Solution methods for the taxi pooling problem

In Taiwan, taxi pooling is currently performed by some taxi companies using a trial-and-error experience-based method, which is neither effective nor efficient. There is, however, little in the literature on effective models and solution methods for solving the taxi pooling problem. Thus, in this study we employ network flow techniques and a mathematical programming method to develop a taxi pooling solution method. This method is composed of three models. First, a fleet routing/scheduling model is constructed to produce fleet/passenger routes and schedules. A solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the fleet routing/scheduling model. Then, two single taxi-passenger matching models are constructed with the goals of decreasing number of passenger transfers and matching all passengers and taxis. These two taxi-passenger matching models are directly solved using a mathematical programming solver. For comparison with the solution method, we also develop another heuristic by modifying a heuristic recently proposed for solving a one-to-many taxi pooling problem. The performance of the solution method and the additional heuristic are evaluated by carrying out a case study using real data and suitable assumptions. The test results show that these two solution methods could be useful in practice.     

Optimization of multiple objective gate assignments

This paper proposes a multiple objective model to help airport authorities to efficiently and effectively solve gate assignment problems. The model is formulated as a multiple objective zero–one integer program. To efficiently solve large-scale problems in practice, we used the weighting method, the column generation approach, the simplex method and the branch-and-bound technique to develop a solution algorithm. To test how well the model may be applied in actual operations, a case study regarding the operation of Chiang Kai-Shek (CKS) Airport was performed. The results show that the model could be useful for actual operations.     

A Heuristic Algorithm for the Allocation of Airport Runway System Capacity

Abstract

This paper develops a heuristic algorithm for the allocation of airport runway capacity to minimise the cost of arrival and departure aircraft/flight delays. The algorithm is developed as a potential alternative to optimisation models based on linear and integer programming. The algorithm is based on heuristic (‘greedy’) criteria that closely reflect the ‘rules of thumb’ used by air traffic controllers. Using inputs such as arrival and departure demand, airport runway system capacity envelopes and cost of aircraft/flight delays, the main output minimises the cost of arrival and departure delays as well as the corresponding interdependent airport runway system arrival and departure capacity allocation. The algorithm is applied to traffic scenarios at three busy US airports. The results are used to validate the performance of the proposed heuristic algorithm against results from selected benchmarking optimisation models.     

Assessing the viability of enabling a round-trip carsharing system to accept one-way trips: Application to Logan Airport in Boston

Although one-way carsharing is suitable for more trip purposes than round-trip carsharing, many companies in the world operate only in the round-trip market. In this paper, we develop a method that optimizes the design of a one-way carsharing service between selected origin–destination pairs of an existing round-trip carsharing system. The goal is to supplement the established round-trip services with new one-way services and increase profitability. We develop an integer programming model to select the set of new one-way services and apply it to the case study of Boston, USA, considering only trips with one endpoint at a station in the round-trip Zipcar service network and the other endpoint at Logan Airport. The airport was chosen as a necessary endpoint for a one-way service because it is a very significant trip generator for which the round-trip carsharing is not suitable. Results show that these supplemental one-way services could be profitable. Enabling relocation operations between the existing round-trip stations and the Airport greatly improves the demand effectively satisfied, leads to an acceptable airport station size (in terms of the number of parking spots required), and is profitable; however, these benefits come with the need to manage relocation operations.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints

This paper presents new models for multiple depot vehicle scheduling problem (MDVS) and multiple depot vehicle scheduling problem with route time constraints (MDVSRTC). The route time constraints are added to the MDVS problem to account for the real world operational restrictions such as fuel consumption. Compared to existing formulations, this formulation decreases the size of the problem by about 40% without eliminating any feasible solution. It also presents an exact and two heuristic solution procedures for solving the MDVSRTC problem. Although these methods can be used to solve medium size problems in reasonable time, real world applications in large cities require that the MDVSRTC problem size be reduced. Two techniques are proposed to decrease the size of the real world problems. For real-world application, the problem of bus transit vehicle scheduling at the mass transit administration (MTA) in Baltimore is studied. The final results of model implementation are compared to the MTA's schedules in January 1998. The comparison indicates that, the proposed model improves upon the MTA schedules in all respects. The improvements are 7.9% in the number of vehicles, 4.66% in the operational time and 5.77% in the total cost.     

Optimal shipment decisions for an airfreight forwarder: Formulation and solution methods

We study the freight forwarder’s shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times.After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems.     

A heuristic for the train pathing and timetabling problem

In a railroad system, train pathing is concerned with the assignment of trains to links and tracks, and train timetabling allocates time slots to trains. These important tasks were traditionally done manually, but there is an increasing move toward automated software based on mathematical models and algorithms. Most published models in the literature either focus on train timetabling only, or are too complicated to solve when facing large instances. In this paper, we present an optimization heuristic that includes both train pathing and train timetabling, and has the ability to solve real-sized instances. This heuristic allows the operation time of trains to depend on the assigned track, and also lets the minimum headway between the trains to depend on the trains’ relative status. It generates an initial solution with a simple rule, and then uses a four-step process to derive the solution iteratively. Each iteration starts by altering the order the trains travel between stations, then it assigns the services to the tracks in the stations with a binary integer program, determines the order they pass through the stations with a linear program, and uses another linear program to produce a timetable. After these four steps, the heuristic accepts or rejects the new solution according to a Threshold Accepting rule. By decomposing the original complex problem into four parts, and by attacking each part with simpler neighborhood-search processes or mathematical programs, the heuristic is able to solve realistic instances. When tested with two real-world examples, one from a 159.3 km, 29-station railroad that offers 44 daily services, and another from a 345 km, eight-station high-speed rail with 128 services, the heuristic obtained timetables that are at least as good as real schedules.     

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.     

The European freight railway system as a hub-and-spoke network

This paper addresses a hub-and-spoke network problem for railroad freight, where a central planner is to find transport routes, frequency of service, length of trains to be used, and transportation volume. Hub-and-spoke networks, often found in air freight, have not been favoured by railways in the past. Such a structure could be profitable, however, if there exist concentrated freight flows on some service links. We formulate a linear integer programming model whose objective function includes not only the typical operational cost, but also cost due to the transit time spent by freight in the network. We then develop heuristic algorithms to solve large scale instances occurring in rail freight systems in France plus Italy; Germany; and a 10-country European network. By assuming that every node is equipped with consolidation capability, we let the final solution naturally reveal potential hub locations, the impact of several of which is studied by sensitivity analysis.     

Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.     

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.     

Air traffic assignment to reduce population noise exposure using activity-based approach

Aircraft noise has been regarded as one of the major environmental issues related to air transport. Many airports have introduced a variety of measures to reduce its impact. Several air traffic assignment strategies have been proposed in order to allocate noise more wisely. Even though each decision regarding the assignment of aircraft to routes should consider population exposure to noise, none of the air traffic assignment strategies has addressed daily migrations of population and number of people exposed to noise. The aim of this research is to develop a mathematical model and a heuristic algorithm that could assign aircraft to departure and arrival routes so that number of people exposed to noise is as low as possible, taking into account temporal and spatial variations in population in an airport’s vicinity. The approach was demonstrated on Belgrade airport to show the benefits of the proposed model. Numerical example showed that population exposure to noise could be reduced significantly by applying the proposed air traffic assignment model. As a consequence of the proposed air traffic assignment, overall fuel consumption increased by less than 1%.     

Integrated sequencing and merging aircraft to parallel runways with automated conflict resolution and advanced avionics capabilities

Congestion in Terminal Maneuvering Area (TMA) in hub airports is the main problem in Chinese air transportation. In this paper we propose a new system to integrated sequence and merge aircraft to parallel runways at Beijing Capital International Airport (BCIA). This system is based on the advanced avionics capabilities. Our methodology integrates a Multi-Level Point Merge (ML-PM) system, an economical descent approaches procedure, and a tailored heuristic algorithm to find a good, systematic, operationally-acceptable solution. First, Receding Horizontal Control (RHC) technique is applied to divide the entire 24 h of traffic into several sub-problems. Then in each sub-problem, it is optimized on given objectives (conflict, deviation from Estimated Time of Arrival (ETA) on the runway and makespan of the arrival flow). Four decision variables are designed to control the trajectory: the entry time, the entry speed, the turning time on the sequencing leg, and the landing runway allocation. Based on these variables, the real time trajectories are generated by the simulation module. Simulated Annealing (SA) algorithm is used to search the best solution for aircraft to execute. Finally, the conflict-free, least-delay, and user-preferred trajectories from the entry point of TMA to the landing runway are defined. Numerical results show that our optimization system has very stable de-conflict performance to handle continuously dense arrivals in transition airspace. It can also provide the decision support to assist flow controllers to handle the asymmetric arrival flows on different runways with less fuel consumption, and to assist tactical controllers to easily re-sequence aircraft with more relaxed position shifting. Moreover, our system can provide the fuel consumption prediction, and runway assignment information to assist airport and airlines managers for optimal decision making. Theoretically, it realizes an automated, cooperative and green control of routine arrival flows. Although the methodology defined here is applied to the airport BCIA, it could also be applied to other airports in the world.     

Development of efficient stop planning optimization process for high‐speed rail systems

The Taiwan High Speed Rail (THSR) has recently added three additional stations to its original network. Although the three additional stations can improve accessibility to the system, these new stations can present difficulties in the transportation planning process, particularly for planning of train stops. The additional stations may benefit some passengers, but may also lengthen the travel time for the other passengers. Therefore, the main challenge faced by THSR is finding an efficient way to design appropriate stopping patterns. Past studies on stop planning usually adopted meta‐heuristics or decomposition methods to solve this complex problem. Although these solution techniques can improve solution efficiency, none of them can guarantee the optimality of the solution and capture the transfer movement of different stopping patterns. In this research, we proposed an innovative network structure to address complex stop planning problems for high‐speed rail systems. Given its special network structure, two binary integer programming models were developed to simultaneously form and determine the optimal stopping patterns for real‐world THSR stop planning problems. An optimization process was also developed to accurately estimate the station transfer time corresponding to the variation in stopping patterns and passenger flow. Results of the case studies suggest that the proposed binary integer programming models exhibit superior solution quality and efficiency over existing exact optimization models. Consequently, using this stop planning optimization process can help high‐speed rail system planners in designing optimal stopping patterns that correspond to passenger demand. Copyright © 2017 John Wiley & Sons, Ltd.     

A network model for gate assignment

In this research we developed a network model that will help the airport authorities assign flights to gates both efficiently and effectively. The model was formulated as a multi-commodity network flow problem. An algorithm based on the Lagrangian relaxation, with subgradient methods, accompanied by a shortest path algorithm and a Lagrangian heuristic was developed to solve the problem. The model was tested using data from Chiang Chiek-Shek Airport.     

Analysis of an O(N2) heuristic for the single vehicle many-to-many Euclidean dial-a-ride problem

We develop an O(N²) heuristic to solve the single vehicle many-to-many Euclidean Dial-A-Ride problem. The heuristic is based on the Minimum Spanning Tree of the modes of the problem. The algorithm's worst case performance is four times the length of the optimal Dial-A-Ride tour. An analysis of the algorithm's average performance reveals that in terms of sizes of single-vehicle problems that are likely to be encountered in the real world (up to 100 nodes) and in terms of computational complexity, the O(N²) heuristic performs equally well, or, in many cases, better than heuristics described earlier by Stein for the same problem. The performance of the heuristic exhibits statistical stability over a broad range of problem sizes.     

Inter-city bus routing and timetable setting under stochastic demands

Vehicle fleet routing and timetable setting are essential to the enhancement of an inter-city bus carrier’s operating cost, profit, level of service and competitiveness in the market. In past research the average passenger demand has usually served as input in the production of the final fleet routes and timetables, meaning that stochastic disturbances arising from variations in daily passenger demand in actual operations are neglected. To incorporate the stochastic disturbances of daily passenger demands that occur in actual operations, in this research, we established a stochastic-demand scheduling model. We applied a simulation technique, coupled with link-based and path-based routing strategies, to develop two heuristic algorithms to solve the model. To evaluate the performance of the proposed model and the two solution algorithms, we developed an evaluation method. The test results, regarding a major Taiwan inter-city bus operation, were good, showing that the model and the solution algorithms could be useful in practice.     

Optimization of refuelling truck fleets at an airport

This paper considers the process of aircraft refuelling using refuelling trucks at an airport. The problem which arises is to determine the minimum number of refuelling trucks and their routes for the given demand (schedule and fuel quantities). The constraint is that there is no aircraft departure delay due to the refuelling process. The optimum solution is found here using the branch-and-bound technique. This solution is compared with results obtained on the basis of random assignment and a few conclusions are made. The paper also presents a model application example based on real life data from a medium-sized airport.     

A decision support system for integrated hazardous materials routing and emergency response decisions

Hazardous materials routing constitutes a critical decision in mitigating the associated transportation risk. This paper presents a decision support system for assessing alternative distribution routes in terms of travel time, risk and evacuation implications while coordinating the emergency response deployment decisions with the hazardous materials routes. The proposed system provides the following functionalities: (i) determination of alternative non-dominated hazardous materials distribution routes in terms of cost and risk minimization, (ii) specification of the hazardous materials first-response emergency service units locations in order to achieve timely response to an accident, and (iii) determination of evacuation paths from the impacted area to designated shelters and estimation of the associated evacuation time. The proposed system has been implemented, used and evaluated for assessing alternative hazardous materials routing decisions within the heavily industrialized area of Thriasion Pedion of Attica, Greece. The implementation of the aforementioned functionalities is based on two new integer programming models for the hazardous materials routing and the emergency response units location problems, respectively. A simplified version of the routing model is solved by an existing heuristic algorithm developed by the authors. A new Lagrangean relaxation heuristic algorithm has been developed for solving the emergency response units location problem. The focus of this paper is on the exposition of the proposed decision support system components and functionalities. Special emphasis is placed on the presentation of the two new mathematical models and the new solution method for the location model.