A multi-objective train scheduling model and solution

This paper develops a multi-objective optimization model for the passenger train-scheduling problem on a railroad network which includes single and multiple tracks, as well as multiple platforms with different train capacities. In this study, lowering the fuel consumption cost is the measure of satisfaction of the railway company and shortening the total passenger-time is being regarded as the passenger satisfaction criterion. The solution of the problem consists of two steps. First the Pareto frontier is determined using the -constraint method, and second, based on the obtained Pareto frontier detailed multi-objective optimization is performed using the distance-based method with three types of distances. Numerical examples are given to illustrate the model and solution methodology.     

A Value-at-Risk (VAR) approach to routing rail hazmat shipments

Hazardous materials (hazmat) accidents are rare though the consequences could be disastrous. Given the possibility of low probability – high consequence event, a risk-averse routing hazmat shipment is necessary. We propose a value-at-risk (VaR) approach to route rail hazmat shipments, using the best train configuration, over a given railroad network with limited number of train services such that the transport risk as measured by VaR is minimized. Freight train derailment reports of the Federal Railroad Administration were analyzed to develop expressions that would incorporate characteristics of railroad accidents, and then to estimate the different inputs. The proposed methodology was used to study several problem instances generated using the realistic network of a railroad operator, and to demonstrate that it is possible to develop different routes for shipments depending on the risk preference of the decision maker.     

Train design and routing optimization for evaluating criticality of freight railroad infrastructures

Freight transportation by railroads is an integral part of the U.S. economy. Identifying critical rail infrastructures can help stakeholders prioritize protection initiatives or add necessary redundancy to maximize rail network resiliency. The criticality of an infrastructure element, link or yard, is based on the increased cost (delay) incurred when that element is disrupted. An event of disruption can cause heavy congestion so that the capacity at links and yards should be considered when freight is re-routed. This paper proposes an optimization model for making-up and routing of trains in a disruptive situation to minimize the system-wide total cost, including classification time at yards and travel time along links. Train design optimization seeks to determine the optimal number of trains, their routes, and associated blocks, subject to various capacity and operational constraints at rail links and yards. An iterative heuristic algorithm is proposed to attack the computational burden for real-world networks. The solution algorithm considers the impact of volume on travel time in a congested or near-congested network. The proposed heuristics provide quality solutions with high speed, demonstrated by numerical experiments for small instances. A case study is conducted for the network of a major U.S. Class-I railroad based on publicly available data. The paper provides maps showing the criticality of infrastructure in the study area from the viewpoint of strategic planning.     

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

This paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal design of a short‐turning strategy considering seat availability

We develop a methodology to optimize the schedule coordination of a full‐stop service pattern and a short‐turning service pattern on a bus route. To capture the influence of bus crowding and seat availability on passengers' riding experience, we develop a Markov model to describe the seat‐searching process of a passenger and an approach to estimate the transition probabilities of the Markov model. An optimization model that incorporates the Markov model is proposed to design the short‐turning strategy. The proposed model minimizes the total cost, which includes operational cost, passengers' waiting time cost and passengers' in‐vehicle travel time cost. Algorithm is developed to produce optimal values of the decision variables. The proposed methodology is evaluated in a case study. Compared with methodologies that ignore the effect of bus crowding, the proposed methodology could better balance bus load along the route and between two service patterns, provide passengers with better riding experience and reduce the total cost. In addition, it is shown that the optimal design of the short‐turning strategy is sensitive to seat capacity. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimizing train operational plan in an urban rail corridor based on the maximum headway function

The train operational plan (TOP) plays a crucial role in the efficient and effective operation of an urban rail system. We optimize the train operational plan in a special network layout, an urban rail corridor with one terminal yard, by decomposing it into two sub-problems, i.e., the train departure profile optimization and the rolling stock circulation optimization. The first sub-problem synthetically optimizes frequency setting, timetabling and the rolling stock circulation at the terminal without a yard. The maximum headway function is generated to ensure the service of the train operational plan without considering travel demand, then we present a model to minimize the number of train trips, and design a heuristic algorithm to maximize the train headway. On the basis of a given timetable, the rolling stock circulation optimization only involves the terminal with a yard. We propose a model to minimize the number of trains and yard–station runs, and an algorithm to find the optimal assignment of train-trip pair connections is designed. The computational complexities of the two algorithms are both linear. Finally, a real case study shows that the train operational plan developed by our approach enables a better match of train headway and travel demand, and reduces the operational cost while satisfying the requirement of the level of service.     

Macroscopic multiple-station short-turning model in case of complete railway blockages

In case of railway disruptions, traffic controllers are responsible for dealing with disrupted traffic and reduce the negative impact for the rest of the network. In case of a complete blockage when no train can use an entire track, a common practice is to short-turn trains. Trains approaching the blockage cannot proceed according to their original plans and have to short-turn at a station close to the disruption on both sides. This paper presents a Mixed Integer Linear Program that computes the optimal station and times for short-turning the affected train services during the three phases of a disruption. The proposed solution approach takes into account the interaction of the traffic between both sides of the blockage before and after the disruption. The model is applied to a busy corridor of the Dutch railway network. The computation time meets the real-time solution requirement. The case study gives insight into the importance of the disruption period in computing the optimal solution. It is concluded that different optimal short-turning solutions may exist depending on the start time of the disruption and the disruption length. For periodic timetables, the optimal short-turning choices repeat due to the periodicity of the timetable. In addition, it is observed that a minor extension of the disruption length may result in less delay propagation at the cost of more cancellations.     

Optimizing the freight train connection service network of a large-scale rail system

This paper presents a formulation and solution for the train connection services (TCSs) problem in a large-scale rail network in order to determine the optimal freight train services, the frequency of services, and the distribution of classification workload among yards. TCS problem is modeled as a bi-level programming problem. The upper-level is intended to find an optimal train connection service, and the lower-level is used for assigning each shipment to a sequence of train services and determining the frequency of services.Our model solves the TCS problem of the China railway system, which is one of the largest railway systems in the world. The system consists of 5544 stations, and over 520,000 shipments using this system for a year period. A subnetwork is defined with 127 yards having some minimum level of reclassification resources and 14,440 demands obtained by aggregating 520,000 shipments to the subnetwork. We apply a simulated annealing algorithm to the data for optimal computation after pre-processing and get an excellent result. Comparing our optimal solution with the existing plan result, there are improvements of about 20.8% in the total cost.     

Metro disruption management: Optimal initiation time of substitute bus services under uncertain system recovery time

Determining the initiation time of substitute bus (SB) services is critical for metro disruption management, especially under uncertain recovery time. This study develops a mathematical formulation to determine the optimal initiation time (OIT) of SB services by trading-off their initiation cost and passenger delay cost, thereby minimizing the total system cost. Given the probability distribution of metro disruption duration, we determine the OIT by formulating an optimization problem to minimize the expected total system cost. We then conduct sensitivity analyses of the initiation cost of SB services, passenger value of time, and SB services rate. The results show that SB services ought to be activated only if the metro incident lasts longer than a certain time interval, depending on the factors mentioned earlier, and the OIT should advance with the predicted incident duration. This paper derives analytical results for the case of linear passenger arrival, and determines the results numerically for the case of non-linear passenger arrival when analytical closed-form solutions are not available. The findings will facilitate transit operators to develop response plans in the aftermath of a metro disruption.     

A stochastic optimization approach for the selection of reflective cracking mitigation techniques

PurposeIn Hot Mix Asphalt (HMA) overlays, the existing cracks in the underlying pavements can propagate upward to the new added overlay and may cause Reflective Cracks (RC). These cracks allow water infiltration to the underlying layers and causes further moisture damage as well as weakening the unbound layers. Over the years, several methods have been developed for mitigating the RCs. This study aims to investigate the current reflective cracking mitigation methods and develop a methodology for the selection of appropriate mitigation technique. The developed model is then applied to a case study in the state of Florida.MethodTo accomplish this goal, a nationwide literature review was conducted to better understand the current in practice methods in the United States. Moreover, a life cycle cost analysis (LCCA) in five different road types was performed to find the annuity of roadway rehabilitation for each of the mitigation methods. The uncertainty in the LCCA results is represented using Exploratory Modeling and Analysis (EMA) method. Then through a Multi Criteria Decision Making (MCDM) model, a stochastic optimization model was developed to find the appropriate reflective cracking mitigation solution under Florida’s climate and road conditions, based on different cost and performance weights.ResultsBased on the available data for the state of Florida, the LCCA results indicate that the annuity of maintaining the roadway with Fabrics and ISAC are lower compared to other methods. However, the results of stochastic optimization model reveal that while looking at the performance and cost at the same time, different methods would be more feasible. For instance, while the cost of the used method does not matter at all and only performance matters, STRATA® is more probable to be the appropriate mitigation technique. The findings of this research are critical for decision makers to better understand the most cost-effective mitigation technique in different conditions.     

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.     

A cost and expected consequence approach to planning and managing railroad transportation of hazardous materials

Although hazardous materials (hazmat) account for around 140 million tons of all railroad freight traffic in the US, it has not received much attention from academic researchers. This is surprising especially when one considers the volume of hazmat moved by railroads in both North America and Europe. In this paper we develop a bi-objective optimization model, where cost is determined based on the characteristics of railroad industry and the determination of transport risk incorporates the dynamics of railroad accident. The optimization model and the solution framework is used to solve a realistic-size problem instance based in south-east US, which is then analyzed to gain managerial insights. In addition, a risk-cost frontier depicting non-dominated solutions is developed, followed by conclusion.     

Optimization of headways with stop‐skipping control: a case study of bus rapid transit system

Bus rapid transit system is designed to provide high‐quality and cost‐efficient passenger transportation services. In order to achieve this design objective, effective scheduling strategies are required. This research aims at improving the operation efficiency and service quality of a BRT system through integrated optimization of its service headways and stop‐skipping strategy. Based on cost analysis for both passengers and operation agencies, an optimization model is established. A genetic algorithms based algorithm and an application‐oriented solution method are developed. Beijing BRT Line 2 has been chosen as a case study, and the effectiveness of the optimal headways with stop‐skipping services under different demand levels has been analyzed. The results has shown that, at a certain demand level, the proposed operating strategy can be most advantageous for passengers with an accepted increase of operating costs, under which the optimum headway is between 3.5 and 5.5 min for stop‐skipping services during the morning peak hour depending on the demand with the provision of stop‐skipping services. The effectiveness of the optimal headways with stop‐skipping services is compared with those of existing headways and optimal headways without stop‐skipping services. The results show that operating strategies under the optimal headways with stop‐skipping services outperforms the other two operating strategies with respect to total costs and in‐vehicle time for passengers. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi-objective optimization of train routing problem combined with train scheduling on a high-speed railway network

Based on train scheduling, this paper puts forward a multi-objective optimization model for train routing on high-speed railway network, which can offer an important reference for train plan to provide a better service. The model does not only consider the average travel time of trains, but also take the energy consumption and the user satisfaction into account. Based on this model, an improved GA is designed to solve the train routing problem. The simulation results demonstrate that the accurate algorithm is suitable for a small-scale network, while the improved genetic algorithm based on train control (GATC) applies to a large-scale network. Finally, a sensitivity analysis of the parameters is performed to obtain the ideal parameters; a perturbation analysis shows that the proposed method can quickly handle the train disturbance.     

Non-discriminatory train dispatching in a rail transport market with multiple competing and collaborative train operating companies

Train dispatching is vital for the punctuality of train services, which is critical for a train operating company (TOC) to maintain its competitiveness. Due to the introduction of competition in the railway transport market, the issue of discrimination is attracting more and more attention. This paper focuses on delivering non-discriminatory train dispatching solutions while multiple TOCs are competing in a rail transport market, and investigating impacting factors of the inequity of train dispatching solutions. A mixed integer linear programming (MILP) model is first proposed, in which the inequity of competitors (i.e., trains and TOCs) is formalized by a set of constraints. In order to provide a more flexible framework, a model is further reformulated where the inequity of competitors is formalized as the maximum individual deviation of competitors’ delay cost from average delay cost in the objective function. Complex infrastructure capacity constraints are considered and modelled through a big M-based approach. The proposed models are solved by a standard MILP solver. A set of comprehensive experiments is conducted on a real-world dataset adapted from the Dutch railway network to test the efficiency, effectiveness, and applicability of the proposed models, as well as determine the trade-off between train delays and delay equity.     

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.     

Strategies for customer service level protection under multi-echelon supply chain disruption risk

We model a multi-echelon system where disruptions can occur at any stage and evaluate multiple strategies for protecting customer service if a disruption should occur. The strategies considered take advantage of the network itself and include satisfying demand from an alternate location in the network, procuring material or transportation from an alternate source or route, and holding strategic inventory reserves throughout the network. Unmet demand is modeled using a mix of backordering and lost sales. We conduct numerical analysis and provide recommendations on selecting strategic mitigation methods to diminish the impact of disruptions on customer service. We demonstrate that the greatest service level improvements can be made by providing both proactive inventory placement to cover short disruptions or the start of long disruptions, and reactive back-up methods to help the supply chain recover after long or permanent disruptions.     

Probabilistic analysis of the release of liquefied natural gas (LNG) tenders due to freight-train derailments

Liquefied natural gas (LNG) has emerged as a possible alternative fuel for freight railroads in the United States, due to the availability of cheap domestic natural gas and continued pursuit of environmental and energy sustainability. A safety concern regarding the deployment of LNG-powered trains is the risk of breaching the LNG tender car (a special type of hazardous materials car that stores fuel for adjacent locomotives) in a train accident. When a train is derailed, an LNG tender car might be derailed or damaged, causing a release and possible fire. This paper describes the first study that focuses on modeling the probability of an LNG tender car release incident due to a freight train derailment on a mainline. The model accounts for a number of factors such as FRA track class, method of operation, annual traffic density level, train length, the point of derailment, accident speed, the position(s) of the LNG tender(s) in a train, and LNG tender car design. The model can be applied to any specified route or network with LNG-fueled trains. The implementation of the model can be undertaken by the railroad industry to develop proactive risk management solutions when using LNG as an alternative railroad fuel.     

Optimizing train stopping patterns and schedules for high-speed passenger rail corridors

High-speed railway (HSR) systems have been developing rapidly in China and various other countries throughout the past decade; as a result, the question of how to efficiently operate such large-scale systems is posing a new challenge to the railway industry. A high-quality train timetable should take full advantage of the system’s capacity to meet transportation demands. This paper presents a mathematical model for optimizing a train timetable for an HSR system. We propose an innovative methodology using a column-generation-based heuristic algorithm to simultaneously account for both passenger service demands and train scheduling. First, we transform a mathematical model into a simple linear programming problem using a Lagrangian relaxation method. Second, we search for the optimal solution by updating the restricted master problem (RMP) and the sub-problems in an iterative process using the column-generation-based algorithm. Finally, we consider the Beijing–Shanghai HSR line as a real-world application of the methodology; the results show that the optimization model and algorithm can improve the defined profit function by approximately 30% and increase the line capacity by approximately 27%. This methodology has the potential to improve the service level and capacity of HSR lines with no additional high-cost capital investment (e.g., the addition of new tracks, bridges and tunnels on the mainline and/or at stations).     

Predicting disruptions and their passenger delay impacts for public transport stops

Disruptions in public transport can have major implications for passengers and service providers. Our study objective is to develop a generic approach to predict how often different disruption types occur at different stations of a public transport network, and to predict the impact related to these disruptions as measured in terms of passenger delays. We propose a supervised learning approach to perform these predictions, as this allows for predictions for individual stations for each time period, without the requirement of having sufficient empirical disruption observations available for each location and time period. This approach also enables a fast prediction of disruption impacts for a large number of disruption instances, hence addressing the computational challenges that rise when typical public transport assignment or simulation models would be used for real-world public transport networks. To improve transferability of our study results, we cluster stations based on their contribution to network vulnerability using unsupervised learning. This supports public transport agencies to apply the appropriate type of measure aimed to reduce disruptions or to mitigate disruption impacts for each station type. Applied to the Washington metro network, we predict a yearly passenger delay of 5.9 million hours for the total metro network. Based on the clustering, five different types of station are distinguished. Stations with high train frequencies and high passenger volumes located at central trunk sections of the network show to be most critical, along with start/terminal and transfer stations. Intermediate stations located at branches of a line are least critical.