A stochastic multimodal reliable network design problem under adverse weather conditions

This paper formulates a network design problem (NDP) for finding the optimal public transport service frequencies and link capacity expansions in a multimodal network with consideration of impacts from adverse weather conditions. The proposed NDP aims to minimize the sum of expected total travel time, operational cost of transit services, and construction cost of link capacity expansions under an acceptable level of variance of total travel time. Auto, transit, bus, and walking modes are considered in the multimodal network model for finding the equilibrium flows and travel times. In the proposed network model, demands are assumed to follow Poisson distribution, and weather‐dependent link travel time functions are adopted. A probit‐based stochastic user equilibrium, which is based on the perceived expected travel disutility, is used to determine the multimodal route of the travelers. This model also considers the strategic behavior of the public transport travelers in choosing their routes, that is, common‐line network. Based on the stochastic multimodal model, the mean and variance of total travel time are analytical estimated for setting up the NDP. A sensitivity‐based solution algorithm is proposed for solving the NDP, and two numerical examples are adopted to demonstrate the characteristics of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd.     

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach

This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature.     

A reliability‐based network design problem

This paper presents a reliability‐based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity‐reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability‐based network design problem is formulated as a bi‐level program in which the lower level sub‐program is the probit‐based stochastic user equilibrium problem and the upper level sub‐program is the maximization of the new capacity reliability index. The lower level sub‐program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic‐flow pattern, and Monte Carlo stochastic loading. The upper level sub‐program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework.     

The transit network design problem with elastic demand and internalisation of external costs: An application to rail frequency optimisation

In this paper we examine the transit network design problem under the assumption of elastic demand, focusing on the problem of designing the frequencies of a regional metro. In this problem, investments in transit services have appreciable effects on modal split. Neglecting demand elasticity can lead to solutions that may not represent the actual objectives of the design. We propose four different objective functions that can be adopted to assume demand as elastic, considering the costs of all transportation systems (car, bus and rail) as well as the external costs, and we define the constraints of the problem. Heuristic and meta-heuristic solution algorithms are also proposed. The models and algorithms are tested on a small network and on a real-scale network.     

Multicriteria evaluation on accessibility‐based transportation equity in road network design problem

This paper investigates the performance of accessibility‐based equity measurements in transportation and proposes a multiobjective optimization model to simulate the trade‐offs between equity maximization and cost minimization of network construction. The equity is defined as the spatial distribution of accessibilities across zone areas. Six representative indicators were formulated, including GINI coefficient, Theil index, mean log deviation, relative mean deviation, coefficient of variation, and Atkinson index, and incorporated into an equity maximization model to evaluate the performance sensitivity. A bilevel multiobjective optimization model was proposed to obtain the Pareto‐optimal solutions for link capacity enhancement in a stochastic road network design problem. A numerical analysis using the Sioux Falls data was implemented. Results verified that the equity indicators are quite sensitive to the pattern of network scenarios in the sense that the level of equity varies according to the amount of overall capacity enhancement as well as the assignment of improved link segments. The suggested multiobjective model that enables representing the Pareto‐optimal solutions can provide multiple options in the decision making of road network design. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling and solving discrete network design problem with stochastic user equilibrium

In this paper, we address the discrete network design problem, which determines the addition of new roads to existing transportation network to optimize the transportation system performance. Road users are assumed to follow the traffic assignment principle of stochastic user equilibrium. A mixed‐integer nonlinear nonconvex problem is developed to model this discrete network design problem with stochastic user equilibrium. The original problem is relaxed into a convex mixed‐integer nonlinear program, whose solution provides a lower bound of the original problem. The relaxed problem is then embedded into two proposed global optimization solution algorithms to obtain the global optimal solution of the problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Sustainable urban transit network design

Sustainability is a requirement for modern public transportation networks, as these are expected to play a critical role in environment-friendly transportation systems. This paper focuses on developing an efficient model for solving a sustainable oriented variant of the Transit Route Network Design Problem. The model incorporates sustainable design objectives, considers emission-free (electric) vehicles and introduces a direct route design approach with route structure and directness control. An application in a real world case, highlights the performance and benefits of the proposed model.     

Segment-based alteration for container liner shipping network design

Container liner shipping companies only partially alter their shipping networks to cope with the changing demand, rather than entirely redesign and change the network. In view of the practice, this paper proposes an optimal container liner shipping network alteration problem based on an interesting idea of segment, which is a sequence of legs from a head port to a tail port that are visited by the same type of ship more than once in the existing shipping network. In segment-based network alteration, the segments are intact and each port is visited by the same type of ship and from the same previous ports. As a result, the designed network needs minimum modification before implementation. A mixed-integer linear programming model with a polynomial number of variables is developed for the proposed segmented-based liner shipping network alternation problem. The developed model is applied to an Asia–Europe–Oceania liner shipping network with a total of 46 ports and 11 ship routes. Results demonstrate that the problem could be solved efficiently and the optimized network reduces the total cost of the initial network considerably.     

Pruning and ranking the Pareto optimal set,application for the dynamic multi‐objective network design problem

Solving the multi‐objective network design problem (MONDP) resorts to a Pareto optimal set. This set can provide additional information like trade‐offs between objectives for the decision making process, which is not available if the compensation principle would be chosen in advance. However, the Pareto optimal set of solutions can become large, especially if the objectives are mainly opposed. As a consequence, the Pareto optimal set may become difficult to analyze and to comprehend. In this case, pruning and ranking becomes attractive to reduce the Pareto optimal set and to rank the solutions to assist the decision maker. Because the method used, may influence the eventual decisions taken, it is important to choose a method that corresponds best with the underlying decision process and is in accordance with the qualities of the data used. We provided a review of some methods to prune and rank the Pareto optimal set to illustrate the advantages and disadvantages of these methods. The methods are applied using the outcome of solving the dynamic MONDP in which minimizing externalities of traffic are the objectives, and dynamic traffic management measures are the decision variables. For this, we solved the dynamic MONDP for a realistic network of the city Almelo in the Netherlands using the non‐dominated sorting genetic algorithm II. For ranking, we propose to use a fuzzy outranking method that can take uncertainties regarding the data quality and the perception of decision makers into account; and for pruning, a method that explicitly reckons with significant trade‐offs has been identified as the more suitable method to assist the decision making process. Copyright © 2012 John Wiley & Sons, Ltd.     

Global optimization method for network design problem with stochastic user equilibrium

In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.     

A multi-commodity flow network design problem

There exist systems which can be usefully described by a network containingarcs through which a commodity of one type flows. This paper is concerned with finding a solution procedure for a particular multi-commodity flow network design problem. The problem is to identify a set of arcs in the network such that if travel is prohibited in them all flow travels by feasible paths and its total cost is minimal. The total flow in each arc may not exced its capacity, which is a known constant. Each arc and each node of the network has a non-negative constant unit traversal cost. Between each pair of distinct nodes there is a given non-negative rate of flow from the first vertex to the second which may be split up among a number of paths according to some constant traversal cost flow assignment process. The optimality criterion is the total traversal cost of all flow, which is to be minimized. Previous work on network design problems of this type is surveyed. The principal contribution of this paper is the presentation of a solution procedure for the above problem based on branch and bound enumeration. An illustrative numerical example is included. Computational experience gained in using the procedure with a FORTRAN IV program on an IBM 370 is favourable.     

Using intelligent agents for Transportation Regulation Support System design

This paper presents an agent-based approach used to design a Transportation Regulation Support System (TRSS), that reports the network activity in real-time and thus assists the bus network regulators. The objective is to combine the functionalities of the existing information system with the functionalities of a decision support system in order to propose a generic model of a traffic regulation support system. Unlike the other approaches that only deal with a specific task, the original feature of our generic model is that it proposes a global approach to the regulation function under normal conditions (network monitoring, dynamic timetable management) and under disrupted conditions (disturbance assessment and action planning of feasible solutions). Following the introduction, the second section presents the notions of the domain and highlights the main regulation problems. The third section details and motivates our choice of the components of the generic model. Based on our generic model, in the fourth section, we present a TRSS prototype called SATIR (Système Automatique de Traitement des Incidents en Réseau – Automatic System for Network Incident Processing) that we have developed. SATIR has been tested on the Brussels transportation network (STIB). The results are presented in the fifth section. Lastly, we show how using the multi-agent paradigm opens perspectives regarding the development of new functionalities to improve the management of a bus network.     

Multi-fleet ferry service network design with passenger preferences for differential services

This paper investigates a multi-fleet ferry routing and scheduling problem that takes into account ferry services with different operation characteristics and passengers with different preferred arrival time windows. The logit model is used to represent passengers’ service choices. The full problem is formulated as a mixed integer nonlinear programming problem and solved with a heuristic procedure that first fixes the demand and then decomposes the resultant model by ferry services. At each iteration of the algorithm, the demand is updated and the relaxed problem is re-solved. Numerical results for the case of ferry service network design in Hong Kong are provided to illustrate the properties of the model and the performance of the heuristic.     

Transit network design for small-medium size cities

This paper proposes a novel heuristic to solve the network design problem for public transport in small-medium size cities. Such cities can be defined as those with a diameter of a few kilometers with up to a few hundred thousand residents. These urban centers present a specific spatial configuration affecting the land use and mobility system. Transportation demand is widespread in origin and concentrated in a small number of attraction points close to each other. This particular structure of demand (‘many-to-few’) suggests the need for specific methodologies for the design of a transit system at a network level. In this paper, such design methodologies are defined in terms of models and solution procedures and tested on a selected case study. The solution methods show promising results. The key variables of the model are the routes and their frequencies. The constraints of the problem affect the overall demand to be served, the quality of the proposed service (transfer, load factors) and the definition of routes.     

Robust transit network design with stochastic demand considering development density

This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.     

Aggregation effects on the network design problem

This article examines the effects of various network extraction schemes on the network design problem. Given an original network, many criteria can be used to identify subnetworks on which the network design problem is solved. For the purposes of this article, these subnetworks are obtained using an extraction algorithm which preserves the magnitude of the user equilibrium flows on the links of these subnetworks. The results of the implementation of the network design problem on the original and the extracted subnetworks are presented and compared. We conclude that very good solutions to the network design problem can be obtained from the use of highly aggregate networks.     

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.     

Build-to-order supply chain network design under supply and demand uncertainties

Supply chain disruptions are unintended, unwanted situations resulting in a negative supply chain performance. We study the supply chain network design under supply and demand uncertainty with embedded supply chain disruption mitigation strategies, postponement with downward substitution, centralized stocking and supplier sourcing base. We designed an integrated supply-side, manufacturing and demand-side operations network in such that the total expected operating cost is minimized. We modeled it in a deterministic equivalent formulation. An L-shaped decomposition with an additional decomposition step in the master problem is proposed. The computational results showed that parallel sourcing has a cost advantage against single sourcing under supply disruptions. In addition, the build-to-order (BTO) manufacturing mitigation process has its greatest impact with high variations on demands and is integrated with the component downward substitution. Lastly, the manufacturer needs to order differentiated components to cover its requirement for maximal product demand to prevent the loss of sale, even with fewer modules in stock.     

Solutions to the optimal network design problem with shipments related to transportation cost

Two versions of an optimal network design problem with shipments proportional to transportation costs are formulated. Extensions of an algorithm developed in prior research for solving these problems are proposed and tested. The performance of the algorithms is found to improve substantially as the dependence of shipments on costs is increased. Moreover, the optimal solutions obtained are unexpectedly robust with respect to a wide range of transportation cost assumptions. These findings could have important computational and policy implications if applicable to larger networks.