Airline Schedule Optimization (Fleet Assignment I) Saba Neyshabouri.

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Slide 2 Airline Schedule Optimization (Fleet Assignment I) Saba Neyshabouri Slide 3 Agenda Airline scheduling process Fleet Assignment problem Time-Space network concept Slide 4 Airline Schedule Single most important indicator of airlines 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 Slide 5 Airlines 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. Slide 6 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 Slide 7 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 Slide 8 Breaking Down the Problems In order to handle airlines 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 Slide 9 Fleet Assignment Problem The objective: Finding a profit maximizing assignment of aircrafts to flight legs in airlines network. Complicating factors: Satisfying passenger demand Fleet composition Fleet balance (flow balance) Other side constraints Slide 10 The Schedule Design Problem The goal is to design the airlines 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 Slide 11 Sample Flight Schedule This example for flight schedule connects only 3 markets and has 10 flights. Slide 12 Example Flight network Fleet composition Slide 13 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: Slide 14 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: Slide 15 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. Slide 16 Greedy Solution to Example Considering the most profit generating assignments, the greedy solution will be: This solution is not feasible! Slide 17 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 Slide 18 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 Slide 19 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. Slide 20 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} Slide 21 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. Slide 22 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. BOS LGA ORD 8:009:00 10:00 11:0012:00 13:00 Slide 23 Time-Space Network In our example: Not all the arcs exists. The size of the network is much bigger than the static network. BOS LGA ORD 8:009:00 10:00 11:0012:00 13:00 Slide 24 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. Slide 25 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 arcs origin node, and arrival location and arrival plus turn time represented by the arcs destination node. A ground arc: representing aircraft on the ground during the period spanned by the times associated with the arcs end nodes. Slide 26 Time-Space Network for our Example Our static network will change to another network that will capture the temporal behavior of the system: Ground arc Flight arc Slide 27 Optimal Fleet Assignment In our network, the optimal fleet assignment is shown on the following network (Flow Balance): Slide 28 Optimal Fleet Assignment In our network, the optimal fleet assignment is shown on the following network (Same location for aircrafts requirement):