JB
J. Bom
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Robust Tail Assignment
Incorporating Delay Predictions into a Tail Assignment Model to Decrease Flight Operation Costs
In this thesis a novel model is proposed to solve the Robust Tail Assignment problem. The Robust Tail Assignment problem aims to assign aircraft to flights, while minimize expected costs of operating a flight schedule, including expected delay costs. This problem is difficult, because delays can propagate between successive flights in the schedule, creating dependencies between flights assigned to the same aircraft.
Using probability distributions of delay for every individual flight, as well as expected costs associated with delaying flights, the expected delay costs of a full flight schedule can be estimated. The workings of a simulator are described, which can be used to evaluate the total expected costs of solution schedules for the Robust Tail Assignment problem.
To be able to incorporate expected delay costs in a mathematical model, the construction of a multi-commodity flow network is described, which uses departure and arrival states for flight rotations, corresponding to discrete amounts of delay. The amount of flow through edges of this network represents the probability of these states transitioning into other states. By activating and deactivating edges, based on the assignment of aircraft to rotations, this network can be used in a model to approximate the total expected delay costs of a model solution.
The proposed robust flow model uses such a state network in a MIP model, that can be solved using an iterative solver to find good solutions to the Robust Tail Assignment problem. Delay costs are imposed on edges in the network, to quantify the expected delay costs. In the model, the network size is reduced by only considering connections between rotations that have high probabilities of propagating delay. This reduces the accuracy of the model, but shortens the run-time of the optimization process significantly.
Several experiments are done to test the run-time and performance of the robust flow model. The model proved hard to solve to optimality, but is able to find good solutions, if the model parameters are well tuned. Recommendations are given for using the model, as well as future research directions. ...
Using probability distributions of delay for every individual flight, as well as expected costs associated with delaying flights, the expected delay costs of a full flight schedule can be estimated. The workings of a simulator are described, which can be used to evaluate the total expected costs of solution schedules for the Robust Tail Assignment problem.
To be able to incorporate expected delay costs in a mathematical model, the construction of a multi-commodity flow network is described, which uses departure and arrival states for flight rotations, corresponding to discrete amounts of delay. The amount of flow through edges of this network represents the probability of these states transitioning into other states. By activating and deactivating edges, based on the assignment of aircraft to rotations, this network can be used in a model to approximate the total expected delay costs of a model solution.
The proposed robust flow model uses such a state network in a MIP model, that can be solved using an iterative solver to find good solutions to the Robust Tail Assignment problem. Delay costs are imposed on edges in the network, to quantify the expected delay costs. In the model, the network size is reduced by only considering connections between rotations that have high probabilities of propagating delay. This reduces the accuracy of the model, but shortens the run-time of the optimization process significantly.
Several experiments are done to test the run-time and performance of the robust flow model. The model proved hard to solve to optimality, but is able to find good solutions, if the model parameters are well tuned. Recommendations are given for using the model, as well as future research directions. ...
In this thesis a novel model is proposed to solve the Robust Tail Assignment problem. The Robust Tail Assignment problem aims to assign aircraft to flights, while minimize expected costs of operating a flight schedule, including expected delay costs. This problem is difficult, because delays can propagate between successive flights in the schedule, creating dependencies between flights assigned to the same aircraft.
Using probability distributions of delay for every individual flight, as well as expected costs associated with delaying flights, the expected delay costs of a full flight schedule can be estimated. The workings of a simulator are described, which can be used to evaluate the total expected costs of solution schedules for the Robust Tail Assignment problem.
To be able to incorporate expected delay costs in a mathematical model, the construction of a multi-commodity flow network is described, which uses departure and arrival states for flight rotations, corresponding to discrete amounts of delay. The amount of flow through edges of this network represents the probability of these states transitioning into other states. By activating and deactivating edges, based on the assignment of aircraft to rotations, this network can be used in a model to approximate the total expected delay costs of a model solution.
The proposed robust flow model uses such a state network in a MIP model, that can be solved using an iterative solver to find good solutions to the Robust Tail Assignment problem. Delay costs are imposed on edges in the network, to quantify the expected delay costs. In the model, the network size is reduced by only considering connections between rotations that have high probabilities of propagating delay. This reduces the accuracy of the model, but shortens the run-time of the optimization process significantly.
Several experiments are done to test the run-time and performance of the robust flow model. The model proved hard to solve to optimality, but is able to find good solutions, if the model parameters are well tuned. Recommendations are given for using the model, as well as future research directions.
Using probability distributions of delay for every individual flight, as well as expected costs associated with delaying flights, the expected delay costs of a full flight schedule can be estimated. The workings of a simulator are described, which can be used to evaluate the total expected costs of solution schedules for the Robust Tail Assignment problem.
To be able to incorporate expected delay costs in a mathematical model, the construction of a multi-commodity flow network is described, which uses departure and arrival states for flight rotations, corresponding to discrete amounts of delay. The amount of flow through edges of this network represents the probability of these states transitioning into other states. By activating and deactivating edges, based on the assignment of aircraft to rotations, this network can be used in a model to approximate the total expected delay costs of a model solution.
The proposed robust flow model uses such a state network in a MIP model, that can be solved using an iterative solver to find good solutions to the Robust Tail Assignment problem. Delay costs are imposed on edges in the network, to quantify the expected delay costs. In the model, the network size is reduced by only considering connections between rotations that have high probabilities of propagating delay. This reduces the accuracy of the model, but shortens the run-time of the optimization process significantly.
Several experiments are done to test the run-time and performance of the robust flow model. The model proved hard to solve to optimality, but is able to find good solutions, if the model parameters are well tuned. Recommendations are given for using the model, as well as future research directions.
Binary erasure-repairing codes protect information stored on multiple servers by adding parity servers. A characteristic of a code is its cooperative locality; a measure of the amount of servers that need to be accessed to repair erased servers. This report discusses the cooperative locality of Hamming codes and shortened Hamming codes, using the row space of parity-check matrices of these codes. In some cases, an equality for this locality is found, in other cases a bound is given.
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Binary erasure-repairing codes protect information stored on multiple servers by adding parity servers. A characteristic of a code is its cooperative locality; a measure of the amount of servers that need to be accessed to repair erased servers. This report discusses the cooperative locality of Hamming codes and shortened Hamming codes, using the row space of parity-check matrices of these codes. In some cases, an equality for this locality is found, in other cases a bound is given.