Browsing by Subject "Chance constraints"

Now showing 1 - 3 of 3

Open Access
Airline scheduling to minimize operational costs and variability
(2021-08) Şimşek, Deniz
Airlines tend to design their ﬂights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling deﬁned as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the ﬂight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and ﬂeet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate ﬂight delay probabilities to calculate the airport congestion coeﬃcients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our ﬁrst objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variabilities from the average in our second objective to generate balanced schedules in terms of resilience. We follow an ε-constraint approach to scalarize and solve our problem via commercial solvers and we also devise a discretized approximation and search algorithm to solve large instances. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis. As a key contribution, we show that in the schedule generation phase, designing resilient schedules by allowing them to deviate from the minimum cost within the trade-oﬀ between the operational costs and the variability, the potential recovery costs in case of unexpected disruptions can be reduced signiﬁcantly.
Open Access
Integrated aircraft-path assignment and robust schedule design with cruise speed control
(Elsevier, 2017-08) Şafak, Ö.; Gürel, S.; Aktürk, M. S.
Assignment of aircraft types, each having different seat capacity, operational expenses and availabilities, critically affects airlines’ overall cost. In this paper, we assign fleet types to paths by considering not only flight timing and passenger demand, as commonly done in the literature, but also operational expenses, such as fuel burn and carbon emission costs associated with adjusting the cruise speed to ensure the passenger connections. In response to flight time uncertainty due to the airport congestions, we allow minor adjustments on the flight departure times in addition to cruise speed control, thereby satisfying the passenger connections at a desired service level. We model the uncertainty in flight duration via a random variable arising in chance constraints to ensure the passenger connections. Nonlinear fuel and carbon emission cost functions, chance constraints and binary aircraft assignment decisions make the problem significantly more difficult. To handle them, we use mixed-integer second order cone programming. We compare the performance of a schedule generated by the proposed model to the published schedule for a major U.S. airline. On the average, there exists a 20% overall operational cost saving compared to the published schedule. To solve the large scale problems in a reasonable time, we also develop a two-stage algorithm, which decomposes the problem into planning stages such as aircraft-path assignment and robust schedule generation, and then solves them sequentially.
Open Access
Resilient airline scheduling to minimize delay risks
(Elsevier Ltd, 2022-06-06) Şi̇mşek, D.; Aktürk, M. Seli̇m
Airlines tend to design their flights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling defined as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the flight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and fleet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate flight delay probabilities to calculate the airport congestion coefficients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our first objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variability’s from the average in our second objective to generate balanced schedules in terms of resilience. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis.