Scatter Search and Bionomic Algorithms for the aircraft landing problem

The problem of deciding how to land aircraft approaching an airport involves assigning each aircraft to an appropriate runway, computing a landing sequence for each runway and scheduling the landing time for each aircraft. Runway allocation, sequencing and scheduling for each aircraft must ensure the scheduled landing time lies within a predefined time window and meet separation time requirements with other aircraft. The objective is to achieve effective runway use.In this paper, the multiple runway case of the static Aircraft Landing Problem is considered. Two heuristic techniques are presented: Scatter Search and the Bionomic Algorithm, population heuristic approaches that have not been applied to this problem before.Computational results are presented for publicly available test problems involving up to 500 aircraft and five runways showing that feasible solutions of good quality can be produced relatively quickly.     

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.     

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.     

Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact solver. Since the problem is very difficult to solve, we also propose a heuristic procedure where the problem is decomposed and it is locally exactly solved. Computational results show that the proposed approach provides satisfactory results.     

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.     

A decision support model for establishing an air taxi service: a case study

Recent availability of relatively cheap small jet aircraft creates opportunities for a new air transport business: Air taxi, an on-demand service in which travellers call in one or a few days in advance to book transportation. In this paper, we present a methodology and simulation study supporting important strategic decisions, like for instance determining the required number of aircraft, for a company planning to establish an air taxi service in Norway. The methodology is based on a module simulating incoming bookings, built around a heuristic for solving the underlying dial-a-flight problem. The heuristic includes a separate method for solving the important subproblem of determining the best distribution of waiting time along a single aircraft schedule. The methodology has proved to provide reliable decision support to the company.     

A branch-and-price approach for operational aircraft maintenance routing

In recent years, considerable effort in the field of operations research has been paid to optimizing airline operations, including the logistics of an airline’s fleet of aircraft. We focus on the problem of aircraft routing, which involves generating and selecting a particular route for each aircraft of a sub-fleet that is already assigned to a set of feasible sequences of flight legs. Similar studies typically focus on long-term route planning. However, stochastic events such as severe weather changes, equipment failures, variable maintenance times, or even new regulations mandated by the Federal Aviation Administration (FAA) play havoc on these long-term plans. In addition, these long-term plans ignore detailed maintenance requirements by considering only one or two of the primary maintenance checks that must be performed on a regular, long-term basis. As a result, these plans are often ignored by personnel in airline operations who are forced on a daily basis to develop quick, ad hoc methods to address these maintenance requirements and other irregular events. To address this problem, we develop an operational aircraft maintenance routing problem formulation that includes maintenance resource availability constraints. We propose a branch-and-price algorithm for solving this problem, which, due to the resource constraints, entails a modification of the branch-on, follow-on branching rule typically used for solving similar problems. Through computational testing, we explore the efficiency of this solution approach under a combination of heuristic choices for column (route) generation and selection.     

Improvements to a large neighborhood search heuristic for an integrated aircraft and passenger recovery problem

Because most commercial passenger airlines operate on a hub-and-spoke network, small disturbances can cause major disruptions in their planned schedules and have a significant impact on their operational costs and performance. When a disturbance occurs, the airline often applies a recovery policy in order to quickly resume normal operations. We present in this paper a large neighborhood search heuristic to solve an integrated aircraft and passenger recovery problem. The problem consists of creating new aircraft routes and passenger itineraries to produce a feasible schedule during the recovery period. The method is based on an existing heuristic, developed in the context of the 2009 ROADEF Challenge, which alternates between three phases: construction, repair and improvement. We introduce a number of refinements in each phase so as to perform a more thorough search of the solution space. The resulting heuristic performs very well on the instances introduced for the challenge, obtaining the best known solution for 17 out of 22 instances within five minutes of computing time and 21 out of 22 instances within 10 minutes of computing time.     

Scheduling programs with repetitive projects: A comparison of a simulated annealing,a genetic and a pair-wise swap algorithm

We address the problem of scheduling in programs involving the production of multiple units of the same product. Our study was motivated by a construction program for fast naval patrol boats. Other applications of this problem include procurement of multiple copies of aircraft, spacecraft, and weapon systems. In this problem we must decide how many units of the product to assign to each of a number of available crews (individuals, teams, subcontractors, etc.). These types of problems are characterized by two potentially conflicting considerations: 1) the need to complete each unit by its contractual due date, and 2) learning effects. Because of the first consideration, there is a tendency to use multiple crews for simultaneous production, so that meeting due dates is assured. However, the second consideration encourages assigning many units to a single crew so that learning effects are maximized. We study this scheduling problem with two different penalty cost structures and develop models for both versions. The models trade-off the penalty associated with late deliveries and the savings due to learning (and possibly incentive payments for early completion). We discuss different heuristic algorithms — simulated annealing, a genetic algorithm, and a pair-wise swap heuristic — as well as an exhaustive search to determine a baseline for comparisons. Our computational results show that the pair-wise swap algorithm is the most efficient solution procedure for these models.     

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.     

An interactive system for the loading of cargo aircraft

The paper describes an interactice, computer based procedure for solving the variant of the vehicle loading problem encountered when loading containers and pallets into an aircraft. The procedure is heuristic and practical oriented; it is presently being implemented by Scandinavian Airlines.     

A Heuristic Algorithm for Assigning Crews Among Bases in an Airlift Operation

In this paper, the optimum assignment of crews among the bases in an airlift operation is considered. An airlift operation consists of transporting large quantities of equipment and personnel among various bases. The crews operating the aircraft rest for a constant period of time after arriving at the bases, before flying again. In order to minimize the waiting times of the aircraft at the bases for want of rested crews, the available crews are distributed initially among the bases.Using earlier results of the mean waiting time of an aircraft at a single base and the probability distribution of the inter-departure times of the aircraft from the base, the problem of optimum allocation of crews is formulated as a non-linear integer programming problem. A heuristic algorithm is developed using the Lagrange multiplier. Its solution is compared with the exact solution for a number of test cases, and the algorithm is found to perform well.     

The nozzle guide vane problem: Partitioning a heterogeneous inventory

In this paper we describe a problem which is encountered in the maintenance of gas turbine engines used in commercial and military aircraft. In particular, we address the problem of selecting a set of nozzle guide vanes, from a heterogeneous inventory of vanes, for the nozzle assembly of an engine. We formulate this problem as a partitioning problem for a heterogeneous population. Given the combinatorial complexity of the problem we develop a heuristic algorithm which is shown to be very effective in obtaining the maximum number of partitions.     

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.     

Effective algorithm and heuristic for the generalized assignment problem

We present new Branch-and-Bound algorithm for the generalized assignment problem. A standard subgradient method (SM), used at each node of the decision tree to solve the Lagrangian dual, provides an upper bound. Our key contribution in this paper is a new heuristic, applied at each iteration of the SM, which tries to exploit the solution of the relaxed problem, by solving a smaller generalized assignment problem. The feasible solution found is then subjected to a solution improvement heuristic. We consider processing the root node as a Lagrangian heuristic. Computational comparisons are made with new existing methods.     

Assigning arriving flights at an airport to the available gates

Unexpected changes in the flight schedules may disrupt the initial aircraft-gate assignments, and result in congestions and delays in getting aircraft onto gates. A mathematical model is developed to assign the flights with the minimum range of unutilised time periods of gates, subject to the level of service offered to passengers and other physical and managerial considerations. (The assignments are expected to be flexible enough to absorb the minor modifications in the flight schedules.) Interactive optimum and heuristic procedures, both utilising lower bounds on the ranges of future solutions, are proposed to cope with the major changes in disrupting the initial gate-assignments. Over randomly generated schedules, 74 flights can be optimally assigned to seven gates within 17 seconds when the gates are re-utilised within 30 minutes after each departure. The heuristic reaches the optimal solution after evaluating at most 20 partial solutions at one level. Over data obtained from Riyadh’s International Airport, the heuristic outperforms the existing practice: On average, 72.03% and 54.28% improvements are obtained on the number of remote served aircraft and towed aircraft, respectively.     

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.     

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.     

面向靠桥率及道口冲突率的航班-机位指派问题优化模型及其启发式算法研究

在给定航班时刻表条件下,对于进出港航班的机位分配,除了必须满足航班、飞机和机位之间的技术性要求之外,还要考虑尽量提高整个机场的机位利用率,且方便旅客出入港及时、安全和便捷.文章以飞机机型、所属航空公司、客运/货运航班、国内/国际航班等匹配条件为约束条件,以航班-机位分配完成率、靠桥率、道口非冲突率为目标,建立了一个航班-机位指派问题的全局优化模型.基于国内某机场的真实应用场景及其待决策变量维度的超大规模,导致模型求解成为一个NP-COMPLETE的混合整数规划问题.文章提出一种启发式快速求解算法,基于贪婪规则建立若干优先级队列的航班冲突调整方案,按照3个指标重要程度渐次探求近似最优解.而且,对于每一步贪婪规则的改进,文章都进行了算法有效性检验以及计算性能的对比实验.最终多重对比实验的结果表明,新算法的结果在与理论最优解差距不足3%的代价下,可节约超过90%求解时间.     

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.