes. A little over a decade ago, Rachel had been an honor gradu- ate of a leading MBA program. She had enjoyed the manage- ment science course she took then and she has decided to apply spreadsheet modeling to analyze her problem. The leasing cost for each airplane is $30,000 per day. At the end of the day, an airplane might remain in the city where it landed on its last flight. Another option is to fly empty overnight to another city to be ready to start a flight from there the next morning. The cost of this latter option is $5,000. Flight Number From To Depart Arrive Expected Revenue ($000) 1257 Seattle San Francisco 8:00 AM 10:00 AM 37 2576 Seattle Portland 9:30 AM 10:30 AM 20 8312 Seattle San Francisco 9:30 AM 11:30 AM 25 1109 Seattle San Francisco 12:00 PM 2:00 PM 27 3752 Seattle San Francisco 2:30 PM 4:30 PM 23 2498 Seattle Portland 3:00 PM 4:00 PM 18 8787 Seattle San Francisco 5:00 PM 7:00 PM 29 8423 Seattle Portland 6:30 PM 7:30 PM 27 7922 Portland Seattle 9:00 AM 10:00 AM 5623 Portland San Francisco 9:30 AM 11:00 AM 2448 Portland San Francisco 11:00 AM 12:30 PM 1842 Portland Seattle 12:00 PM 1:00 PM 21 3487 Portland Seattle 2:00 PM 3:00 PM 4361 Portland San Francisco 4:00 PM 5:30 PM 4299 Portland Seattle 6:00 PM 7:00 PM 1288 San Francisco Seattle 8:00 AM 10:00 AM 3335 San Francisco Portland 8:30 AM 10:00 AM 9348 San Francisco Seattle 10:30 AM 12:30 PM 7400 San Francisco Seattle 12:00 PM 2:00 PM 7328 San Francisco Portland 12:00 PM 1:30 PM 6386 San Francisco Portland 4:00 PM 6923 San Francisco Seattle 5:00 PM 5:30 PM 7:00 PM 222222222222 20 23 19 29 27 32 26 24 27 24 28 32 The accompanying table shows the 22 possible flights that are being considered for the coming year. The last column gives the estimated net revenue (in thousands of dollars) for each flight, given the average number of passengers anticipated for that flight. a. To simplify the analysis, assume for now that there is vir- tually no turnaround time between flights so the next flight can begin as soon as the current flight ends. (If an immediate next flight is not available, the airplane would wait until the next scheduled flight from that city.) Develop a network that displays some of the feasible routings of the flights. (Hint: Include separate nodes for each half hour between 8:00 AM and 7:30 PM in each city.) Then develop and apply the corre- sponding spreadsheet model that finds the feasible combina- tion of flights that maximizes the total profit.