Answered step-by-stepA regional airline, Northwest Commuter, has started operating on...
A regional airline, Northwest Commuter, has started operating on the west coast of the United States. It has become established as a no-frills airline providing low-cost commuter flights between the west coast cities of Seattle, Portland, and San Francisco. The company has been able to achieve fast turnaround times between flights, but in order to further keep the costs low, the management needs to find new ways for Northwest Commuter to become a more efficient airline. In particular, management wants to start by dropping unprofitable flights and then identifying the most profitable flights.
Imagine that any number of airplanes desired can be leased for now. The leasing and operating costs for each airplane is $30,000 per day, that is incurred (accounted) at 12 midnight every day. At the end of the day, an airplane might remain in the city where it landed on its last flight which does not have any additional daily operating cost (on top of $30,000). 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 an additional $5,000.
The following table shows the 22 possible flights that are being considered for the coming year. The last column gives the estimated net revenue (with the unit of thousands of dollars) for each flight, given the average number of passengers anticipated for that flight. To simplify the analysis, assume for now that there is virtually no turnaround time between flights so the next flight can begin as soon as the current flight ends. Also, if an immediate next flight is not available, the airplane would wait in the airport until the next scheduled flight from that city.
Flight # | From | To | Depart | Arrive | Expected Revenue ($1000's) |
1257 | Seattle | San Francisco | 8 AM | 10 AM | 37 |
2576 | Seattle | Portland | 10 AM | 11 AM | 20 |
8312 | Seattle | San Francisco | 10 AM | 12 PM | 25 |
1109 | Seattle | San Francisco | 12 PM | 2 PM | 27 |
3752 | Seattle | San Francisco | 3 PM | 5 PM | 23 |
2498 | Seattle | Portland | 3 PM | 4 PM | 18 |
8787 | Seattle | San Francisco | 5 PM | 7 PM | 29 |
8423 | Seattle | Portland | 7 PM | 8 PM | 27 |
7922 | Portland | Seattle | 9 AM | 10 AM | 20 |
5623 | Portland | San Francisco | 10 AM | 12 PM | 23 |
2448 | Portland | San Francisco | 11 AM | 1 PM | 19 |
1842 | Portland | Seattle | 12 PM | 1 PM | 21 |
3487 | Portland | Seattle | 2 PM | 3 PM | 22 |
4361 | Portland | San Francisco | 4 PM | 6 PM | 29 |
4299 | Portland | Seattle | 6 PM | 7 PM | 27 |
1288 | San Francisco | Seattle | 8 AM | 10 AM | 32 |
3335 | San Francisco | Portland | 9 AM | 10 AM | 26 |
9348 | San Francisco | Seattle | 11 AM | 1 PM | 24 |
7400 | San Francisco | Seattle | 12 PM | 2 PM | 27 |
7328 | San Francisco | Portland | 12 PM | 2 PM | 24 |
6386 | San Francisco | Portland | 4 PM | 6 PM | 28 |
6923 | San Francisco | Seattle | 5 PM | 7 PM | 32 |
Flag question: Spacer
Management developed a network associated with the above flight list that displays the feasible routings of the flights, that is "partially" shown below. There are separate nodes for each combination of city and each hour between 8am to 8pm. The forward cross arcs represent the flight options according to the above table, and the forward horizontal arcs show the option of a plane staying in the same city for the next hour at each point in time. The backward arcs from 8pm to 8am represent the case that airplane remains in the same airport until the next day or fly empty overnight to another city to prepare for the next day.
You are asked to assist in developing a network model that finds the best combination of flights that maximizes the total profit.
In the process of model setup, note the following:
- Since the airplanes are circulating only in the above network, the net-flows of all nodes is 0 (there is no airplane entering from outside the network or exiting the network).
- Each flight as scheduled in the above table cannot be operated by more than one airplane simultaneously.
- Airline is attempting to maximize profit
For now, assume that there is no limit on the number of airplanes that is leased, and the airline can lease any number of airplanes it would like.
Flag question: Question 1Question 11 pts
Which of the following best represents the type of this network problem?
Group of answer choices
General network problem
Inventory management problem
Shortest path problem
Flag question: Question 2Question 21 pts
What type of node is the node "SEA 10AM"?
Group of answer choices
Transshipment node
Supply node
Demand node
Dummy node
Flag question: Question 3Question 31 pts
What is the profit for the flow of one plane along the arc "SEA 10AM" to "POR 11AM"? (enter in the unit of thousands of dollars)
Flag question: Question 4Question 41 pts
What should be the capacity of the flow along the arc "SEA 10AM" to "POR 11AM"? If it can be any large number, enter 1000.
Flag question: Question 5Question 51 pts
What is the profit for the flow of one plane along the arc "SFO 8PM" to "POR 8AM"? (enter in the unit of thousands of dollars)
Flag question: Question 6Question 61 pts
What should be the capacity of the flow along the arc "SFO 8PM" to "POR 8AM"? If it can be any large number, enter 1000.
Flag question: Question 7Question 71 pts
Now solve the problem as a network problem. What is the optimal profit the firm can obtain? (enter in the unit of thousands of dollars)
Flag question: Question 8Question 81 pts
Which of the following flights end up to be unscheduled?
Group of answer choices
SEA 8AM --> SFO 10AM
SFO 11AM --> SEA 1PM
POR 12PM --> SEA 1PM
SFO 5PM --> SEA 7PM
Flag question: Question 9Question 91 pts
How many flights are optimally scheduled?
Flag question: Question 10Question 101 pts
How many airplanes turn out to be optimally used?
Flag question: Question 11Question 111 pts
Now, add the limitation that the airline has only 3 planes on lease right now. What would be the new optimal profit? (enter in the unit of thousands of dollars)
Flag question: Question 12Question 121 pts
Bonus question: Now going back to question 7, consider the more realistic assumption that there is a minimum turnaround time of 1 hour on the ground for unloading and cleaning each airplane before it is ready to fly for another flight. Assume that each of the three airports in the three cities can provide services to the airplanes by 9pm if needed, as the unloading for flights that arrive at 8pm might take one more hour. What is now the optimal number of airplanes that need to be leased?
[You would not see the bonus point applied right after the deadline, but it would be added later.]
Answer & Explanation
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