The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.     

Operational aircraft maintenance routing problem with remaining time consideration

The aircraft maintenance routing problem is one of the most studied problems in the airline industry. Most of the studies focus on finding a unique rotation that will be repeated by each aircraft in the fleet with a certain lag. In practice, using a single rotation for the entire fleet is not applicable due to stochasticity and operational considerations in the airline industry. In this study, our aim is to develop a fast responsive methodology which provides maintenance feasible routes for each aircraft in the fleet over a weekly planning horizon with the objective of maximizing utilization of the total remaining flying time of fleet. For this purpose, we formulate an integer linear programming (ILP) model by modifying the connection network representation. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. A heuristic method based on compressed annealing is applied to the same problem and a comparison of exact and heuristic methods are provided. The model and the heuristic method are extended to incorporate maintenance capacity constraints. Additionally, a rolling horizon based procedure is proposed to update the existing routes when some of the maintenance decisions are already fixed.     

Network flow-based approaches for integrated aircraft fleeting and routing

Given a schedule of flights to be flown, the aircraft fleeting and routing problem (AFRP) consists of determining a minimum-cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance requirements and other activity constraints. We investigate network flow-based heuristic approaches for this problem. Computational experiments conducted on real-data given by TunisAir show that the proposed heuristic consistently yields very near-optimal solutions while requiring modest CPU effort.     

Heuristics for flight and maintenance planning of mission aircraft

Flight and Maintenance Planning (FMP) of mission aircraft addresses the question of which available aircraft to fly and for how long, and which grounded aircraft to perform maintenance operations on, in a group of aircraft that comprise a unit. The objective is to achieve maximum fleet availability of the unit over a given planning horizon, while also satisfying certain flight and maintenance requirements. The application of exact methodologies for the solution of the problem is quite limited, as a result of their excessive computational requirements. In this work, we prove several important properties of the FMP problem, and we use them to develop two heuristic procedures for solving large-scale FMP instances. The first heuristic is based on a graphical procedure which is currently used for generating flight and maintenance plans of mission aircraft by many Air Force organizations worldwide. The second heuristic is based on the idea of splitting the original problem into smaller sub-problems and solving each sub-problem separately. Both heuristics have been roughly sketched in earlier works that have appeared in the related literature. The present paper develops the theoretical background on which these heuristics are based, provides in detail the algorithmic steps required for their implementation, analyzes their worst-case computational complexity, presents computational results illustrating their computational performance on random problem instances, and evaluates the quality of the solutions that they produce. The size and parameter values of some of the randomly tested problem instances are quite realistic, making it possible to infer the performance of the heuristics on real world problem instances. Our computational results demonstrate that, under careful consideration, even large FMP instances can be handled quite effectively. The theoretical results and insights that we develop establish a fundamental background that can be very useful for future theoretical and practical developments related to the FMP problem.     

The Aircraft Maintenance Base Location Problem

Aviation authorities such as the Federal Aviation Administration (FAA) provide stringent guidelines for aircraft maintenance, with violations leading to significant penalties for airlines. Moreover, poorly maintained aircraft can lead to mass cancellation of flights, causing tremendous inconvenience to passengers and resulting in a significant erosion in brand image for the airline in question. Aircraft maintenance operations of a complex and extended nature can only be performed at designated maintenance bases. Aircraft maintenance planning literature has focused on developing good tail-number routing plans, while assuming that the locations of the maintenance bases themselves are fixed. This paper considers an inverse optimization problem, viz., locating a minimal number of maintenance bases on an Euler tour, while ensuring that all required aircraft maintenance activities can be performed with a stipulated periodicity. The Aircraft Maintenance Base Location Problem (AMBLP) is shown to be NP-complete and a new lower bound is developed for the problem. The performance of four simple “quick and dirty” heuristics for obtaining feasible solutions to AMBLP is analyzed.     

Static target search path planning optimization with heterogeneous agents

Disruptions in airline operations can result in infeasibilities in aircraft and passenger schedules. Airlines typically recover aircraft schedules and disruptions in passenger itineraries sequentially. However, passengers are severely affected by disruptions and recovery decisions. In this paper, we present a mathematical formulation for the integrated aircraft and passenger recovery problem that considers aircraft and passenger related costs simultaneously. Using the superimposition of aircraft and passenger itinerary networks, passengers are explicitly modeled in order to use realistic passenger related costs. In addition to the common routing recovery actions, we integrate several passenger recovery actions and cruise speed control in our solution approach. Cruise speed control is a very beneficial action for mitigating delays. On the other hand, it adds complexity to the problem due to the nonlinearity in fuel cost function. The problem is formulated as a mixed integer nonlinear programming (MINLP) model. We show that the problem can be reformulated as conic quadratic mixed integer programming (CQMIP) problem which can be solved with commercial optimization software such as IBM ILOG CPLEX. Our computational experiments have shown that we could handle several simultaneous disruptions optimally on a four-hub network of a major U.S. airline within less than a minute on the average. We conclude that proposed approach is able to find optimal tradeoff between operating and passenger-related costs in real time.     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.     

Exact approaches for integrated aircraft fleeting and routing at TunisAir

We describe models and exact solutions approaches for an integrated aircraft fleeting and routing problem arising at TunisAir. Given a schedule of flights to be flown, the problem consists of determining a minimum cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance activity constraints. We investigate two tailored approaches for this problem: Benders decomposition and branch-and-price. Computational experiments conducted on real-data provide evidence that the branch-and-price approach outperforms the Benders decomposition approach and delivers optimal solutions within moderate CPU times. On the other hand, the Benders algorithm yields very quickly high quality near-optimal solutions.     

A heuristic approach for an integrated fleet-assignment,aircraft-routing and crew-pairing problem

This paper deals with the fleet-assignment, aircraft-routing and crew-pairing problems of an airline flying between Canary Islands. There are two major airports (bases). The company is subdivided in three operators. There are no flight during the night. A crew route leaves from and returns to the same base. An aircraft route starts from one base and arrive to the other base due to maintenance requirements. Therefore some crews must change aircrafts, which is an undesired operation. This paper presents a mathematical formulation based on a binary variable for each potential crew and aircraft route, and describes a column-generation algorithm for obtaining heuristic solutions. Computational results on real-world instances are given and compared to manual solutions by the airline.     

Flexible aircraft fleeting and routing at <Emphasis Type="Italic">TunisAir</Emphasis>

This paper addresses a Flexible Aircraft Fleeting and Routing Problem, which is motivated by the Tunisian national carrier TunisAir. A solution to this problem specifies the departure time of each flight, the subset of aircraft to be chartered or rented out, the individual aircraft assigned to each flight, as well as the sequence of flights to be flown by each aircraft. The objective is to maximize the expected total net profit, while satisfying activity constraints and long-term maintenance requirements. Tailored optimization-based heuristics are developed for solving this complex integrated problem. Computational experiments conducted on real data demonstrate that the proposed procedures are effective and robust, and significantly improve upon TunisAir's solutions.     

District design for arc-routing applications

In this paper we address the problem of district design for the organisation of arc-routing activities. In particular, the focus is on operations like winter gritting and road maintenance. The problem involves how to allocate the road network edges to a set of depots with given locations. The collection of edges assigned to a facility forms a district in which routes have to be designed that start and end at the facility. Apart from the ability to support good arc routing, well-designed districts for road-maintenance operations should have the road network to be serviced connected and should define clear geographical boundaries. We present three districting heuristics and evaluate the quality of the partitions by solving capacitated arc routing problems in the districts, and by comparing the solution values with a multi-depot CARP cutting plane lower bound. Our experiments reveal that based on global information about the distribution system (ie the number of facilities or districts, the average edge demand and the vehicle capacity) and by using simple guidelines, an adequate districting policy may be selected.     

A large neighbourhood search heuristic for the aircraft and passenger recovery problem

This paper introduces a large neighbourhood search heuristic for an airline recovery problem combining fleet assignment, aircraft routing and passenger assignment. Given an initial schedule, a list of disruptions, and a recovery period, the problem consists in constructing aircraft routes and passenger itineraries for the recovery period that allow the resumption of regular operations and minimize operating costs and impacts on passengers. The heuristic alternates between construction, repair and improvement phases, which iteratively destroy and repair parts of the solution. The aim of the first two phases is to produce an initial solution that satisfies a set of operational and functional constraints. The third phase then attempts to identify an improved solution by considering large schedule changes while retaining feasibility. The whole process is iterated by including some randomness in the construction phase so as to diversify the search. This work was initiated in the context of the 2009 ROADEF Challenge, a competition organized jointly by the French Operational Research and Decision Analysis Society and the Spanish firm Amadeus S.A.S., in which our team won the first prize.     

Network design: taxi planning

The effect of managing aircraft movements on the airport’s ground is an important tool that can alleviate the delays of flights, specially in peak hours or congested situations. Although some strategic design decisions regarding aeronautical and safety aspects have a main impact on the airport’s topology, there exists a number of other additional factors that must be evaluated according to the on ground operations, i.e. previous to the taking-off or after landing. Among these factors one can consider capacities at waiting points and directions of some corridors. These factors are related to the demand situation of a given period and influence the aircraft’s routing on the ground or short term Taxi Planning problem (or TP-S). While the TP-S problem studies the aircraft routing and scheduling on the airport’s ground under a dynamic point of view, this paper presents a Taxi Planning network design model (or TPND), attending to these additional factors of the airport’s topology and the conflicting movements of the aircraft on them with the same modelling approach used in the TP-S problem. The TPND model is formulated as a binary multicommodity network flow problem with additional side constraints under a multiobjective approach. The side constraints included are the classical limitations due to capacity and also as a distinctive approach, constraints that restrict the interference of aircraft in order to decrease the intervention of human controllers during the operations or increase their safety margins. The multiobjective approach adopted for the TPND model balances conflicting objectives: airport’s throughput, travel times, safety of operations and costs. In the paper computational results are included on two test airports solving the TPND model by “Branch and Bound” showing the effect of the conflicting objectives in the design decisions. Research supported under Research Project TRA-2005-09068-C03-01/MODAL from the “Ministerio de Educación y Ciencia”.     

Fleet assignment and routing with schedule synchronization constraints

This paper introduces a new type of constraints, related to schedule synchronization, in the problem formulation of aircraft fleet assignment and routing problems and it proposes an optimal solution approach. This approach is based on Dantzig–Wolfe decomposition/column generation. The resulting master problem consists of flight covering constraints, as in usual applications, and of schedule synchronization constraints. The corresponding subproblem is a shortest path problem with time windows and linear costs on the time variables and it is solved by an optimal dynamic programming algorithm. This column generation procedure is embedded into a branch and bound scheme to obtain integer solutions. A dedicated branching scheme was devised in this paper where the branching decisions are imposed on the time variables. Computational experiments were conducted using weekly fleet routing and scheduling problem data coming from an European airline. The test problems are solved to optimality. A detailed result analysis highlights the advantages of this approach: an extremely short subproblem solution time and, after several improvements, a very efficient master problem solution time.     

A genetic local search algorithm with a threshold accepting mechanism for solving the runway dependent aircraft landing problem

As the demand for air transportation continues to grow, some flights cannot land at their preferred landing times because the airport is near its runway capacity. Extra fuel consumption and air pollution are then caused by the landing delays. Moreover, such delays may possibly yield extra costs for both passengers and airline companies that result from rescheduling transfer passengers and crew members. Consequently, how to increase the handling efficiency of congested airports is a crucial management issue. Building new runways at existing airports is often not feasible due to environmental, financial and geographical constraints. Therefore, devising a method for tackling the aircraft landing problem (ALP) in order to optimize the usage of existing runways at airports is the focus of this paper. This paper aims to develop a solution procedure based on a genetic local search (GLS) algorithm for solving the ALP with runway dependent attributes. A set of numerical experiments were conducted to test the validity of the proposed algorithm based on five test instances created and investigated by previous studies. The numerical results showed that the proposed GLS algorithm can effectively and efficiently determine the runway allocation, sequence and landing time for arriving aircraft for the five test cases by minimizing total delays under the separation constraints in comparison with the outcomes yielded by previous studies.     

Robust vehicle routing DSS and road networks on a European scale?

During the last decades we have been involved in the development of an assortment of DSS in the area of Logistics. It comprises systems to support organisations to decide upon logistic network structures on a country. European or even Global level in response to social, economic, market, organisational, technological and environmental changes. Further, it encompasses operational vehicle route planning systems (VRP-DSS) with their incorporated Road Network System (RNS) that are used to support the determination of operational vehicle routing plans within the previously mentioned logistic networks.From our experience we have learned about the complexity and the spectrum of logistic problems and the variety of ways in which these problems are being solved. We have perceived that the functional and performance requirements for VRP-DSS have changed rapidly over the last decade in response to the increased importance of logistic processes, changing practical quantitative and qualitative routing constraints, evolving organisational procedures for planning and alterations in the registration of distribution processes. Many current VRP-DSS and RNS do not satisfy basic functional and performance requirements.In this paper we describe developments regarding the problem domains for VRP and RNS, the variety of requirements for these systems, including quantitative and qualitative routing constraints and National and European Road Networks. Finally, we pay attention to logical architectures for these systems and RNS that satisfy user requirements.     

Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research.     

A multi-depot period vehicle routing problem arising in the utilities sector

This paper considers the resource planning problem of a utility company that provides preventive maintenance services to a set of customers using a fleet of depot-based mobile gangs. The problem is to determine the boundaries of the geographic areas served by each depot, the list of customers visited each day and the routes followed by the gangs. The objective is to provide improved customer service at minimum operating cost subject to constraints on frequency of visits, service time requirements, customer preferences for visiting on particular days and other routing constraints. The problem is solved as a Multi-Depot Period Vehicle Routing Problem (MDPVRP). The computational implementation of the complete planning model is described with reference to a pilot study and results are presented. The solution algorithm is used to construct cost-service trade-off curves for all depots so that management can evaluate the impact of different customer service levels on total routing costs.     

Combining column generation and constraint programming to solve the tail assignment problem

Within the area of short term airline operational planning, Tail Assignment is the problem of assigning flight legs to individual identified aircraft while satisfying all operational constraints, and optimizing some objective function. In this article, we propose that Tail Assignment should be solved as part of both the short and the long term airline planning. We further present a hybrid column generation and constraint programming solution approach. This approach can be used to quickly produce solutions for operations management, and also to produce close-to-optimal solutions for long and mid term planning scenarios. We present computational results which illustrate the practical usefulness of the approach.     

Solving a manpower scheduling problem for airline catering using metaheuristics

We study a manpower scheduling problem with job time windows and job-skills compatibility constraints. This problem is motivated by airline catering operations, whereby airline meals and other supplies are delivered to aircrafts on the tarmac just before the flights take-off. Jobs (flights) must be serviced within a given time-window by a team consisting of a driver and loader. Each driver/loader has the skills to service some, but not all, of the airline/aircraft/configuration of the jobs. Given the jobs to be serviced and the roster of workers for each shift, the problem is to form teams and assign teams and start-times for the jobs, so as to service as many flights as possible. Only teams with the appropriate skills can be assigned to a flight. Workload balance among the teams is also a consideration. We present model formulations and investigate a tabu search heuristic and a simulated annealing heuristic approach to solve the problem. Computational experiments show that the tabu search approach outperforms the simulated annealing approach, and is capable of finding good solutions.