a b s t r a c tWe describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based only on the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation.
Airline operations are subject to frequent disruptions typically due to unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights and increasing cruise stage speed when possible in an effort to contain the delays. However, there is a critical trade-off between fuel consumption (and its adverse impact on air quality and greenhouse gas emissions) and cruise speed. Here we consider delays caused by such disruptions and propose a flight rescheduling model that includes adjusting cruise stage speed on a set of affected and unaffected flights as well as swapping aircraft optimally. To the best of our knowledge, this is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs. The proposed model allows one to investigate the trade-off between flight delays and the cost of recovery. We show that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation. Flight time controllability, nonlinear delay, fuel burn and CO2 emission cost functions, and binary aircraft swapping decisions complicate the aircraft recovery problem significantly. In order to mitigate the computational difficulty we utilize the recent advances in conic mixed integer programming and propose a strengthened formulation so that the nonlinear mixed integer recovery optimization model can be solved efficiently. Our computational tests on realistic cases indicate that the proposed model may be used by operations controllers to manage disruptions in real time in an optimal manner instead of relying on ad-hoc heuristic approaches.
Airline schedules are generally tight and fragile to disruptions. Disruptions can have severe effects on existing aircraft routings, crew pairings, and passenger itineraries that lead to high delay and recovery costs. A recovery approach should integrate the recovery decisions for all entities (aircraft, crew, passengers) in the system as recovery decisions about an entity directly affect the others' schedules. Because of the size of airline flight networks and the requirement for quick recovery decisions, the integrated airline recovery problem is highly complex. In the past decade, an increasing effort has been made to integrate passenger and crew related recovery decisions with aircraft recovery decisions both in practice and in the literature. In this paper, we develop a new flight network based representation for the integrated airline recovery problem. Our approach is based on the flow of each aircraft, crew member, and passenger through the flight network of the airline. The proposed network structure allows common recovery decisions such as departure delays, aircraft/crew rerouting, passenger reaccommodation, ticket cancellations, and flight cancellations. Furthermore, we can implement aircraft cruise speed (flight time) decisions on the flight network. For the integrated airline recovery problem defined over this network, we propose a conic quadratic mixed integer programming formulation that can be solved in reasonable CPU times for practical size instances. Moreover, we place a special emphasis on passenger recovery. In addition to aggregation and approximation methods, our model allows explicit modeling of passengers and evaluating a more realistic measure of passenger delay costs. Finally, we propose methods based on the proposed network representation to control the problem size and to deal with large airline networks.
Robust airline schedules can be considered as flight schedules that are likely to minimize passenger delay. Airlines usually add an additional time-e.g., schedule padding-to scheduled gate-to-gate flight times to make their schedules less susceptible to variability and disruptions. There is a critical trade-off between any kind of buffer time and daily aircraft productivity. Aircraft speed control is a practical alternative to inserting idle times into schedules. In this study, block times are considered in two parts: Cruise times that are controllable and non-cruise times that are subject to uncertainty. Cruise time controllability is used together with idle time insertion to satisfy passenger connection service levels while ensuring minimum costs. To handle the nonlinearity of the cost functions, they are represented via second-order conic inequalities. The uncertainty in non-cruise times is modeled through chance constraints on passenger connection service levels, which are then expressed using second-order conic inequalities. Overall, it is shown, that a 2% increase in fuel costs cuts down 60% of idle time costs. A computational study shows that exact solutions can be obtained by commercial solvers in seconds for a single-hub schedule and in minutes for a four-hub daily schedule of a major U.S. carrier.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.