Airline Schedule Optimization (Fleet Assignment I)

1. Airline Schedule Optimization (Fleet Assignment I) Saba Neyshabouri

2. Agenda • Airline scheduling process • Fleet Assignment problem • Time-Space network concept

3. Airline Schedule • Single most important indicator of airline’s business strategy. • Markets to be served • Level of service • There are many restrictions that makes the planning very difficult: • Gates and slots • Operational restrictions • Airport Restrictions • Location of the crew and maintenance plans

4. Airline’s Goals • Airlines are operating in a competitive market. • The ultimate goal of airlines is maximizing the profit. • There can be some other goals that will lead to profit such as: • Operational goals • Marketing goals • Strategic goals • Airlines are trying to find the best (in terms of profit) schedules that are consistent with their other goals.

5. Airlines and Decision making • Decision making process in airline industry is a very complicated process due to: • Numerous airport location with different restrictions • Different aircraft types with different operational characteristics • Crew scheduling and regulations • Large number of O/D routes and markets

6. Complicating Factors in Decision making • In modeling and solving optimization problems in airline industry, 2 major complicating factor are known: • The huge size of the problem • Inherent uncertainty of the system

7. Breaking Down the Problems • In order to handle airline’s operational problems, it has been broken down to several hierarchical problems: • The schedule design problem • The fleet assignment problem • The maintenance routing problem • The crew scheduling problem

8. Fleet Assignment Problem • The objective: • Finding a profit maximizing assignment of aircrafts to flight legs in airline’s network. • Complicating factors: • Satisfying passenger demand • Fleet composition • Fleet balance (flow balance) • Other side constraints

9. The Schedule Design Problem • The goal is to design the airline’s flights schedule specifically: • Flight legs to be operated by airline • Scheduled departure times • Estimated scheduled arrivals • Frequency plan and the days that on which flight leg is operated

10. Sample Flight Schedule • This example for flight schedule connects only 3 markets and has 10 flights.

11. Example • Flight network • Fleet composition

12. Example • Given this example the goal is to find a profit-maximizing assignment of fleet types to flight legs in a way such that: • Not more than available number of aircrafts are used • Balance of aircrafts at each location is maintained • The objective function tries to maximize the profit therefore the profit of assigning a fleet type to a flight leg should be calculated:

13. Profit Calculation • After doing the calculation for each possible assignment, the resulting profit for each assignment of fleet type to flight leg is summarized in the following table:

14. Greedy Solution • Greedy methods: heuristic method to find a solution to a complicated problem which reduces the time of computation however it is not guaranteed to be optimal or even feasible. • The main idea of a greedy algorithm is to be greedy in each step of decision making! • Being greedy is like not considering long-term effects of decisions. • Being greedy in some cases might not even provide any feasible solution.

15. Greedy Solution to Example • Considering the most profit generating assignments, the greedy solution will be: • This solution is not feasible!

16. Greedy Solution to Example • This solution is not feasible! • The aircraft balance is not achieved. • Using a network of distances (static network) makes it difficult to determine the number of necessary aircrafts to fly for each day of operations

17. Time-Space Networks • In many problems in optimization, time is playing an important role in the model. • However having time as a changing parameter in the model, usually increases the complexity of the problem in hand. • Example of the problems that deal with time related constraints: • Job shop scheduling- Minimizing tardiness • Vehicle routing problem with time windows • Flow shop scheduling problems with job availability constraints

18. Time-Space Network • Decisions that are needed to be made at different times require adding variables that keeps track of time. • Time is a continuous variable! • Adding a continuous variable to an IP problem makes the problem even more complicated to solve. • There has to be an smart way to deal with time in our models.

19. Time-Space Network Concept • Graph G=(N,E) is made of set of nodes (N) and set edges (E) • N: usually represents the locations • E: usually represents the arcs (connections/roads) between two locations • N={ORD,BOS,LGA} • E={CL50x,CL55x,CL30x,CL33x}

20. Time-Space Network • As it can be seen in the graph, there is no indication of the times of flights: • However in managing the flights, keeping track of time is important since one aircraft can fly multiple legs.

21. Sample Time-Space Network • In general, in time-space networks, each node represents a location in a specific time (of the day/month/year). • Arcs are moving between two locations considering the time it takes for that movement. ORD LGA BOS 10:00 8:00 9:00 11:00 12:00 13:00

22. Time-Space Network • In our example: • Not all the arcs exists. • The size of the network is much bigger than the static network. ORD LGA BOS 10:00 8:00 9:00 11:00 12:00 13:00

23. Time-Space Networks: Pros & Cons • Time-space networks are used so the optimization problem does not become a mixed-integer programming (MIP) which are generally more difficult to handle. • Using time-space networks, may cause the problem to transform into one of the well-known network problems which can be handled efficiently. • Using time space network will cause the size of the problem to grow very fast • N= Number of locations * Number of time windows (or significant times for each node) • E= Every possible movements between 2 locations throughout the day.

24. Time-Space Network for our Example • In our example: a time-space flight network is an expansion of the static flight network in which each node represents both a location and a point in time. • In this network, two different arcs are possible: • A flight arc: representing a flight leg with departure location and time represented by the arc’s origin node, and arrival location and arrival plus turn time represented by the arc’s destination node. • A ground arc: representing aircraft on the ground during the period spanned by the times associated with the arc’s end nodes.

25. Time-Space Network for our Example • Our static network will change to another network that will capture the temporal behavior of the system: Flight arc Ground arc

26. Optimal Fleet Assignment • In our network, the optimal fleet assignment is shown on the following network (Flow Balance):

27. Optimal Fleet Assignment • In our network, the optimal fleet assignment is shown on the following network (Same location for aircrafts requirement):