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Airline Schedule Optimization (Fleet Assignment I) Saba Neyshabouri

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

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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

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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.

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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

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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

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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

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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

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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

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

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Example Flight network Fleet composition

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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:

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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:

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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.

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

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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

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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

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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.

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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}

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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.

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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

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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

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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.

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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.

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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

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

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

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