Probabilistic Airline Reserve Crew Scheduling Model

This paper introduces a probabilistic model for airline reserve crew scheduling. The model can be applied to any schedules which consist of a stream of departures from a single airport. We assume that reserve crew demand can be captured by an independent probability of crew absence for each departure. The aim of our model is to assign some fixed number of available reserve crew in such a way that the overall probability of crew unavailability in an uncertain operating environment is minimised. A comparison of different probabilistic objective functions, in terms of the most desirable simulation results, is carried out, complete with an interpretation of the results. A sample of heuristic solution methods are then tested and compared to the optimal solutions on a set of problem instances, based on the best objective function found. The current model can be applied in the early planning phase of reserve crew scheduling, when very little information is known about crew absence related disruptions. The main conclusions include the finding that the probabilistic objective function approach gives solutions whose objective values correlate strongly with the results that these solutions will get on average in repeated simulations. Minimisation of the sum of the probabilities of crew unavailability was observed to be the best surrogate objective function for reserve crew schedules that perform well in simulation. A list of extensions that could be made to the model is then provided, followed by conclusions that summarise the findings and important results obtained

Airline reserve crew scheduling under uncertainty

This thesis addresses the problem of airline reserve crew scheduling under crew absence and journey time uncertainty. This work is primarily concerned with the allocation of reserve crew to standby duty periods. The times at which reserve crew are on duty, determine which possible crew absence or delay disruptions they can be used to absorb. When scheduling reserve crew, the goal is to minimise the expected levels of delay and cancellation disruptions that occur on the day of operation. This work introduces detailed probabilistic models of the occurrence of crew absence and delay disruptions and how reserve crew are used to absorb such disruptions. Firstly, separate probabilistic models are developed for crew absence and delay disruptions. Then, an integrated probabilistic model of absence and delay disruptions is introduced, which accounts for: delays from all causes; delay propagation; cancellations resulting from excessive delays and crew absence; the use of reserve crew to cover such disruptions given a reserve policy; and the possibility of swap recovery actions as an alternative delay recovery action. The model yields delay and cancellation predictions that match those derived from simulation to a high level of accuracy and does so in a fraction of the time required by simulation. The various probabilistic models are used in various search methodologies to find disruption minimising reserve crew schedules. The results show that high quality reserve crew schedules can be derived using a probabilistic model. A scenario-based mixed integer programming approach to modelling operational uncertainty and reserve crew use is also developed in this thesis and applied to the problem of reserve crew scheduling. A scenario selection heuristic is introduced which improves reserve crew schedule quality using fewer input scenarios. The secondary objective of this thesis is to investigate the effect of the reserve policy used on the day of operation, that is, determining when and which reserve crew should be utilised. The questions of how reserve policies can be improved and how they should be taken into account when scheduling reserve crew are addressed. It was found that the approaches developed for reserve crew scheduling lend themselves well to an online application, that is, using them to evaluate alternative reserve decisions to ensure reserve crew are used as effectively as possible. In general it is shown that `day of operation' disruptions can be significantly reduced through both improved reserve crew schedules and/or reserve policies. This thesis also points the way towards future research based on the proposed approaches

Scheduling airline reserve crew using a probabilistic crew absence and recovery model

Airlines require reserve crew to replace delayed or absent crew, with the aim of preventing consequent flight cancellations. A reserve crew schedule specifies the duty periods for which different reserve crew will be on standby to replace any absent crew. For both legal and health-and-safety reasons the reserve crew's duty period is limited, so it is vital that these reserve crew are available at the right times, when they are most likely to be needed and will be most effective. Scheduling a reserve crew unnecessarily, or earlier than needed, wastes reserve crew capacity. Scheduling a reserve crew too late means either an unrecoverable cancellation or a delay waiting for the reserve crew to be available. Determining when to schedule these crew can be a complex problem , since one crew member could potentially cover a vacancy on any one of a number of different flights, and flights interact with each other, so a delay or cancellation for one flight can affect a number of later flights. This work develops an enhanced mathematical model for assessing the impact of any given reserve crew schedule, in terms of reduced total expected cancellations and any resultant reserve induced delays, whilst taking all of the available information into account, including the schedule structure and interactions between flights, the uncertainties involved, and the potential for multiple crew absences on a single flight. The interactions between flights have traditionally made it very hard to predict the effects of cancellations or delays, and hence to predict when best to allocate reserve crew and lengthy simulation runs have traditionally been used to make these predictions. This work is motivated by the airline industry's need for improved mathematical models to replace the time-consuming simulation-based approaches. The improved predictive probabilistic model which is introduced here is shown to produce results that match a simulation model to a high degree of accuracy, in a much shorter time, making it an effective and accurate surrogate for simulation. The modelling of the problem also provides insights into the complexity of the problem that a purely simulation based approach would miss. The increased speed enables potential deployment within a real time decision support context, comparing alternative recovery decisions as disruptions occur. To illustrate this, the model is used in this paper as a fitness function in meta-heuristics algorithms to generate disruption minimising reserve crew schedules for a real airline schedule. These are shown to be of a high quality, demonstrating the effectiveness and reliability of the proposed approach

Airline reserve crew scheduling under uncertainty

This thesis addresses the problem of airline reserve crew scheduling under crew absence and journey time uncertainty. This work is primarily concerned with the allocation of reserve crew to standby duty periods. The times at which reserve crew are on duty, determine which possible crew absence or delay disruptions they can be used to absorb. When scheduling reserve crew, the goal is to minimise the expected levels of delay and cancellation disruptions that occur on the day of operation. This work introduces detailed probabilistic models of the occurrence of crew absence and delay disruptions and how reserve crew are used to absorb such disruptions. Firstly, separate probabilistic models are developed for crew absence and delay disruptions. Then, an integrated probabilistic model of absence and delay disruptions is introduced, which accounts for: delays from all causes; delay propagation; cancellations resulting from excessive delays and crew absence; the use of reserve crew to cover such disruptions given a reserve policy; and the possibility of swap recovery actions as an alternative delay recovery action. The model yields delay and cancellation predictions that match those derived from simulation to a high level of accuracy and does so in a fraction of the time required by simulation. The various probabilistic models are used in various search methodologies to find disruption minimising reserve crew schedules. The results show that high quality reserve crew schedules can be derived using a probabilistic model. A scenario-based mixed integer programming approach to modelling operational uncertainty and reserve crew use is also developed in this thesis and applied to the problem of reserve crew scheduling. A scenario selection heuristic is introduced which improves reserve crew schedule quality using fewer input scenarios. The secondary objective of this thesis is to investigate the effect of the reserve policy used on the day of operation, that is, determining when and which reserve crew should be utilised. The questions of how reserve policies can be improved and how they should be taken into account when scheduling reserve crew are addressed. It was found that the approaches developed for reserve crew scheduling lend themselves well to an online application, that is, using them to evaluate alternative reserve decisions to ensure reserve crew are used as effectively as possible. In general it is shown that `day of operation' disruptions can be significantly reduced through both improved reserve crew schedules and/or reserve policies. This thesis also points the way towards future research based on the proposed approaches

A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

The environment in which airlines operate is uncertain for many reasons, for example due to the effects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence uncertainty and delay for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. This work proposes a mixed integer programming approach to scheduling the airline’s reserve crew. A simulation of the airline’s operations with stochastic journey time and crew absence inputs (without reserve crew) is used to generate input disruption scenarios for the mixed integer programming simulation scenario model (MIPSSM) formulation. Each disruption scenario corresponds to a record of all of the disruptions that may occur on the day of operation which are solvable by using reserve crew. A set of disruption scenarios form the input of the MIPSSM formulation, which has the objective of finding the reserve crew schedule that minimises the overall level of disruption over the set of input scenarios. Additionally, modifications of the MIPSSM are explored, a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as the quantity of disruption scenarios that are added to the MIPSSM. An investigation into what makes a good set of scenarios is also presented

A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

Airlines operate in an uncertain environment for many reasons, for example due to the efects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence and journey time uncertainty for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. Given an airline's crew schedule and aircraft routings we propose a Mixed Integer Programming approach to scheduling the airline's reserve crew. A simulation of the airline's operations with stochastic journey time and crew absence inputs and without reserve crew is used to generate disruption scenarios for the MIPSSM formulation (Mixed Integer Programming Simulation Scenario Model). Each disruption scenario corresponds to a record of all of the disruptions in a simulation for which reserve crew use would have been beneficial. For each disruption in a disruption scenario there is a record of all reserve crew that could have been used to solve or reduce the disruption. This information forms the input to the MIPSSM formulation, which has the objective of finding the reserve schedule that minimises the overall level of disruption over a set of scenarios. Additionally, modifications of the MIPSSM are explored, and a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed Mixed Integer Programming Simulation Scenario Model or MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as ensuring that enough disruption scenarios are added to the MIPSSM

A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

Airlines operate in an uncertain environment for many reasons, for example due to the efects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence and journey time uncertainty for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. Given an airline's crew schedule and aircraft routings we propose a Mixed Integer Programming approach to scheduling the airline's reserve crew. A simulation of the airline's operations with stochastic journey time and crew absence inputs and without reserve crew is used to generate disruption scenarios for the MIPSSM formulation (Mixed Integer Programming Simulation Scenario Model). Each disruption scenario corresponds to a record of all of the disruptions in a simulation for which reserve crew use would have been beneficial. For each disruption in a disruption scenario there is a record of all reserve crew that could have been used to solve or reduce the disruption. This information forms the input to the MIPSSM formulation, which has the objective of finding the reserve schedule that minimises the overall level of disruption over a set of scenarios. Additionally, modifications of the MIPSSM are explored, and a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed Mixed Integer Programming Simulation Scenario Model or MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as ensuring that enough disruption scenarios are added to the MIPSSM

FLIGHT RISK MANAGEMENT AND CREW RESERVE OPTIMIZATION

There are two key concerns in the development process of aviation. One is safety, and the other is cost. An airline running with high safety and low cost must be the most competitive one in the market. This work investigates two research efforts respectively relevant to these two concerns. When building support of a real time Flight Risk Assessment and Mitigation System (FRAMS), a sequential multi-stage approach is developed. The whole risk management process is considered in order to improve the safety of each flight by integrating AHP and FTA technique to describe the framework of all levels of risks through risk score. Unlike traditional fault tree analysis, severity level, time level and synergy effect are taken into account when calculating the risk score for each flight. A risk tree is designed for risk data with flat shape structure and a time sensitive optimization model is developed to support decision making of how to mitigate risk with as little cost as possible. A case study is solved in reasonable time to approve that the model is practical for the real time system. On the other hand, an intense competitive environment makes cost controlling more and more important for airlines. An integrated approach is developed for improving the efficiency of reserve crew scheduling which can contribute to decrease cost. Unlike the other technique, this approach integrates the demand forecasting, reserve pattern generation and optimization. A reserve forecasting tool is developed based on a large data base. The expected value of each type of dropped trip is the output of this tool based on the predicted dropping rate and the total scheduled trips. The rounding step in current applied methods is avoided to keep as much information as possible. The forecasting stage is extended to the optimization stage through the input of these expected values. A novel optimization model with column generation algorithm is developed to generate patterns to cover these expected level reserve demands with minimization to the total cost. The many-to-many covering mode makes the model avoid the influence of forecasting errors caused by high uncertainty as much as possible

airline revenue management

With the increasing interest in decision support systems and the continuous advance of computer science, revenue management is a discipline which has received a great deal of interest in recent years. Although revenue management has seen many new applications throughout the years, the main focus of research continues to be the airline industry. Ever since Littlewood (1972) first proposed a solution method for the airline revenue management problem, a variety of solution methods have been introduced. In this paper we will give an overview of the solution methods presented throughout the literature.revenue management;seat inventory control;OR techniques;mathematical programming

Reliable Reserve-Crew Scheduling for Airlines

We study the practical setting in which regular- and reserve-crew schedules are dynamically maintained up to the day of executing the schedule. At each day preceding the execution of the schedule, disruptions occur due to sudden unavailability of personnel, making the planned regular and reserve-crew schedules infeasible for its execution day. This paper studies the fundamental question how to repair the schedules' infeasibility in the days preceding the execution, taking into account labor regulations. We propose a robust repair strategy that maintains flexibility in order to cope with additional future disruptions. The flexibility in reserve-crew usage is explicitly considered through evaluating the expected shortfall of the reserve-crew schedule based on a Markov chain formulation. The core of our approach relies on iteratively solving a set-covering formulation, which we call the Robust Crew Recovery Problem, which encapsulates this flexibility notion for reserve crew usage. A tailored branch-and-price algorithm is developed for solving the Robust Crew Recovery Problem to optimality. The corresponding pricing problem is efficiently solved by a newly developed pulse algorithm. Based on actual data from a medium-sized hub-and-spoke airline, we show that embracing our approach leads to fewer flight cancellations and fewer last-minute alterations, compared to repairing disrupted schedules without considering our robust measure