Coordinated scheduling models for allied airlines

Recently, as a means of forming global networks and improving operation efficiency, major air carriers have increasingly entered into alliances with other carriers. Fleet routing and flight scheduling are not only important in individual airline operations, but also affect the alliances. The setting of a good flight schedule can not only enhance allied airline operating performance, but can also be a useful reference for alliance decision-making. In this research, we develop several coordinated scheduling models, which will help the allied airlines solve for the most satisfactory fleet routes and timetables under the alliance. We employ network flow techniques to construct the models. The models are formulated as multiple commodity network flow problems which can be solved using a mathematical programming solver. Finally, to evaluate the models, we perform a case study based on real operating data from two Taiwan airlines. The preliminary results are good, showing that the models could be useful for airline alliances.     

Optimal scheduling of a taxi fleet with mixed electric and gasoline vehicles to service advance reservations

This study addresses the problem of scheduling a fleet of taxis that are appointed to solely service customers with advance reservations. In contrast to previous studies that have dealt with the planning and operations of a taxi fleet with only electric vehicles (EVs), we consider that most taxi companies may have to operate with fleets comprised of both gasoline vehicles (GVs) and plug-in EVs during the transition from GV to (complete) EV taxi fleets. This paper presents an innovative multi-layer taxi-flow time-space network which effectively describes the movements of the taxis in the dimensions of space and time. An optimization model is then developed based on the time-space network to determine an optimal schedule for the taxi fleet. The objective is to minimize the total operating cost of the fleet, with a set of operating constraints for the EVs and GVs included in the model. Given that the model is formulated as an integer multi-commodity network flow problem, which is characterized as NP-hard, we propose two simple but effective decomposition-based heuristics to efficiently solve the problem with practical sizes. Test instances generated based on the data provided by a Taiwan taxi company are solved to evaluate the solution algorithms. The results show that the gaps between the objective values of the heuristic solutions and those of the optimal solutions are less than 3%, and the heuristics require much less time to obtain the good quality solutions. As a result, it is shown that the model, coupled with the algorithms, can be an effective planning tool to assist the company in routing and scheduling its fleet to service reservation customers.     

An online speed profile generation approach for efficient airport ground movement

The precise guidance and control of taxiing aircraft based on four-dimensional trajectories (4DTs) has been recognised as a promising means to ensure safe and efficient airport ground movement in the context of ever growing air traffic demand. In this paper, a systematic approach for online speed profile generation is proposed. The aim is to generate fuel-efficient speed profiles respecting the timing constraints imposed by routing and scheduling, which ensures conflict-free movement of aircraft in the planning stage. The problem is first formulated as a nonlinear optimisation model, which uses a more flexible edge-based speed profile definition. A decomposed solution approach (following the framework of matheuristic) is then proposed to generate feasible speed profiles in real time. The decomposed solution approach reduces the nonlinear optimisation model into three tractable constituent problems. The control point arrival time allocation problem is solved using linear programming. The control point speed allocation problem is solved using particle swarm optimisation. And the complete speed profile between control points is determined using enumeration. Finally, improved speed profiles are generated through further optimisation upon the feasible speed profiles. The effectiveness and advantages of the proposed approach are validated using datasets of real-world airports.     

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.     

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.     

Scheduling railway freight delivery appointments using a bid price approach

This paper proposes a method for establishing aggressive but achievable delivery appointment times for railroad shipments, taking into account individual customer needs and forecasted available train capacity. The concept of scheduling appointment times is directly patterned after current motor carrier industry practice, so that customers can plan for rail or truck deliveries in the same way.A shipment routing problem is decomposed into a deterministic “dynamic car scheduling” (DCS) process for shipments already accepted and a stochastic “train segment pricing” (TSP) process for forecasting future demands which have not yet called in and for which delivery appointments have yet to be scheduled. Both are formulated as multi-commodity network flow (MCNF) problems, where each shipment is treated as a separate commodity. Gain coefficients represent recapture probabilities that a specific customer will accept a carrier’s service offer.A comparison with a widely used revenue management formulation is given. A Lagrangian heuristic for obtaining a primal solution is also described. The problem is solved within a 1% gap using the subgradient algorithm.     

Airline flight scheduling for oligopolistic competition with direct flights and a point to point network

In this research, we consider a flight scheduling problem for oligopolistic competition with direct flights and a point to point network. In this type of market situation, passengers are sensitive to the departure time of a flight rather than the transfer time. The airline needs to carefully consider the departure times of their competitors when determining their own. Therefore, unlike past approaches which have only considered one departure time for a competitor's flight, a flight scheduling framework is developed which takes into consideration possible competitor departure times. The framework includes two dependent stages which are repeatedly solved during the solution process. In addition, an upper bound model is also designed to evaluate the solution quality. Numerical tests are performed using data for Taiwan's outlying island route which is characterized by the above market situation. Satisfactory results are obtained, showing the good performance of the framework. Copyright © 2017 John Wiley & Sons, Ltd.     

Network-oriented household activity pattern problem for system optimization

The recently emerging trend of self-driving vehicles and information sharing technologies, made available by private technology vendors, starts creating a revolutionary paradigm shift in the coming years for traveler mobility applications. By considering a deterministic traveler decision making framework at the household level in congested transportation networks, this paper aims to address the challenges of how to optimally schedule individuals’ daily travel patterns under the complex activity constraints and interactions. We reformulate two special cases of household activity pattern problem (HAPP) through a high-dimensional network construct, and offer a systematic comparison with the classical mathematical programming models proposed by Recker (1995). Furthermore, we consider the tight road capacity constraint as another special case of HAPP to model complex interactions between multiple household activity scheduling decisions, and this attempt offers another household-based framework for linking activity-based model (ABM) and dynamic traffic assignment (DTA) tools. Through embedding temporal and spatial relations among household members, vehicles and mandatory/optional activities in an integrated space-time-state network, we develop two 0–1 integer linear programming models that can seamlessly incorporate constraints for a number of key decisions related to vehicle selection, activity performing and ridesharing patterns under congested networks. The well-structured network models can be directly solved by standard optimization solvers, and further converted to a set of time-dependent state-dependent least cost path-finding problems through Lagrangian relaxation, which permit the use of computationally efficient algorithms on large-scale high-fidelity transportation networks.     

A math-heuristic algorithm for the integrated air service recovery

A sophisticated flight schedule might be easily disrupted due to adverse weather, aircraft mechanical failures, crew absences, etc. Airlines incur huge costs stemming from such flight schedule disruptions in addition to the serious inconveniences experienced by passengers. Therefore, an efficient recovery solution that simultaneously decreases an airline's recovery cost while simultaneously mitigating passenger dissatisfaction is of great importance to the airline industry. In this paper, we study the integrated airline service recovery problem in which the aircraft and passenger schedule recovery problems are simultaneously addressed, with the objective of minimizing aircraft recovery and operating costs, passenger itinerary delay cost, and passenger itinerary cancellation cost.Recognizing the inherent difficulty in modeling the integrated airline service recovery problem within a single formulation (due to its huge solution space and quick response requirement), we propose a three-stage sequential math-heuristic framework to efficiently solve this problem, wherein the flight schedules and aircraft rotations are recovered in the first stage, Then, a flight rescheduling problem and passenger schedule recovery problems are iteratively solved in the next two stages. Time-space network flow representations, along with mixed-integer programming formulations, and algorithms that take advantages of the underlying problem structures, are proposed for each of three stages. This algorithm was tested on realistic data provided by the ROADEF 2009 challenge and the computational results reveal that our algorithm generated the best solution in nearly 72% of the test instances, and a near-optimal solution was achieved in the remaining instances within an acceptable timeframe. Furthermore, we also ran additional computational runs to explore the underlying characteristics of the proposed algorithm, and the recorded insights can serve as a useful guide during practical implementations of this algorithm.     

Within day rescheduling microsimulation combined with macrosimulated traffic

The concept of rescheduling is essential to activity-based modeling in order to calculate effects of both unexpected incidents and adaptation of individuals to traffic demand management measures. When collaboration between individuals is involved or timetable based public transportation modes are chosen, rescheduling becomes complex. This paper describes a new framework to investigate algorithms for rescheduling at a large scale. The framework allows to explicitly model the information flow between traffic information services and travelers. It combines macroscopic traffic assignment with microscopic simulation of agents adapting their schedules. Perception filtering is introduced to allow for traveler specific interpretation of perceived macroscopic data and for information going unnoticed; perception filters feed person specific short term predictions about the environment required for schedule adaptation. Individuals are assumed to maximize schedule utility. Initial agendas are created by the FEATHERS activity-based schedule generator for mutually independent individuals using an undisturbed loaded transportation network. The new framework allows both actor behavior and external phenomena to influence the transportation network state; individuals interpret the state changes via perception filtering and start adapting their schedules, again affecting the network via updated traffic demand. The first rescheduling mechanism that has been investigated uses marginal utility that monotonically decreases with activity duration and a monotonically converging relaxation algorithm to efficiently determine the new activity timing. The current framework implementation is aimed to support re-timing, re-location and activity re-sequencing; re-routing at the level of the individual however, requires microscopic travel simulation.     

The time slot allocation problem under uncertain capacity

This paper presents two stochastic programming models for the allocation of time slots over a network of airports. The proposed models address three key issues. First, they provide an optimization tool to allocate time slots, which takes several operational aspects and airline preferences into account; second, they execute the process on a network of airports; and third they explicitly include uncertainty. To the best of our knowledge, these are the first models for time slot allocation to consider both the stochastic nature of capacity reductions and the problem’s network structure. From a practical viewpoint, the proposed models provide important insights for the allocation of time slots. Specifically, they highlight the tradeoff between the schedule/request discrepancies, i.e., the time difference between allocated time slots and airline requests, and operational delays. Increasing schedule/request discrepancies enables a reduction in operational delays. Moreover, the models are computationally viable. A set of realistic test instances that consider the scheduling of four calendar days on different European airport networks has been solved within reasonable – for the application’s context – computation times. In one of our test instances, we were able to reduce the sum of schedule/request discrepancies and operational delays by up to 58%. This work provides slot coordinators with a valuable decision making tool, and it indicates that the proposed approach is very promising and may lead to relevant monetary savings for airlines and aircraft operators.     

Evolutionary crew scheduling with adaptive chromosomes

This paper presents an adaptive evolutionary approach incorporating a hybrid genetic algorithm (GA) for public transport crew scheduling problems, which are well-known to be NP-hard. To ensure the search efficiency, a suitable chromosome representation has to be determined first. Unlike a canonical GA for crew scheduling where the chromosome length is fixed, the chromosome length in the proposed approach may vary adaptively during the iterative process, and its initial value is elaborately designated as the lower bound of the number of shifts to be used in an unachievable optimal solution. Next, the hybrid GA with such a short chromosome length is employed to find a feasible schedule. During the GA process, the adaptation on chromosome lengths is achieved by genetic operations of crossover and mutation with removal and replenishment strategies aided by a simple greedy algorithm. If a feasible schedule cannot be found when the GA’s termination condition is met, the GA will restart with one more gene added. The above process is repeated until a feasible solution is found. Computational experiments based on 11 real-world crew scheduling problems in China show that, compared to a fuzzy GA known to be well performed for crew scheduling, better solutions are found for all the testing problems. Moreover, the algorithm works fast, has achieved results close to the lower bounds obtained by a standard linear programming solver in terms of the number of shifts, and has much potential for future developments.     

Network traffic control based on a mesoscopic dynamic flow model

The paper focuses on Network Traffic Control based on aggregate traffic flow variables, aiming at signal settings which are consistent with within-day traffic flow dynamics. The proposed optimisation strategy is based on two successive steps: the first step refers to each single junction optimisation (green timings), the second to network coordination (offsets). Both of the optimisation problems are solved through meta-heuristic algorithms: the optimisation of green timings is carried out through a multi-criteria Genetic Algorithm whereas offset optimisation is achieved with the mono-criterion Hill Climbing algorithm. To guarantee proper queuing and spillback simulation, an advanced mesoscopic traffic flow model is embedded within the network optimisation method. The adopted mesoscopic traffic flow model also includes link horizontal queue modelling. The results attained through the proposed optimisation framework are compared with those obtained through benchmark tools.     

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.     

Traveler delay costs and value of time with trip chains, flexible activity scheduling and information

The delay costs of traffic disruptions and congestion and the value of travel time reliability are typically evaluated using single trip scheduling models, which treat the trip in isolation of previous and subsequent trips and activities. In practice, however, when activity scheduling to some extent is flexible, the impact of delay on one trip will depend on the actual and predicted travel time on itself as well as other trips, which is important to consider for long-lasting disturbances and when assessing the value of travel information. In this paper we extend the single trip approach into a two trips chain and activity scheduling model. Preferences are represented as marginal activity utility functions that take scheduling flexibility into account. We analytically derive trip timing optimality conditions, the value of travel time and schedule adjustments in response to travel time increases. We show how the single trip models are special cases of the present model and can be generalized to a setting with trip chains and flexible scheduling. We investigate numerically how the delay cost depends on the delay duration and its distribution on different trips during the day, the accuracy of delay prediction and travel information, and the scheduling flexibility of work hours. The extension of the model framework to more complex schedules is discussed.     

Integrated airline planning: Robust update of scheduling and fleet balancing under demand uncertainty

The airline schedule planning problem is defined as the sequence of decisions that need to be made to obtain a fully operational flight schedule. Historically, the airline scheduling problem has been sequentially solved. However, there have already been many attempts in order to obtain airline schedules in an integrated way. But due to tractability issues it is nowadays impossible to determine a fully operative and optimal schedule with an integrated model which accounts for all the key airline related aspects such as competitive effects, stochastic demand figures and uncertain operating conditions. Airlines usually develop base schedules, which are obtained much time in advance to the day of operations and not accounting for all the related uncertainty. This paper proposes a mathematical model in order to update base schedules in terms of timetable and fleet assignments while considering stochastic demand figures and uncertain operating conditions, and where robust itineraries are introduced in order to ameliorate miss-connected passengers. The proposed model leads to a large-scale problem which is difficult to be solved. Therefore, a novel improved and accelerated Benders decomposition approach is proposed. The analytical work is supported with case studies involving the Spanish legacy airline, IBERIA. The presented approach shows that the number of miss-connected passengers may be reduced when robust planning is applied.     

A rolling horizon algorithm for auto-carrier transportation

This paper introduces a rolling horizon algorithm to plan the delivery of vehicles to automotive dealers by a heterogeneous fleet of auto-carriers. The problem consists in scheduling the deliveries over a multiple-day planning horizon during which requests for transportation arrive dynamically. In addition, the routing of the auto-carriers must take into account constraints related to the loading of the vehicles on the carriers. The objective is to minimize the sum of traveled distances, fixed costs for auto-carrier operation, service costs, and penalties for late deliveries. The problem is solved by a heuristic that first selects the vehicles to be delivered in the next few days and then optimizes the deliveries by an iterated local search procedure. A branch-and-bound search is used to check the feasibility of the loading. To handle the dynamic nature of the problem, the complete algorithm is applied repeatedly in a rolling horizon framework. Computational results on data from a major European logistics service provider show that the heuristic is fast and yields significant improvements compared to the sequential solution of independent daily problems.     

Service network design with asset management: Formulations and comparative analyses

In this paper, we address the service network design with asset management problem, which integrates asset management considerations into service network design models for consolidation-based freight carriers. We propose model formulations based on arc variables for both flow and design, as well as formulations with path flow variables and new cycle design variables. Problem instances reflecting actual planning problems are used in the computational study to analyze the strengths and weaknesses of the various model formulations and the impact of asset management considerations on the transportation plan and the computational effort. Experimental results indicate that formulations based on cycle variables outperform traditional arc-based formulations, and that considering asset management issues may significantly impact the outcome of service planning models.     

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.     

The vehicle platooning problem: Computational complexity and heuristics

We create a mathematical framework for modeling trucks traveling in road networks, and we define a routing problem called the platooning problem. We prove that this problem is NP-hard, even when the graph used to represent the road network is planar. We present integer linear programming formulations for instances of the platooning problem where deadlines are discarded, which we call the unlimited platooning problem. These allow us to calculate fuel-optimal solutions to the platooning problem for large-scale, real-world examples. The problems solved are orders of magnitude larger than problems previously solved exactly in the literature. We present several heuristics and compare their performance with the optimal solutions on the German Autobahn road network. The proposed heuristics find optimal or near-optimal solutions in most of the problem instances considered, especially when a final local search is applied. Assuming a fuel reduction factor of 10% from platooning, we find fuel savings from platooning of 1–2% for as few as 10 trucks in the road network; the percentage of savings increases with the number of trucks. If all trucks start at the same point, savings of up to 9% are obtained for only 200 trucks.