Solving a robust airline crew pairing problem with column generation

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness in this case is related to the ability of accommodating these extra flights at the time of operation by disrupting the original plans as minimally as possible. We focus on the crew pairing aspect of robustness and prescribe that the planned crew pairings incorporate a number of predefined recovery solutions for each potential extra flight. These solutions are implemented only if necessary for recovery purposes and involve either inserting an extra flight into an existing pairing or partially swapping the flights in two existing pairings in order to cover an extra flight. The resulting mathematical programming model follows the conventional set covering formulation of the airline crew pairing problem typically solved by column generation with an additional complication. The model includes constraints that depend on the columns due to the robustness consideration and grows not only column-wise but also row-wise as new columns are generated. To solve this dicult model, we propose a row and column generation approach. This approach requires a set of modifications to the multi-label shortest path problem for pricing out new columns (pairings) and various mechanisms to handle the simultaneous increase in the number of rows and columns in the restricted master problem during column generation. We conduct computational experiments on a set of real instances compiled from a local airline in Turkey

Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows

In this paper, we develop a simultaneous column-and-row generation algorithm that could be applied to a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on-the-fly within an efficient solution approach. We emphasize that the generated rows are structural constraints and distinguish our work from the branch-and-cut-and-price framework. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm. These assumptions are general enough and cover all problems with column-dependent-rows studied in the literature up until now to the best of our knowledge. We then introduce in detail a set of pricing subproblems, which are used within the proposed column-and-row generation algorithm. This is followed by a formal discussion on the optimality of the algorithm. To illustrate the proposed approach, the paper is concluded by applying the proposed framework to the multi-stage cutting stock and the quadratic set covering problems

Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows

In this paper, we develop a simultaneous column-and-row generation algorithm for a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints. These constraints are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on the fly within an efficient solution method. We emphasize that the generated rows are structural constraints and distinguish our work from the branch-and-cut-and-price framework. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm and then introduce the associated set of pricing subproblems in detail. The proposed methodology is demonstrated on numerical examples for the multi-stage cutting stock and the quadratic set covering problems

A multi-agent system for a bus crew rescheduling system

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Unpredictable events (UE) are major factors that cause disruption to everyday bus operation. In the occurrence of UE, the main resources - crews and vehicles - are affected, and this leads to crew schedule disruption. One way to deal with the problem is crew rescheduling. Most of the current approaches are based on static schedules do not support rescheduling in a real-time scenario. They have the ability to reschedule but a new complete schedule is produced without concerning the real time situation. The mathematical approaches which are used by most scheduling packages have the ability to search for optimum or near optimum schedules but they are usually slow to produce results in real-time because they are computationally intensive when faced with complex situations. In practice, crew or bus rescheduling is managed manually, based on the supervisor's capabilities and experience in managing UE. However, manual rescheduling is complex, prone to error and not optimum, especially when dealing with many UE at the same time. This research proposes the CRSMAS (Crew Rescheduling System with Multi Agent System) approach as an alternative that may help supervisors to make quick rescheduling decisions by automating the crew rescheduling process. A Multi Agent System (MAS) is considered suitable to support this rescheduling because agents can dynamically adapt their behaviour to changing environments and they can find solutions quickly via negotiations and cooperation between them. To evaluate the CRSMAS, two types of experiment are carried out: Single Event and Multiple Events. The Single Event experiment is used to find characteristics of crew schedules that influence the crew rescheduling process while the Multiple Events experiment is used to test the capability of CRSMAS in dealing with numerous events that occur randomly. A wide range of simulation results, based on real-world data, are reported and analysed. Based on the experiment it is concluded that CRSMAS is suitable for automating the crew rescheduling process and capable of quick rescheduling whether facing single events or multiple events at the same time, the success of rescheduling is not only dependant on the tool but also to other factors such as the characteristics of crew schedules and the period of the UE, and one limitation of CRSMAS that was discovered is it cannot simulate different type of events at the same time. This limitation is because in different events there are different rules but, in Virtual World, agents can only negotiate with one set of rules at a time.Financial support was obtained from the Universiti Teknikal Malaysia Melaka (UTeM)

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

Approaches to Incorporating Robustness into Airline Scheduling

The airline scheduling process used by major airlines today aims to develop opti- mal schedules which maximize revenue. However, these schedules are often far from \optimal" once deployed in the real world because they do not accurately take into account possible weather, air tra c control (ATC), and other disruptions that can occur during operation. The resulting ight delays and cancellations can cause sig- ni cant revenue loss, not to mention service disruptions and customer dissatisfaction. A novel approach to addressing this problem is to design schedules that are robust to schedule disruptions and can be degraded at any airport location or in any region with minimal impact on the entire schedule. This research project suggests new methods for creating more robust airline schedules which can be easily recovered in the face of irregular operations. We show how to create multiple optimal solutions to the Aircraft Routing problem and suggest how to evaluate robustness of those solutions. Other potential methods for increasing robustness of airline schedules are reviewed.NASA grant NAG1-218