An optimization model for aircraft maintenance scheduling and re-assignment

The aircraft maintenance scheduling is one among the major decisions an airline has to make during its operation. Though maintenance scheduling comes as an end stage in an airline operation, it has potential for cost savings. Maintenance scheduling is an easily understood but difficult to solve problem. Given a flight schedule with aircraft assigned to it, the aircraft maintenance-scheduling problem is to determine which aircraft should fly which segment and when and where each aircraft should undergo different levels of maintenance check required by the Federal Aviation Administration. The objective is to minimize the maintenance cost and any costs incurred during the re-assignment of aircraft to the flight segments.This paper provides a complete formulation for maintenance scheduling and a heuristic approach to solve the problem. The heuristic procedure provides good solutions in reasonable computation time. This model can be used by mid-sized airline corporations to optimize their maintenance costs.     

Effective aircraft maintenance schedule adjustment following incidents

In the real world, planned aircraft maintenance schedules are often affected by incidents. Airlines may thus need to adjust their aircraft maintenance schedules following the incidents that occur during routine operations. In tradition, such aircraft maintenance schedule adjustment has been performed manually, a process which is neither effective nor efficient, especially when the problem scale is large. In this study, an aircraft maintenance schedule adjustment model is developed, with the objective of minimizing the total system cost, subject to the related operating constraints. The model is formulated as a zero-one integer program and is solved using a mathematical programing solver. The effectiveness of the model is evaluated by application to a case study using data from an aircraft maintenance center in Taiwan. The test results show the proposed model, as well as the scheduling rules abstracted from the results are useful for the decision maker to adjust good maintenance schedules.     

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and meta-heuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective.     

Perspectives on the commercial development of landing gear health monitoring systems

The development of health monitoring technologies for aerospace systems creates a number of challenges for the community of engineers and technical specialists as they seek to integrate the technology into well defined working practices. These challenges do not just extend to the technical, but require a number of commercial questions to be addressed. It is of vital importance, that there is a clearly identified need for aerospace health monitoring, both from a technological and commercial viewpoint. If these needs cannot be identified, then any attempt for marketing health monitoring as a necessary future technological requirement is doomed for failure. Health monitoring technology will need to either deliver significant cost saving benefits to the aircraft operator or demonstrated increases in aircraft safety. The objective of the paper is to provide an assessment of the commercial benefits and development of aircraft landing gear health monitoring. The commercial need and challenges for health monitoring systems are explored in this paper within the context of a changing aerospace maintenance industry and the role in which new systems technology will play. The key findings of the research study are that within the aerospace industry there is a desired paradigm shift within aircraft maintenance towards offering maintenance systems with predictive capabilities. This maintenance revolution will not just incorporate new technologies, but will result in aircraft maintenance packages tailored towards individual customer requirements. The study illustrates the state-of-the-art in health monitoring currently restricts aerospace integration and a number of key technical and commercial issues need to be addressed. Predictive health monitoring offers a variety of commercial benefits for maintenance providers, aircraft operators and manufacturers. However, in order for these benefits to be realised increased transparency in maintenance related information is required between these key players.     

A multiobjective model for maximizing fleet availability under the presence of flight and maintenance requirements

Every aircraft, military or civilian, must be grounded for maintenance after it has completed a certain number of flight hours since its last maintenance check. In this paper, we address the problem of deciding which available aircraft should fly and for how long, and which grounded aircraft should perform maintenance operations, in a group of aircraft that comprise a combat unit. The objective is to achieve maximum availability of the unit over the planning horizon. We develop a multiobjective optimization model for this problem, and we illustrate its application and solution on a real life instance drawn from the Hellenic Air Force. We also propose two heuristic approaches for solving large scale instances of the problem. We conclude with a discussion that gives insight into the behavior of the model and of the heuristics, based on the analysis of the results obtained.     

Scheduling of airport runway operations using stochastic branch and bound methods

In this paper we present a solution methodology based on the stochastic branch and bound algorithm to find optimal, or close to optimal, solutions to the stochastic airport runway scheduling problem. The objective of the scheduling problem is to find a sequence of aircraft operations on one or several runways that minimizes the total makespan, given uncertain aircraft availability at the runway. Enhancements to the general stochastic branch and bound algorithm are proposed and we give the specific details pertaining to runway scheduling. We show how the algorithm can be terminated early with solutions that are close to optimal, and investigate the impact of the uncertainty level. The computational experiment indicates that the sequences obtained using the stochastic branch and bound algorithm have, on average, 5–7% shorter makespans than sequences obtained using deterministic sequencing models. In addition, the proposed algorithm is able to solve instances with 14 aircraft using less than 1 min of computation time.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

Metaheuristics for efficient aircraft scheduling and re-routing at busy terminal control areas

Intelligent decision support systems for the real-time management of landing and take-off operations can be very effective in helping air traffic controllers to limit airport congestion at busy terminal control areas. The key optimization problem to be solved regards the assignment of airport resources to take-off and landing aircraft and the aircraft sequencing on them. The problem can be formulated as a mixed integer linear program. However, since this problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY solver (a state-of-the-art optimization solver to deal with complex routing and scheduling problems) in order to improve the possibility of finding good quality solutions quickly. The proposed framework starts from a good initial solution for the aircraft scheduling problem with fixed routes (given the resources to be traversed by each aircraft), computed via a truncated branch-and-bound algorithm. A metaheuristic is then applied to improve the solution by re-routing some aircraft in the terminal control area. New metaheuristics, based on variable neighbourhood search, tabu search and hybrid schemes, are introduced. Computational experiments are performed on an Italian terminal control area under various types of disturbances, including multiple aircraft delays and a temporarily disrupted runway. The metaheuristics achieve solutions of remarkable quality, within a small computation time, compared with a commercial solver and with the previous versions of AGLIBRARY.     

Flight schedule punctuality control and management: a stochastic approach

The insufficiency of infrastructure capacity in an air transport system is usually blamed for poor punctuality performance when implementing flight schedules. However, investigations have revealed that ground operations of airlines have become the second major cause of flight delay at airports. A stochastic approach is used in this paper to model the operation of aircraft turnaround and the departure punctuality of a turnaround aircraft at an airport. The aircraft turnaround model is then used to investigate the punctuality problem of turnaround aircraft. Model results reveal that the departure punctuality of a turnaround aircraft is influenced by the length of scheduled turnaround time, the arrival punctuality of inbound aircraft as well as the operational efficiency of aircraft ground services. The aircraft turnaround model proposed is then employed to evaluate the endogenous schedule punctuality of two turnaround aircraft. Model results, when compared with observation data, show that the operational efficiency of aircraft ground services varies among turnarounds. Hence, it is recommended that the improvement of departure punctuality of turnaround aircraft may be achieved from two approaches: airline scheduling control and the management of operational efficiency of aircraft ground services.     

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.     

The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery

Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.     

A hybrid optimization-simulation approach for robust weekly aircraft routing and retiming

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on-time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8–16.0%, cumulative delay was reduced by 25.4–33.1%, and the number of delayed passengers was reduced by 8.2–51.6%.     

Future electricity demand from battery‐powered vehicles

An important decision faced by airline schedulers is how to adapt the flight schedule and aircraft assignment to unforeseen perturbations in an established schedule. In the face of unforeseen aircraft delays, schedulers have to decide which flights to delay, and when delays become excessive, which to cancel. Current scheduling models deal with simple decision problems of delay or cancellation, but not with both simultaneously. But in practice the optimal decision may involve results from the integration of both flight cancellations and delays. In Part I of this paper, a quadratic programming model for the integration decision problem is given. The model can formulate the integration of flight cancellations and delays as well as some special cases, such as the ferrying of surplus aircraft and the possibility of swapping different types of aircraft. In this paper, based on the special structure of the model, an effective algorithm is presented, sufficient computational experiments are conducted and some results are reported. These show that we can expect to obtain a sufficiently good solution in terms of reasonable CPU time.     

An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations

The consideration of pollution in routing decisions gives rise to a new routing framework where measures of the environmental implications are traded off with business performance measures. To address this type of routing decisions, we formulate and solve a bi-objective time, load and path-dependent vehicle routing problem with time windows (BTL-VRPTW). The proposed formulation incorporates a travel time model representing realistically time varying traffic conditions. A key feature of the problem under consideration is the need to address simultaneously routing and path finding decisions. To cope with the computational burden arising from this property of the problem we propose a network reduction approach. Computational tests on the effect of the network reduction approach on determining non-dominated solutions are reported. A generic solution framework is proposed to address the BTL-VRPTW. The proposed framework combines any technique that creates capacity-feasible routes with a routing and scheduling method that aims to convert the identified routes to problem solutions. We show that transforming a set of routes to BTL-VRPTW solutions is equivalent to solving a bi-objective time dependent shortest path problem on a specially structured graph. We propose a backward label setting technique to solve the emerging problem that takes advantage of the special structure of the graph. The proposed generic solution framework is implemented by integrating the routing and scheduling method into an Ant Colony System algorithm. The accuracy of the proposed algorithm was assessed on the basis of its capability to determine minimum travel time and fuel consumption solutions. Although the computational results are encouraging, there is ample room for future research in algorithmic advances on addressing the proposed problem.     

A decision support framework for handling schedule perturbation

Perturbations of flight schedules may occur everyday. Poor scheduling of flights may result in a substantial loss of profit and decreased levels of service for air carriers. This research aims at developing a framework to help carriers in handling schedule perturbations caused by the breakdown of aircraft. The framework is based on a basic schedule perturbation model constructed as a dynamic network from which several perturbed network models are developed for scheduling following incidents. These network models are formulated as pure network flow problems or network flow problems with side constraints. The former are solved using the network simplex method while the latter are solved using Lagrangian relaxation with subgradient methods. To show how to apply the framework in the real world, a case study focusing on the operations of a major Taiwan air carrier in East Asia is presented.     

Bus maintenance systems and maintenance scheduling: model formulations and solutions

This paper deals with the problem of scheduling bus maintenance activities. The scheduling of maintenance activities is an important component in bus transit operations planning process. The other components include network route design, setting timetables, scheduling vehicles, and assignment of drivers. This paper presents a mathematical programming approach to the problem. This approach takes as input a given daily operating schedule for all buses assigned to a depot along with available maintenance resources. It, then, attempts to design daily inspection and maintenance schedules for the buses that are due for inspection so as to minimize the interruptions in the daily bus operating schedule, and maximize the utilization of the maintenance facilities. Three integer programming formulations are presented and different properties of the problem are discussed. Several heuristic methods are presented and tested. Some of these procedures produce very close to optimal solutions very efficiently. In some cases, the computational times required to obtain these solutions are less than 1% of the computational time required for the conventional branch and bound algorithm. Several small examples are offered and the computational results of solving the problem for an actual, 181-bus transit property are reported.     

Impact of continuous climb operations on airport capacity

The full benefits of Continuous Climb Operations (CCO) are realised when CCO are performed without interruption. However, CCO require safe departures that necessarily implies a reduction in capacity at high density traffic airports. This paper quantifies the capacity impact due to the integration of CCO (conflict-free with other departures and arrivals) in a high density traffic airport. The methodology develops a scheduling algorithm, a conflict-detection and resolution algorithm, and Monte Carlo simulations. The scheduling algorithm calculates two schedules, one for departures and another for arrivals, considering the CCO Rate. The conflict-detection and resolution algorithm compares CCO and arrival trajectories to detect which aircraft pairs are in conflict. The Air Traffic Control (ATC) intervention required to solve the conflict is modelled by delaying the CCO take-off. Numerical simulations based on Monte Carlo techniques are used to analyse scheduling combinations that are statistically significant in terms of conflict, ATC interventions, total delay and capacity. The results show a 32% reduction in the maximum theoretical capacity with a CCO Rate of 100%. Despite the reduction, the number of CCO departures is above the maximum operational capacity (50% of the maximum theoretical capacity). This implies that with optimised scheduling it is possible for all departures to be CCO.     

An autonomous system for maintenance scheduling data-rich complex infrastructure: Fusing the railways’ condition,planning and cost

National railways are typically large and complex systems. Their network infrastructure usually includes extended track sections, bridges, stations and other supporting assets. In recent years, railways have also become a data-rich environment.Railway infrastructure assets have a very long life, but inherently degrade. Interventions are necessary but they can cause lateness, damage and hazards. Every day, thousands of discrete maintenance jobs are scheduled according to time and urgency. Service disruption has a direct economic impact. Planning for maintenance can be complex, expensive and uncertain.Autonomous scheduling of maintenance jobs is essential. The design strategy of a novel integrated system for automatic job scheduling is presented; from concept formulation to the examination of the data to information transitional level interface, and at the decision making level. The underlying architecture configures high-level fusion of technical and business drivers; scheduling optimized intervention plans that factor-in cost impact and added value.A proof of concept demonstrator was developed to validate the system principle and to test algorithm functionality. It employs a dashboard for visualization of the system response and to present key information. Real track incident and inspection datasets were analyzed to raise degradation alarms that initiate the automatic scheduling of maintenance tasks. Optimum scheduling was realized through data analytics and job sequencing heuristic and genetic algorithms, taking into account specific cost & value inputs from comprehensive task cost modelling. Formal face validation was conducted with railway infrastructure specialists and stakeholders. The demonstrator structure was found fit for purpose with logical component relationships, offering further scope for research and commercial exploitation.     

Routing and fleet deployment in liner shipping with spot voyages

The routing, scheduling and fleet deployment is an important integrated planning problem faced by liner shipping companies which also lift load from the spot market. This paper is concerned with coordinating the decisions of the assignment of ships to contractual and spot voyages, and the determination of ship routes and schedules in order to maximize profit. We propose a new model for representing voyages as nodes of a directed graph which is used to build a mixed integer programming formulation. Besides contractual and spot nodes, another type of node is put forward to represent a combination of a contractual voyage with one or more spot voyages. In addition, the concept of dominated nodes is introduced in order to discard them and reduce the effort of the search for an optimal solution. A set of test problems has been generated taking into account real world assumptions. The test problems are solved by an optimization software and computational results are reported. The results show the potential of the approach to solve test problems of moderate size.     

An optimization model for a real-time flight scheduling problem

Although airlines plan aircraft routes and crew schedules in advance, perturbations occur everyday. As a result, flight schedules may become infeasible and would need to be updated. This Day of Operations Scheduling problem impacts the entire system of an airline as the decisions enforced are final. When perturbations are relatively small, the airline may be able to at least preserve the planned aircraft and crew itineraries. We propose a model that determines new flight schedules based on planned crew transfers, rest periods, passenger connections, and maintenance. Its dual is shown to be a network model, hence solvable in a real-time environment. In addition, it can be used in more sophisticated operational and planning systems.