Crew Pairing Research Articles

The robust crew pairing problem: model and solution methodology

We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.

Multi‐objective Approaches to the Unit Crewing Problem in Airline Crew Scheduling

ABSTRACTThe goal of the crew pairing problem is to partition a flight schedule into sequences of flights called pairings that crew members can operate at minimum cost. It is solved for each crew rank, for example, captains and first officers. In optimised crew pairings, crew often split and join other crew to operate outgoing flights. Because minimum cost pairings contain little buffer time, crew splitting after a delayed flight contributes to the propagation of delay. This effect can be avoided by unit crewing, that is, by keeping crew of different ranks together for as long as possible during a pairing. However, increasing unit crewing increases cost.We investigate sequential and parallel methods for unit crewing, explicitly considering the two objectives of minimising cost and maximising unit crewing. We apply multi‐objective techniques in the sequential approach, where the (minimum cost) pairing problem for one crew rank is solved first and both objectives feature when solving for the second crew rank. Because the quality of the pairings obtained by this method is limited by the solution for the first crew rank, we then propose to solve the two crew pairing problems simultaneously, again using multi‐objective optimisation methods. We introduce a multi‐objective optimisation model for this problem and propose a new heuristic branching technique that favours unit crewed pairings when applied to a scalarised model with an auxiliary objective function. We compare this with a direct approach with management of the number of unit crewing constraints and a Dantzig–Wolfe decomposition approach.Numerical tests on domestic New Zealand data show that the multi‐objective approaches considerably increase the level of unit crewing, without much increase in cost, even in the sequential approach. Moreover, we show that the parallel approach is superior in terms of quality of the pairing solution but computationally more expensive. The heuristic branching technique provides good quality solutions in reasonable time, as compared with the Dantzig–Wolfe method. Copyright © 2014 John Wiley & Sons, Ltd.

Two-level decomposition algorithm for crew rostering problems with fair working condition

A typical railway crew scheduling problem consists of two phases: a crew pairing problem to determine a set of crew duties and a crew rostering problem. The crew rostering problem aims to find a set of rosters that forms workforce assignment of crew duties and rest periods satisfying several working regulations. In this paper, we present a two-level decomposition approach to solve railway crew rostering problem with the objective of fair working condition. To reduce computational efforts, the original problem is decomposed into the upper-level master problem and the lower-level subproblem. The subproblem can be further decomposed into several subproblems for each roster. These problems are iteratively solved by incorporating cuts into the master problem. We show that the relaxed problem of the master problem can be formulated as a uniform parallel machine scheduling problem to minimize makespan, which is NP-hard. An efficient branch-and-bound algorithm is applied to solve the master problem. Effective valid cuts are developed to reduce feasible search space to tighten the duality gap. Using data provided by the railway company, we demonstrate the effectiveness of the proposed method compared with that of constraint programming techniques for large-scale problems through computational experiments.

A hybrid particle swarm optimization and an improved heuristic algorithm for an airline crew rostering problem

The airline crew scheduling problem is a combinatorial optimization problem and belongs to the class of NP- hard problems. An effective method for solving the airline crew scheduling problem can reduce the crew costs and improve crew satisfaction. Because of its complexity, the problem is divided into two subproblems: the crew pairing problem and the crew rostering problem. In this paper, the crew rostering problem is focused on and the objective is to generate a fairness timetable in which the workloads are distributed among each crew equally. We propose a hybrid particle swarm optimization (PSO) and an improvement heuristic (IH) to solve this problem. The IH is designed to improve the standard deviation of the workloads by picking a workload from the high workload crew and assigning it to the low workload crew. The IH improves the solution of the particle after the particle changes position each generation. The proposed algorithm is tested on actual pairing data from Thai Airways and is compared with PSO without IH and the multi-commodity network flow approach. With the combination of PSO and IH, the algorithm can improve the quality of the solution by more than 20% in most cases, and PSO with IH also outperforms the network approach in 6 out of 9 cases and especially in the large size cases for which the network approach cannot find a feasible solution.

An integrated scenario-based approach for robust aircraft routing, crew pairing and re-timing

For reasons of tractability, the airline scheduling problem has traditionally been sequentially decomposed into various stages (e.g. schedule generation, fleet assignment, aircraft routing, and crew pairing), with the decisions from one stage imposed upon the decision-making process in subsequent stages. Whilst this approach greatly simplifies the solution process, it unfortunately fails to capture many dependencies between the various stages, most notably between those of aircraft routing and crew pairing, and how these dependencies affect the propagation of delays through the flight network. In Dunbar et al. (2012) [9] we introduced a new algorithm to accurately calculate and minimize the cost of propagated delay, in a framework that integrates aircraft routing and crew pairing. In this paper we extend the approach of Dunbar et al. (2012) [9] by proposing two new algorithms that achieve further improvements in delay propagation reduction via the incorporation of stochastic delay information. We additionally propose a heuristic, used in conjunction with these two approaches, capable of re-timing an incumbent aircraft and crew schedule to further minimize the cost of delay propagation. These algorithms provide promising results when applied to a real-world airline network and motivate our final integrated aircraft routing, crew pairing and re-timing approach which provides a substantially significant reduction in delay propagation.

Characteristics of Pilots Involved in U.S. Air Carrier Accidents Between 1991 and 2010

This study used a case control methodology to analyze and describe the pilot characteristics of major U.S. air carrier accidents between 1991 and 2010. This study applied descriptive statistics and Chi-square for statistical analysis. The major findings of this study indicate that of the 50 accidents analyzed between 1991 and 2010, 96% of the first officers involved in a major U.S. air carrier accident possessed at least 2,000 hours of total flight time. Regarding first officer flight certificates (commercial pilot and ATP), the researchers separated the 1991 - 2010 time period into two time period groups (1991-2000 and 2001-2010).Of the two first officers (4%) with less than 1,500 hours of total flight time, neither was involved in an accident that cited pilot performance as a causal or contributing factor. This finding did not support the notion that a 1,500 hour total flight time requirement will contribute to the safety of air carrier operations conducted under 14 CFR 121. While an ATP certification requirement for first officers will not eliminate the possibility of any future accidents involving commercially certificated first officers, it was not possible to predict whether such a change will contribute to the enhancement of safety for 14 CFR 121 air carrier operations. It is possible there will simply be a redistribution of the number of accidents involving ATP certificated first officers. Results of this study also indicate that crew familiarity (captains and first officers) may have a negative effect on accident rates. The evaluation of captain and first officer cockpit interaction indicated that accident rates were higher in instances of lower crew familiarity in each of the three areas measured; first day of crew pairing, first leg of the day, and during the first pairing together.

Integrated Short-Haul Airline Crew Scheduling Using Multiobjective Optimization Genetic Algorithms

This paper proposes an evolutionary alternative to conventional two-phase planning methods for solving the integrated crew scheduling (ICS) problem. The approach models and formulates the ICS problem as a combinational optimization problem with multiple constraints and objectives. An integrated evolutionary framework is proposed for simultaneously considering crew pairing and crew rostering subproblems. To improve the efficiency of the Pareto set explorer, the solution methodology applies a novel variant of the nondominated sorting genetic algorithm II (NSGA-II), one of the most popular multiobjective optimization evolutionary algorithms. The proposed variant features problem-dependent constraint handling and a bounded front policy to reserve diverse individuals. The proposed approach is verified and validated in a case study of a real-world short-haul airline crew scheduling problem. The experimental results obtained by the proposed integrated approach are then compared with a real-world airline plan generated by the conventional sequential method. An aircraft schedule recovery problem is also studied to compare solution performance between the conventional NSGA-II method and the proposed NSGA-II variant. The comparison results confirm that the proposed variant obtains solutions that are superior in two aspects: First, the proposed NSGA-II variant obtains better convergence in the studied problems compared with the original version; second, the results explored by the variant enable decision makers to select from multiple crew schedules, which are superior to the real-world airline crew plan while considering the same objectives and constraints.

Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework

For reasons of tractability, the airline scheduling problem has traditionally been sequentially decomposed into various stages (e.g., schedule generation, fleet assignment, aircraft routing, and crew pairing), with the decisions from one stage imposed upon the decision making process in subsequent stages. Although this approach greatly simplifies the solution process, it unfortunately fails to capture the many dependencies between the various stages, most notably between those of aircraft routing and crew pairing, and how these dependencies affect the propagation of delays through the flight network. Because delays are commonly transferred between late running aircraft and crew, it is important that aircraft routing and crew pairing decisions are made together. The propagated delay may then be accurately estimated to minimize the overall propagated delay for the network and produce a robust solution for both aircraft and crew. In this paper we introduce a new approach to accurately calculate and minimize the cost of propagated delay in a framework that integrates aircraft routing and crew pairing.

Integrated Airline Crew Pairing and Crew Assignment by Dynamic Constraint Aggregation

Traditionally, the airline crew scheduling problem has been decomposed into a crew pairing problem and a crew assignment problem, both of which are solved sequentially. The first consists of generating a set of least-cost crew pairings (sequences of flights starting and ending at the same crew base) that cover all flights. The second aims at finding monthly schedules (sequences of pairings) for crew members that cover all pairings previously built. Pairing and schedule construction must respect all safety and collective agreement rules. In this paper, we focus on the pilot crew scheduling problem in a bidline context where anonymous schedules must be built for pilots and high fixed costs are considered to minimize the number of scheduled pilots. We propose a model that completely integrates the crew pairing and crew assignment problems, and we develop a combined column generation/dynamic constraint aggregation method for solving them. Computational results on real-life data show that integrating crew pairing and crew assignment can yield significant savings—on average, 3.37% on the total cost and 5.54% on the number of schedules for the 7 tested instances. The integrated approach, however, requires much higher computational times than the sequential approach.

An Improved Genetic Algorithm for Crew Pairing Optimization

Crew pairing is a sequence of flights beginning and ending at the same crewbase. Crew pairing planning is one of the primary processes in airline crew scheduling; it is also the primary cost-determining phase in airline crew scheduling. Optimizing crew pairings in an airline timetable helps minimize operational crew costs and maximize crew utilization. There are numerous restrictions that must be considered and just as many regulations that must be satisfied in crew pairing generation. The most important regulations—and the ones that make crew pairing planning a highly constrained optimization problem—are the the limits of the flight and the duty periods. Keeping these restrictions and regulations in mind, the main goal of the optimization is the generation of low cost sets of valid crew pairings which cover all flights in the airline’s timetable. For this research study, We examined studies about crew pairing optimization and used these previously existing methods of crew pairing to develop a new solution of the crew pairing problem using genetic algorithms. As part of the study we created a new genetic operator—called perturbation operator.Unlike traditional genetic algorithm implementations, this new perturbation operator provides much more stable results, an obvious increase in the convergence rate, and takes into account the existence of multiple crewbases.

Crew pairing optimization based on hybrid approaches

The crew pairing problem (CPP) deals with generating crew pairings due to law and restrictions and selecting a set of crew pairings with minimal cost that covers all the flight legs. In this study, we present three different algorithms to solve CPP. The knowledge based random algorithm (KBRA) and the hybrid algorithm (HA) both combine heuristics and exact methods. While KBRA generates a reduced solution space by using the knowledge received from the past, HA starts to generate a reduced search space including high quality legal pairings by using some mechanisms in components of genetic algorithm (GA). Zero-one integer programming model of the set covering problem (SCP) which is an NP-hard problem is then used to select the minimal cost pairings among solutions in the reduced search space. Column generation (CG) which is the most commonly used technique in the CPP literature is used as the third solution technique. While the master problem is formulated as SCP, legal pairings are generated in the pricing problem by solving a shortest path problem on a structured network. In addition, the performance of CG integrated by KBRA (CG_KBRA) and HA (CG_HA) is investigated on randomly generated test problems. Computational results show that HA and CG_HA can be considered as effective and efficient solution algorithms for solving CPP in terms of the computational cost and solution quality.

Solving shortest path problems with a weight constraint and replenishment arcs

This paper tackles a generalization of the weight constrained shortest path problem (WCSPP) in a directed network with replenishment arcs that reset the accumulated weight along the path to zero. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests; and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we review the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We present the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications.

Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods

The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. Given its high complexity, the ICS problem has been traditionally tackled using a sequential two-stage approach, where a crew pairing problem is solved in the first stage and a crew assignment problem in the second stage. Recently, Saddoune et al. (2010b) developed a model and a column generation/dynamic constraint aggregation method for solving the ICS problem in one stage. Their computational results showed that the integrated approach can yield significant savings in total cost and number of schedules, but requires much higher computational times than the sequential approach. In this paper, we enhance this method to obtain lower computational times. In fact, we develop a bi-dynamic constraint aggregation method that exploits a neighborhood structure when generating columns (schedules) in the column generation method. On a set of seven instances derived from real-world flight schedules, this method allows to reduce the computational times by an average factor of 2.3, while improving the quality of the computed solutions.

Implementing a branch and price and cut method for the airline crew pairing optimization problem

We discuss the airline crew pairing optimization problem and present a solution method based on a combination of column and cut generation. The generated cuts are a subclass of subset-row inequalities. The pricing subproblem is solved by a label-setting algorithm with a new backtracking scheme and consideration of the generated cuts. The solution method for the linear relaxation is embedded in a branch-and-bound procedure with a constraint branching strategy and a new search strategy. We test our method on instances from domestic flight schedules of a European Airline.

On a New Rotation Tour Network Model for Aircraft Maintenance Routing Problem

The airline industry currently has a $40-billion plus market and is expected to grow rapidly with the population growth and growth in the overall economy. Everyday, thousands of aircrafts undergo maintenance, repair, and overhaul. The aircraft maintenance problem is one of the important logistic problems in the airline industry. It is aimed at scheduling the aircrafts' routing so that enough maintenance opportunities are provided to every aircraft in the fleet. In this paper, we present a new compact network representation of the aircraft maintenance routing problem (AMR) and propose a new mixed-integer linear programming formulation to solve the problem. The quality of this model was assessed on four real test instances from a major U.S. carrier, and compared with the flight string model proposed in the literature. The computational results show that the proposed model is able to obtain the optimal solutions to all test instances in reasonable time. This study suggests that this model can be applied to integrated problems of the AMR and other planning problems such as the fleet assignment problem and crew pairing problem.

Aircrew pairings with possible repetitions of the same flight number

A crew pairing is a sequence of flights, connections and rests that starts and ends at a crew base and is assigned to a single crew. The crew pairing problem consists of determining a minimum cost set of feasible crew pairings such that each flight is covered exactly once and side constraints are satisfied. Traditionally, this problem has been solved in the industry by a heuristic three-phase approach that solves sequentially a daily, a weekly, and a monthly problem. This approach prohibits or strongly penalizes the repetition of the same flight number in a pairing. In this paper, we highlight two weaknesses of the three-phase approach and propose alternative solution approaches that exploit flight number repetitions in pairings. First, when the flight schedule is irregular, we show that better quality solutions can be obtained in less computational time if the first two phases are skipped and the monthly problem is solved directly using a rolling horizon approach based on column generation. Second, for completely regular flight schedules, we show that better quality solutions can be derived by skipping the daily problem phase and solving the weekly problem directly.

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 difficult 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 local airlines in Turkey.

An iterative approach to robust and integrated aircraft routing and crew scheduling

In airline scheduling a variety of planning and operational decision problems have to be solved. We consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights in a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved later. Also, when minimal cost solutions are used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day. We generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We solve the two original problems iteratively. Starting from a minimal cost solution, we produce a series of solutions which are increasingly robust. Using data from domestic airline schedules we evaluate the benefits of the approach as well as the trade-off between cost and robustness. We extend our approach considering the aircraft routing problem together with two crew pairing problems, one for technical crew and one for flight attendants.

An Effective Deflected Subgradient Optimization Scheme for Implementing Column Generation for Large-Scale Airline Crew Scheduling Problems

We present a new deflected subgradient scheme for generating good quality dual solutions for linear programming (LP) problems and utilize this within the context of large-scale airline crew planning problems that arise in practice. The motivation for the development of this method came from the failure of a black-box-type approach implemented at United Airlines for solving such problems using column generation in concert with a commercial LP solver, where the software was observed to stall while yet remote from optimality. We identify a phenomenon called dual noise to explain this stalling behavior and present an analysis of the desirable properties of dual solutions in this context. The proposed deflected subgradient approach has been embedded within the crew pairing solver at United Airlines and tested using historical data sets. Our computational experience suggests a strong correlation between the dual noise phenomenon and the quality of the final solution produced, as well as with the accompanying algorithmic performance. Although we observed that our deflected subgradient scheme yielded an average speed-up factor of 10 for the column generation scheme over the commercial solver, the average reduction in the optimality gap over the same number of iterations was better by a factor of 26, along with an average reduction in the dual noise by a factor of 30. The results from the column generation implementation suggest that significant benefits can be obtained by using the deflected subgradient-based scheme instead of a black-box-type or standard solver approach to solve the intermediate linear programs that arise within the column generation scheme.

Robust crew pairing for managing extra flights

This paper discusses a modeling approach to robust crew pairing when a set of extra flights is likely to be added to the regular flight schedule. The set of these possible extra flights is known at the planning stage. We demonstrate that these extra flights may be incorporated into the schedule if necessary by modifying the planned crew pairings appropriately and without delaying or canceling existing flights. To this end, we either identify a pair of crews whose schedules may be (partially) swapped while adding an extra flight into the schedule or show that an extra flight may be inserted into the schedule of a crew without affecting others. We note that deadheading may be necessary in either case. For these two types of solutions, we define the appropriate feasibility rules with respect to the common airline regulations. We then propose two robust mathematical programming models that consider incorporating such solutions into the set of selected pairings while keeping the increase in the crew cost at an acceptable level. The baseline solution for comparison is found by a conventional crew pairing model in the literature which ignores robustness at the planning stage and relies on recovery procedures at the time of operation. We also propose the variations of the two models, where the double counting of the possible solutions across extra flights is prevented. Finally, we conduct computational experiments on a set of data generated from the actual data of an airline company. We solve the crew pairing problem both with the proposed robust models and the conventional model. Our results demonstrate the benefits of the proposed modeling approach and indicate that the proposed robust models provide natural options to recovery without disrupting the existing flights at a relatively small incremental cost, which is visible at the planning stage.