Multiple criteria optimization method for the vehicle assignment problem in a bus transportation company

A vehicle assignment problem (VAP) in a road, long‐haul, passenger transportation company with heterogeneous fleet of buses is considered in the paper. The mathematical model of the VAP is formulated in terms of multiobjective, combinatorial optimization. It has a strategic, long‐term character and takes into account four criteria that represent interests of both passengers and the company's management. The decision consists in the definition of weekly operating frequency (number of rides per week) of buses on international routes between Polish and Western European cities. The VAP is solved in a step‐wise procedure. In the first step a sample of efficient (Pareto‐optimal) solutions is generated using an original metaheuristic method called Pareto Memetic Algorithm (PMA). In the second step this sample is reviewed and evaluated by the Decision Maker (DM). In this phase an interactive, multiple criteria analysis method with graphical facilities, called Light Beam Search (LBS), is applied. The method helps the DM to define his/her preferences, direct the search process and select the most satisfactory solution.     

Application of multiple criteria decision making for network improvement

In this paper we propose application of multiple criteria decision making to problems of a metropolitan network improvement plan. Initially, a bilevel multiple objective network design model is considered in two objectives which are minimal government budget and minimal total travel time of road users. We seek feasible improvement alternatives among those bottleneck links in an existing road network structure and travel demand. We present an effective heuristic algorithm to obtain noninferior solutions; then ELECTRE III multiple criteria decision making and group decision making are used to evaluate and to select a compromise solution among those noninferior solutions. From the design phase in multiple criteria decision making, multiple objective mathematical programming is used to formulate a continuous network design model. However, from the phase of evaluation, multiple criteria decision making to solve the discrete network design problem. The network of metropolitan Taipei is taken as an example to illustrate the operation of this model.     

A method for solving the multi‐objective transit frequency optimization problem

Frequency setting takes place at the strategic and tactical planning stages of public transportation systems. The problem consists in determining the time interval between subsequent vehicles for a given set of lines, taking into account interests of users and operators. The result of this stage is considered as input at the operational level. In general, the problem faced by planners is how to distribute a given fleet of buses among a set of given lines. The corresponding decisions determine the frequency of each line, which impacts directly on the waiting time of the users and operator costs. In this work, we consider frequency setting as the problem of minimizing simultaneously users' total travel time and fleet size, which represents the interest of operators. There is a trade‐off between these two measures; therefore, we face a multi‐objective problem. We extend an existing single‐objective formulation to account explicitly for this trade‐off, and propose a Tabu Search solving method to handle efficiently this multi‐objective variant of the problem. The proposed methodology is then applied to a real medium‐sized problem instance, using data of Puerto Montt, Chile. We consider two data sets corresponding to morning‐peak and off‐peak periods. The results obtained show that the proposed methodology is able to improve the current solution in terms of total travel time and fleet size. In addition, the proposed method is able to efficiently suggest (in computational terms) different trade‐off solutions regarding the conflicting objectives of users and operators. Copyright © 2017 John Wiley & Sons, Ltd.     

Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

This paper presents a mathematical model to plan emergencies in a densely populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features an integrated operational framework, which simultaneously guides evacuees through urban streets and crosswalks (referred to as “the pedestrian network”) to designated pickup points (e.g., bus stops), and routes a fleet of buses at different depots to those pick‐up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so‐called “vehicular network.” An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in two networks. Because the large instances of the proposed model are mathematically difficult to solve to optimality, a two‐stage heuristic is developed to solve larger instances of the model. Results from hundreds of numerical examples analysis indicate that proposed heuristic works well in providing (near) optimal or feasibly good solutions for medium‐scale to large‐scale instances that may arise in real transit‐based evacuation situations in a much shorter amount of computational time compared with cplex (can find optimal/feasible solutions for only five instances within 3 hours of running). Copyright © 2016 John Wiley & Sons, Ltd.     

An optimal aircraft fleet management decision model under uncertainty

Decision planning for an efficient fleet management is crucial for airlines to ensure a profit while maintaining a good level of service. Fleet management involves acquisition and leasing of aircraft to meet travelers' demand. Accordingly, the methods used in modeling travelers' demand are crucial as they could affect the robustness and accuracy of the solutions. Compared with most of the existing studies that consider deterministic demand, this study proposes a new methodology to find optimal solutions for a fleet management decision model by considering stochastic demand. The proposed methodology comes in threefold. First, a five‐step modeling framework, which is incorporated with a stochastic demand index (SDI), is proposed to capture the occurrence of uncertain events that could affect the travelers' demand. Second, a probabilistic dynamic programming model is developed to optimize the fleet management model. Third, a probable phenomenon indicator is defined to capture the targeted level of service that could be achieved satisfactorily by the airlines under uncertainty. An illustrative case study is presented to evaluate the applicability of the proposed methodology. The results show that it is viable to provide optimal solutions for the aircraft fleet management model. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Switching service types for multi-region bus systems

Conventional fixed-route bus services are generally preferred to flexible-route services at high demand densities, and vice versa. This paper formulates the problem of integrating conventional and flexible services that connect a main terminal to multiple local regions over multiple time periods. The system’s vehicle size, route spacing (for conventional services), service area (for flexible services), headways and fleet sizes are jointly optimized to minimize the sum of supplier costs and user costs. The route spacing for conventional bus services and service area for flexible bus services are also optimized for each region. The proposed solution method, which uses a genetic algorithm and analytic optimization, finds good solutions quickly. Numerical examples and sensitivity analyses confirm that the single fleet variable-type bus service may outperform either the single fleet conventional bus service or the single fleet flexible bus service when demand densities vary substantially among regions and time periods.     

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.     

Flexible feeder transit route design to enhance service accessibility in urban area

To improve the accessibility of transit system in urban areas, this paper presents a flexible feeder transit routing model that can serve irregular‐shaped networks. By integrating the cost efficiency of fixed‐route transit system and the flexibility of demand responsive transit system, the proposed model is capable of letting operating feeder busses temporarily deviate from their current route so as to serve the reported demand locations. With an objective of minimizing total bus travel time, a new operational mode is then proposed to allow busses to serve passengers on both street sides. In addition, when multiple feeder busses are operating in the target service area, the proposed model can provide an optimal plan to locate the nearest one to response to the demands. A three‐stage solution algorithm is also developed to yield meta‐optimal solutions to the problem in a reasonable amount of time by transforming the problem into a traveling salesman problem. Numerical studies have demonstrated the effectiveness of the proposed model as well as the heuristic solution approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal locations of electric public charging stations using real world vehicle travel patterns

We propose an optimization model based on vehicle travel patterns to capture public charging demand and select the locations of public charging stations to maximize the amount of vehicle-miles-traveled (VMT) being electrified. The formulated model is applied to Beijing, China as a case study using vehicle trajectory data of 11,880 taxis over a period of three weeks. The mathematical problem is formulated in GAMS modeling environment and Cplex optimizer is used to find the optimal solutions. Formulating mathematical model properly, input data transformation, and Cplex option adjustment are considered for accommodating large-scale data. We show that, compared to the 40 existing public charging stations, the 40 optimal ones selected by the model can increase electrified fleet VMT by 59% and 88% for slow and fast charging, respectively. Charging demand for the taxi fleet concentrates in the inner city. When the total number of charging stations increase, the locations of the optimal stations expand outward from the inner city. While more charging stations increase the electrified fleet VMT, the marginal gain diminishes quickly regardless of charging speed.     

Efficient solution algorithm for finding spatially dependent reliable shortest path in road networks

Travel times are generally stochastic and spatially correlated in congested road networks. However, very few existing route guidance systems (RGS) can provide reliable guidance services to aid travellers planning their trips with taking account explicitly travel time reliability constraint. This study aims to develop such a RGS with particular consideration of travellers' concern on travel time reliability in congested road networks with uncertainty. In this study, the spatially dependent reliable shortest path problem (SD‐RSPP) is formulated as a multi‐criteria shortest path‐finding problem in road networks with correlated link travel times. Three effective dominance conditions are established for links with different levels of travel time correlations. An efficient algorithm is proposed to solve SD‐RSPP by adaptively using three established dominance conditions. The complexities of road networks in reality are also explicitly considered. To demonstrate the applicability of proposed algorithm, a comprehensive case study is carried out in Hong Kong. The results of case study show that the proposed solution algorithm is robust to take account of travellers' multiple routing criteria. Computational results demonstrate that the proposed solution algorithm can determine the reliable shortest path on real‐time basis for large‐scale road networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Fleet size determination for a truckload distribution center

This work presents an analysis of the fleet size determination problem for a truckload distribution center in which each customer requests multi‐truckload services. A transformation is made to define this problem as a cutting stock problem which can be resolved by finding the proper set of patterns beneficial for an NP‐hard (non‐deterministic polynomial‐time hard) problem. The genetic algorithm (GA) is combined with cutting stock techniques to solve the problem. Experiments are carried out testing two types of problems, with and without time‐window constraints. To verify the solution quality obtained with the proposed approach, the problem is also solved using only GA. It is shown that the proposed approach can significantly improve the GA solution by 14.68%. Copyright © 2012 John Wiley & Sons, Ltd.     

The fleet size and mix dial-a-ride problem with reconfigurable vehicle capacity

This paper introduces a fleet size and mix dial-a-ride problem with multiple passenger types and a heterogeneous fleet of reconfigurable vehicles. In this new variant of the dial-a-ride problem, en-route modifications of the vehicle’s inner configuration are allowed. The main consequence is that the vehicle capacity is defined by a set of configurations and the choice of vehicle configuration is associated with binary decision variables.The problem is modeled as a mixed-integer program derived from the model of the heterogeneous dial-a-ride problem. Vehicle reconfiguration is a lever to efficiently reduce transportation costs, but the number of passengers and vehicle fleet setting make this problem intractable for exact solution methods. A large neighborhood search metaheuristic combined with a set covering component with a reactive mechanism to automatically adjust its parameters is therefore proposed. The resulting framework is evaluated against benchmarks from the literature, used for similar routing problems. It is also applied to a real case, in the context of the transportation of disabled children from their home to medical centers in the city of Lyon, France.     

Optimal scheduling of public transport fleet at network level

This paper deals with the development of a strategic approach for optimizing the operation of public transport system that considers both user's objective and operator's objective. Passengers of public transport are assumed to seek a minimum wait time to conduct the trips, while on the other hand, operators are concerned with the efficient operation such as minimum fleet size. The average minimum wait time is to be achieved by creating an optimal despatching policy for each vehicle from the terminal. As for efficient operation the utilisation of vehicle should be maximised by having a minimum number of vehicles in operation. User's and operator's objectives are optimized within certain operational constraints such as vehicle capacity to maintain acceptable level of service. The i‐model is contructed in a bi‐level programming form in which the user's objective is minimized by dynamic programming and the operator's objective is minimized by various routing strategies. Furthermore, an algorithm and a contrived example are developed to solve and see the performance of the approach.     

Optimal resource allocation among transit agencies for fleet management

Most transit agencies require government support for the replacement of their aging fleet. A procedure for equitable resource allocation among competing transit agencies for the purpose of transit fleet management is presented in this study. The proposed procedure is a 3-dimensional model that includes the choice of a fleet improvement program, agencies that may receive them, and the timing of investments. Earlier efforts to solve this problem involved the application of 1- or 2-dimensional models for each year of the planning period. These may have resulted in suboptimal solution as the models are blind to the impact of the fleet management program of the subsequent years. Therefore, a new model to address a long-term planning horizon is proposed. The model is formulated as a non-linear optimization problem of maximizing the total weighted average remaining life of the fleet subjected to improvement program and budgetary constraints. Two variants of the problem, one with an annual budget constraint and the other with a single budget constraint for the entire planning period, are formulated. Two independent approaches, namely, branch and bound algorithm and genetic algorithm are used to obtain the solution. An example problem is solved and results are discussed in details. Finally, the model is applied to a large scale real-world problem and a detailed analysis of the results is presented.     

A multi‐class mean‐excess traffic equilibrium model with elastic demand

Recent empirical studies have revealed that travel time variability plays an important role in travelers' route choice decisions. To simultaneously account for both reliability and unreliability aspects of travel time variability, the concept of mean‐excess travel time (METT) was recently proposed as a new risk‐averse route choice criterion. In this paper, we extend the mean‐excess traffic equilibrium model to include heterogeneous risk‐aversion attitudes and elastic demand. Specifically, this model explicitly considers (1) multiple user classes with different risk‐aversions toward travel time variability when making route choice decisions under uncertainty and (2) the elasticity of travel demand as a function of METT when making travel choice decisions under uncertainty. This model is thus capable of modeling travelers' heterogeneous risk‐averse behaviors with both travel choice and route choice considerations. The proposed model is formulated as a variational inequality problem and solved via a route‐based algorithm using the modified alternating direction method. Numerical analyses are also provided to illustrate the features of the proposed model and the applicability of the solution algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

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 stop spacing and headway of congested transit system considering realistic wait times

Abstract

This paper revisits the classical transit scheduling problem and investigates the relationship between stop spacing and headway, considering realistic wait time and operable transit capacity. Headway and stop spacing are important determinants for planning a transit system, which influence the service level as well as the cost of operation. A mathematical model is developed, and the objective function is user travel time which is minimized by the optimized stop spacing and headway, subject to the constraints of operable fleet size and route capacity. Optimal stop spacing and headway solutions are obtained in a numerical example. Sensitivity analysis is conducted, and the effect of model parameters on user travel time is explored.     

A two‐leveled multi‐objective symbiotic evolutionary algorithm for the hub and spoke location problem

We consider a hub and spoke location problem (HSLP) with multiple scenarios. The HSLP consists of four subproblems: hub location, spoke location, spoke allocation, and customer allocation Under multiple scenarios, we aim to provide a set of well‐distributed solutions, close to the true Pareto optimal solutions, for decision makers. We present a novel multi‐objective symbiotic evolutionary algorithm to solve the HSLP under multiple scenarios. The algorithm is modeled as a two‐leveled structure, which we call the two‐leveled multi‐objective symbiotic evolutionary algorithm (TMSEA). In TMSEA, two main processes imitating symbiotic evolution and endosymbiotic evolution are introduced to promote the diversity and convergence of solutions. The evolutionary components suitable for each sub‐problem are defined. TMSEA is tested on a variety of test‐bed problems and compared with existing multi‐objective evolutionary algorithms. The experimental results show that TMSEA is promising in solution convergence and diversity.     

Highway alignment optimization through feasible gates

An efficient optimization approach, called feasible gate (FG), is developed to enhance the computation efficiency and solution quality of the previously developed highway alignment optimization (HAO) model. This approach seeks to realistically represent various user preferences and environmentally sensitive areas and consider them along with geometric design constraints in the optimization process. This is done by avoiding the generation of infeasible solutions that violate various constraints and thus focusing the search on the feasible solutions. The proposed method is simple, but improves significantly the model's computation time and solution quality. Such improvements are demonstrated with two test examples from a real road project.