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.     

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.     

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.     

Ferry service network design: optimal fleet size,routing, and scheduling

The study formulated a ferry network design problem by considering the optimal fleet size, routing, and scheduling for both direct and multi-stop services. The objective function combines both the operator and passengers’ performance measures. Mathematically, the model is formulated as a mixed integer multiple origin–destination network flow problem with ferry capacity constraints. To solve this problem of practical size, this study developed a heuristic algorithm that exploits the polynomial-time performance of shortest path algorithms. Two scenarios of ferry services in Hong Kong were solved to demonstrate the performance of the heuristic algorithm. The results showed that the heuristic produced solutions that were within 1.3% from the CPLEX optimal solutions. The computational time is within tens of seconds even for problem size that is beyond the capability of CPLEX.     

User perspectives in public transport timetable optimisation

The present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line.In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers’ route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence.The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD).     

Optimisation of motorway operations via ramp metering and variable speed limits

This paper presents a modelling and optimisation framework for deriving ramp metering and variable speed control strategies. We formulate the optimal control problems aiming to minimise the travel delay on motorways based upon a macroscopic cell transmission model of traffic. The optimal ramp metering optimisation is formulated as a linear programming (LP) while the variable speed control problem is formulated as a mixed integer LP. The optimisation models are applied to a real scenario over a section of M25 motorway in the UK. This paper also includes various analyses on the sensitivity of the optimal control solutions with respect to different network configurations and model assumptions.     

Traffic signal timing problems with environmental and equity considerations

Traffic signal timings in a road network can not only affect total user travel time and total amount of traffic emissions in the network but also create an inequity problem in terms of the change in travel costs of users traveling between different locations. This paper proposes a multi‐objective bi‐level programming model for design of sustainable and equitable traffic signal timings for a congested signal‐controlled road network. The upper level of the proposed model is a multi‐objective programming problem with an equity constraint that maximizes the reserve capacity of the network and minimizes the total amount of traffic emissions. The lower level is a deterministic network user equilibrium problem that considers the vehicle delays at signalized intersections of the network. To solve the proposed model, an approach for normalizing incommensurable objective functions is presented, and a heuristic solution algorithm that combines a penalty function approach and a simulated annealing method is developed. Two numerical examples are presented to show the effects of reserve capacity improvement and green time proportion on network flow distribution and transportation system performance and the importance of incorporating environmental and equity objectives in the traffic signal timing problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Maximum car ownership under constraints of road capacity and parking space

This paper presents a model for determining the maximum number of cars by zones in view of the capacity of the road network and the number of parking spaces available. In other words, the proposed model is to examine whether existing road network and parking supply is capable of accommodating future zonal car ownership growth (or the reserve capacity in each zone); i.e. the potential maximum zonal car ownership growth that generates the road traffic within the network capacity and parking space constraints. In the proposed model, the vehicular trip production and attraction are dependent on the car ownership, available parking spaces and the accessibility measures by traffic zones. The model is formulated as a bi-level programming problem. The lower-level problem is an equilibrium trip distribution/assignment problem, while the upper-level problem is to maximize the sum of zonal car ownership by considering travellers’ route and destination choice behaviour and satisfying the network capacity and parking space constraints. A sensitivity analysis based heuristic algorithm is developed to solve the proposed bi-level car ownership problem and is illustrated with a numerical example.     

Adding a new station and a road link to a road–rail network in the presence of modal competition

In this paper we study the problem of locating a new station on an existing rail corridor and a new junction on an existing road network, and connecting them with a new road segment under a budget constraint. We consider three objective functions and the corresponding optimization problems, which are modeled by means of mixed integer non-linear programs. For small instances, the models can be solved directly by a standard solver. For large instances, an enumerative algorithm based on a discretization of the problem is proposed. Computational experiments show that the latter approach yields high quality solutions within short computing times.     

Second best toll and capacity optimisation in networks: solution algorithm and policy implications

This paper looks at the first and second best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (Netw. Spat. Econ., 4(2): 161–179, 2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network.

A discrete-convex programming approach to the simultaneous optimization of land use and transportation

Three design problems are discussed in this article. First, it is shown that the network design problem with congestion reduces to an all-or nothing traffic assignment problem under some assumptions on the congestion function and the investment cost function. Second, the land use design problem is formulated as an extension of the Koopmans-Beckmann problem and a heuristic is proposed to solve this problem. Third, it is shown that the seemingly more complex problem of designing jointly a land-use plan and a transportation network reduces to a pure land-use design problem. All that is needed to solve the joint optimization problem is a shortest path algorithm and a heuristic to solve the land use design problem. Computational experience is reported for each algorithm.     

Heuristic ranking and selection procedures for network design problems

Two heuristic approaches to solving discrete non-linear network design problems and other subset selection problems are described and tested. These heuristics operate similarly to other add, delete and interchange heuristics that have been applied to network design problems. However, the selection criterion adopted here is the ratio of objective function change per unit of resource cost, which other authors have described as an effective gradient measure for zero-one integer programming problems. Optimal branch-and-bound algorithms previously developed and tested are reviewed, and those results serve as benchmarks with which to compare these heuristics described in this paper. The first heuristic ranks and deletes alternative network modifications from an entire set of candidate projects, such as new links or link improvements, until the subset of remaining projects fits within the constraint space. This method was found to achieve optimal or near-optimal solutions to each of the test cases, even when the number of candidate projects deleted in each iteration was increased from one to many. The quality of those results led us to investigate a constrained random sampling procedure in which candidate projects are ranked with regard to randomly generated networks, and a solution is then chosen on the basis of these rankings. This second approach was found to achieve solutions that were almost as good as those obtained with the rank and delete heuristic.     

The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions

The tractor and semitrailer routing problem with many-to-many demand (TSRP-MMD) is investigated in this study. The TSRP-MMD extends the existing studies on the rollon–rolloff vehicle routing problem (RRVRP) to a many-to-many problem with an intercity line-haul network background. To demonstrate and utilize the energy efficiency of the tractor and semitrailer combination, the TSRP-MMD takes carbon dioxide (CO₂) emissions per ton-kilometer as the objective. Because the problem is NP-hard, a modified Clarke and Wright Savings heuristic algorithm (CW) followed by an improvement phase and a local search phase is developed to solve the TSRP-MMD. The integer program is used to find optimum solutions for small-scale problems. The computational results show that the developed heuristics can be efficiently used to solve the problem.     

Testing and evaluation of a multi-commodity multi-modal network flow model for disaster relief management

The results of the testing of an optimization model in disaster relief management are presented. The problem is a large-scale multi-commodity, multi-modal network flow problem with time windows. Due to the nature of this problem, the size of the optimization model grows extremely rapidly as the number of modes and/or commodities increase. The formulation is based on the concept of a time-space network. Two heuristic algorithms are developed. One exploits an inherent network structure of the problem with a set of side constraints and the other is an interactive fix-and-run heuristic. The findings of the model-testing and a wide range of sensitivity analyses using an artificially generated data set are presented. Both solution procedures prove to be efficient and effective in providing close to optimal solutions.     

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.     

A multi-objective analysis of a rural road network problem in the hilly regions of Nepal

This paper considers the rural road network upgrading problem, using a multi-objective optimization model, to support decision-makers in the choice of roads to upgrade in the hilly regions of Nepal. The model considers two objectives: minimization of user operation costs and maximization of population covered. The problem was solved for a real-world rural road network in the Gorkha district of Nepal. For this case, all non-dominated solutions were obtained and the ones providing more interesting trade-offs were analysed. The model was found suitable for the case under study, and possibly, easily extendable to rural areas of other developing countries.     

A methodology for classification by priority for action: Selecting road stretches for network noise action plans

Road traffic noise is an element of outstanding importance within the overall context of environmental impact. This problem must be technically addressed from an efficient viewpoint, and solutions or alternatives should be considered by means of appropriate and consolidated procedures.Up to now, there is no regulated guideline for establishing well-founded priorities when dealing with the diverse road stretches included in the corresponding Action Plans against noise under the Environmental Noise Directive (2002/49/EC). To this end, the present study proposes a methodology to sort, by priority, road stretches identified by their noise problems and therefore requiring appropriate action. The methodology is based on the so-called “road stretch priority index” (henceforth referred to as RSPI). This index involves a number of variables (called “road stretch priority variables”) that are weighted according to their influence on the road traffic noise problem. Thus, the RSPI makes it possible to prioritize different stretches of the Action Plan. To illustrate the application of the proposed methodology, this paper also describes a real case entailing a difficult choice, applying the proposed methodology to a review of the Action Plan against Noise 2008–2012 in the province of Almería, for the road network of the regional government of Andalusia, Spain.     

A multi-period optimization model for the deployment of public electric vehicle charging stations on network

A multi-period multipath refueling location model is developed to expand public electric vehicle (EV) charging network to dynamically satisfy origin–destination (O–D) trips with the growth of EV market. The model captures the dynamics in the topological structure of network and determines the cost-effective station rollout scheme on both spatial and temporal dimensions. The multi-period location problem is formulated as a mixed integer linear program and solved by a heuristic based on genetic algorithm. The model and heuristic are justified using the benchmark Sioux Falls road network and implemented in a case study of South Carolina. The results indicate that the charging station rollout scheme is subject to a number of major factors, including geographic distributions of cities, vehicle range, and deviation choice, and is sensitive to the types of charging station sites.     

The multi-objective network design problem using minimizing externalities as objectives: comparison of a genetic algorithm and simulated annealing framework

Incorporation of externalities in the Multi-Objective Network Design Problem (MO NDP) as objectives is an important step in designing sustainable networks. In this research the problem is defined as a bi-level optimization problem in which minimizing externalities are the objectives and link types which are associated with certain link characteristics are the discrete decision variables. Two distinct solution approaches for this multi-objective optimization problem are compared. The first heuristic is the non-dominated sorting genetic algorithm II (NSGA-II) and the second heuristic is the dominance based multi objective simulated annealing (DBMO-SA). Both heuristics have been applied on a small hypothetical test network as well as a realistic case of the city of Almelo in the Netherlands. The results show that both heuristics are capable of solving the MO NDP. However, the NSGA-II outperforms DBMO-SA, because it is more efficient in finding more non-dominated optimal solutions within the same computation time and maximum number of assessed solutions.     

Modelling the provision of transport with planned or market‐determined public transport services

Implications of the difference between planned and market‐determined public transport services for the modelling of the transport system and its use are examined. In the former case, the task for government seeking to optimise performance of the transport system has a standard bi‐level form, but in the latter case, the lower‐level problem in the bi‐level formulation is to determine mutually consistent solutions to a pair of optimisation problems. The relevance of the mutually consistent solution in this context is contrasted with its sometimes misleading role in the context of optimisation of urban traffic signal control.