You will discuss the followings during the 10-minute presentation: Introduction/Motivation/Problem Definition o What is it that you are trying to solve/achieve and why does it matte

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Case 6-3 Airline Scheduling 229

exist, what method should Jake use to convert the Asian holdings from the respective currencies into dollars?

d. In response to the World Trade Organization’s mandate forbidding transaction limits, the Indonesian government introduces a new tax to protect its currency that leads to a 500 percent increase in transaction costs for transactions of rupiahs. Given these new transaction costs but no transaction

limits, what currency transactions should Jake perform to convert the Asian holdings from the respective currencies into dollars?

e. Jake realizes that his analysis is incomplete because he has not included all aspects that might influence his planned currency exchanges. Describe other factors that Jake should examine before he makes his final decision.

Case 6-3

Airline Scheduling Richard Cook is very concerned. Until recently, he has always had the golden touch, having successfully launched two start- up companies that made him a very wealthy man. However, the timing could not have been worse for his 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 company had become fairly well established as a no-frills airline provid- ing low-cost commuter flights between the west coast cities of

(including some new ones) for the coming year that could feasi- bly be flown by the four airplanes.

A little over a decade ago, Richard had been an honor gradu- ate of a leading MBA program. He had enjoyed the management science course he took then and he has decided to apply spread- sheet modeling to analyze his 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

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 20 5623 Portland San Francisco 9:30 AM 11:00 AM 23 2448 Portland San Francisco 11:00 AM 12:30 PM 19 1842 Portland Seattle 12:00 PM 1:00 PM 21 3487 Portland Seattle 2:00 PM 3:00 PM 22 4361 Portland San Francisco 4:00 PM 5:30 PM 29 4299 Portland Seattle 6:00 PM 7:00 PM 27 1288 San Francisco Seattle 8:00 AM 10:00 AM 32 3335 San Francisco Portland 8:30 AM 10:00 AM 26 9348 San Francisco Seattle 10:30 AM 12:30 PM 24 7400 San Francisco Seattle 12:00 PM 2:00 PM 27 7328 San Francisco Portland 12:00 PM 1:30 PM 24 6386 San Francisco Portland 4:00 PM 5:30 PM 28 6923 San Francisco Seattle 5:00 PM 7:00 PM 32

Seattle, Portland, and San Francisco. Achieving fast turnaround times between flights had given Northwest Commuter an impor- tant competitive advantage. Then the cost of jet fuel began spi- raling 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 Richard that he needs to find new ways for Northwest Commuter to become a more efficient airline. In particular, he wants to start by dropping unprofitable flights and then identifying the most profitable combination of flights

to another city to be ready to start a flight from there the next morning. The cost of this latter option is $5,000.

The table above shows the 22 possible flights that are being considered for the coming year. The last column gives the esti- mated 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

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230 Chapter Six Network Optimization Problems

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 !" and 7:30 #" 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.

b. Richard 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 turn- around time.) Does this change the number of flights that can be flown?

d. Richard 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 6-4

Broadcasting the Olympic Games The management of the WBC television network has been celebrating for days. What a coup! After several unsuccessful attempts in recent decades, they finally have hit the big jackpot. They have won the bidding war to gain the rights to broadcast the next Summer Olympic Games!

The price was enormous. However, the advertising income also will be huge. Even if the network loses some money in the process, the gain in prestige should make it all worthwhile. After all, the entire world follows these games closely every four years. Now the entire world receiving the feed of the broadcast from the WBC network will learn what a preeminent network it is.

each link in the network is shown in the diagram below (in GB/s). WBC can divide the transmission and route it through multiple paths of the network from A to G, so long as the total bandwidth required on each link does not exceed the capacity of that link.

a. By utilizing the entire computer network, what is the maxi- mum bandwidth available (in GB/s) for transmission from the general site of the Olympic Games (node A) to the home studios (node G)? Set up and solve a linear programming spreadsheet model.

A

B

C

D

E

F

G

12

9

7

5

10

9

8

13

6 3

4

6

However, reality also is setting in for WBC management. Telecasting the entire Olympic Games will be an enormously complex task. Many different sporting events will be occurring simultaneously in far-flung venues. An unprecedented amount of live television and live-on-the-Internet coverage of the vari- ous sporting events needs to be planned.

Due to the high amount of bandwidth that will be required to transmit the coverage of the games back to its home studios, WBC needs to upgrade its computer network. It operates a pri- vate computer network as shown in the network diagram in the right-hand column. The games will be held near node A. WBC’s home studios are located at node G. At peak times, coverage of the games will require 35 GB/s (GB per second) to be sent through the network from node A to node G. The capacity of

b. WBC would like to expand the capacity of the network so it can handle the peak requirement of 35 GB/s from the Olym- pics site (A) to the home studios (G). WBC can increase the capacity of each link of the computer network by install- ing additional fiber optic cables. The table on the next page shows the existing capacity of each network segment (in GB/s), the maximum additional capacity that can be added (in GB/s), and the cost to increase the capacity (in millions of dollars per unit GB/s added). Make a copy of the spreadsheet model used to solve part a and make any revisions necessary to solve this new problem.

Note: This case will be continued in the next chapter (Case 7-4), so we suggest that you save your spreadsheet model from part b.

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Case 6-3 a&b