Maintenance optimization for transportation systems with demand responsiveness

We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems.     

Optimization of incentive polices for plug-in electric vehicles

High purchase prices and the lack of supporting infrastructure are major hurdles to the adoption of plug-in electric vehicles (PEVs). It is widely recognized that the government could help break these barriers through incentive policies, such as offering rebates to PEV buyers or funding charging stations. The objective of this paper is to propose a modeling framework that can optimize the design of such incentive policies. The proposed model characterizes the impact of the incentives on the dynamic evolution of PEV market penetration over a discrete set of time intervals, by integrating a simplified consumer vehicle choice model and a macroscopic travel and charging model. The optimization problem is formulated as a nonlinear and non-convex mathematical program and solved by a specialized steepest descent direction algorithm. We show that, under mild regularity conditions, the KKT conditions of the proposed model are necessary for local optimum. Results of numerical experiments indicate that the proposed algorithm is able to obtain satisfactory local optimal policies quickly. These optimal policies consistently outperform the alternative policies that mimic the state-of-the-practice by a large margin, in terms of both the total savings in social costs and the market share of PEVs. Importantly, the optimal policy always sets the investment priority on building charging stations. In contrast, providing purchase rebates, which is widely used in current practice, is found to be less effective.     

Cost-based approach for sizing of pedestrian facilities

Pedestrian facility size is currently determined in direct relationship to the design level of service. However, the design level of service is chosen arbitrarily from the six levels of service, which are assumed to represent the freedom available for movement at different levels of pedestrian flow. This direct and simple approach to facility sizing is shown to have two fundamental deficiencies that contribute to wasteful over capacity. In this article, a cost-based approach is introduced to overcome the deficiencies. Two analytical models, one for determining optimal design density and another for determining optimal design flow, are presented. The optimum design parameters minimize the total cost of the facility defined as the sum of construction cost and user cost. The sensitivity of the optimum parameters to the cost and pedestrian flow parameters is demonstrated using a numerical example.     

Joint inventory-location problem under the risk of probabilistic facility disruptions

This paper studies a reliable joint inventory-location problem that optimizes facility locations, customer allocations, and inventory management decisions when facilities are subject to disruption risks (e.g., due to natural or man-made hazards). When a facility fails, its customers may be reassigned to other operational facilities in order to avoid the high penalty costs associated with losing service. We propose an integer programming model that minimizes the sum of facility construction costs, expected inventory holding costs and expected customer costs under normal and failure scenarios. We develop a Lagrangian relaxation solution framework for this problem, including a polynomial-time exact algorithm for the relaxed nonlinear subproblems. Numerical experiment results show that this proposed model is capable of providing a near-optimum solution within a short computation time. Managerial insights on the optimal facility deployment, inventory control strategies, and the corresponding cost constitutions are drawn.     

A continuum approximation approach to competitive facility location design under facility disruption risks

This paper presents game-theoretical models based on a continuous approximation (CA) scheme to optimize service facility location design under spatial competition and facility disruption risks. The share of customer demand in a market depends on the functionality of service facilities and the presence of nearby competitors, as customers normally seek the nearest functioning facility for service. Our game-theoretical models incorporate these complicating factors into an integrated framework, and use continuous and differentiable density functions to represent discrete location decisions. We first analyze the existence of Nash equilibria in a symmetric two-company competition case. Then we build a leader–follower Stackelberg competition model to derive the optimal facility location design when one of the companies has the first mover advantage over its competitor. Both models are solved effectively, and closed-form analytical solutions can be obtained for special cases. Numerical experiments (with hypothetical and empirical data) are conducted to show the impacts of competition, facility disruption risks and transportation cost metrics on the optimal design. Properties of the models are analyzed to cast interesting managerial insights.     

A heterogeneous reliable location model with risk pooling under supply disruptions

This paper investigates a facility location model that considers the disruptions of facilities and the cost savings from the inventory risk-pooling effect and economies of scale. Facilities may have heterogeneous disruption probabilities. When a facility fails, its customers may be reassigned to other surviving ones to hedge against lost-sales costs. We first develop both an exact and an approximate expression for the nonlinear inventory cost, and then formulate the problem as a nonlinear integer programming model. The objective is to minimize the expected total cost across all possible facility failure scenarios. To solve this problem, we design two methods, an exact approach using special ordered sets of type two (SOS2) and a heuristic based on Lagrangian relaxation. We test the model and algorithms on data sets with up to 150 nodes. Computational results show that the proposed algorithms can solve the problem efficiently in reasonable time. Managerial insights on the optimal facility deployment, customer assignments and inventory control strategies are also drawn.     

A reliable location model for heterogeneous systems under partial capacity losses

Due to the interdependency between multiple infrastructure systems, the performance of a facility may depend on the resources or supplies received from other facilities. However, cross-system interdependence has seldom been studied in the location design context, probably due to the lack of a concise model describing interdependence across heterogeneous systems. This paper proposes a new heterogeneous flow scheme to describe cross-system interdependence. This scheme has two features distinguished from existing models in describing an interdependent facility location problem. First, it is a simple linear model upon which a compact facility location model can be built. Secondly, it relaxes the need to maintain flow conservation between different systems and is suitable in describing heterogeneous systems that take in and output different resources or services. Built on this scheme, this paper proposes a reliable location design model for a nexus of interdependent infrastructure systems. This model aims to locate the optimal facility locations in multiple heterogeneous systems to balance the tradeoff between the facility investment and the expected nexus operation performance. Different from other reliable facility location models, this expected performance captures interdependence among heterogeneous systems due to the resource input-output relationships. The consideration of continuous partial capacity losses complements the reliable location literature that mainly focuses on binary disruptions. Two numerical examples are conducted for investigating features and applications of the proposed model. The results indicate that with a standard off-the-shelf integer programming solver, the proposed model is able to solve optimal facility location design for problem instances of realistic scales to the near-optimum solutions with optimality gap assurance. Sensitivity analyses of key parameters indicate that improving facility capacity and reducing interdependency between systems can mitigate impacts of facility capacity losses and reduce the overall system cost.     

Entropy-based estimation of transfers in a terminal

An intermodal transportation terminal is a facility that provides commuters with easy transfer between transit modes and providers such as buses, light rail, subway, taxis, airport shuttles, and commuter rail. The probability of a passenger transferring from one mode to another and the estimation of total transfer demand are of great importance to both practitioners and researchers when determining optimal design alternatives as well as the best control and management policies for daily operation of the terminal. This article presents a study that uses an entropy-based optimization approach to estimate the transfer demands between the available transportation modes in an intermodal transportation terminal. The development and calibration of the entropy model is presented in the first part of the article, which is followed by a case study of the SiHui Intermodal Terminal in Beijing, China.     

Reducing average comprehensive travel cost by rationally allocating trips to different travel modes

To study the effect of different transport policies on reducing the average comprehensive travel cost (CTC) of all travel modes, by increasing public transport modal share and decreasing car trips, an optimization model is developed based on travel cost utility. A nested logit model is applied to analyze trip modal split. A Genetic Algorithm is then used to determine the implementation of optimal solutions in which various transport policies are applied in order to reduce average CTC. The central urban region of Beijing is selected as the study area in this research. Different policies are analyzed for comparison, focusing on their optimal impacts on minimizing the average CTC utility of all travel modes by rationally allocating trips to different travel modes in the study area. It is found that the proposed optimization model provides a reasonable indication of the effect of policies applied.     

Improving transportation service quality based on information fusion

How to improve transportation service quality and thus attract more passengers to use public transportation systems is an important concern for city governments around the world. In this study, we propose a novel information fusion model that addresses the dependent relationships among the various criteria for a method of non-additive weighted gap analysis aimed at evaluating and improving the service quality of transport systems. The hybrid model remedies prior shortcomings and should be more applicable to real-world situations. The proposed model is applied to a real case study of Taipei city bus companies to demonstrate its usefulness. The resulting analysis and the managerial applications for improving the bus service quality are also discussed with regards to the current policies of Taipei city.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

A planning model for multiple‐mode transportation system operations

The problem of generating a set of “good” transportation alternatives during the early and intermediate stages of transportation planning is addressed in this paper. A linear programming model of a multi‐modal transportation system is developed. The model is run interactively to determine optimal operating levels for all modes for various transport policy decisions. The model described is a component of a composite network generation model incorporating dynamic changes. The linear programming component determines optimal operating policies for given points in time. The composite model incorporates these in a dynamic programming framework to determine optimal staged investment policies over several time periods.     

The effect of complex models of externalities on estimated optimal tolls

Transport externalities such as costs of emissions and accidents are increasingly being used within appraisal and optimisation frameworks alongside the more traditional congestion analysis to set optimal transport policies. Models of externalities and costs of externalities may be implemented by a simple constant cost per vehicle-km approach or by more complex flow and speed dependent approaches. This paper investigates the impact of using both simple and more complex models of CO₂ emissions and cost of accidents on the optimal toll for car use and upon resulting welfare levels. The approach adopted is to use a single link model with a technical approach to the representation of the speed-flow relationship as this reflects common modelling practice. It is shown that using a more complex model of CO₂ emitted increases the optimal toll significantly compared to using a fixed cost approach while reducing CO₂ emitted only marginally. A number of accident models are used and the impact on tolls is shown to depend upon the assumptions made. Where speed effects are included in the accident model, accident costs can increase compared to the no toll equilibrium and so tolls should in this case be reduced compared to the congestion optimal toll. Finally it is shown that the effect of adding variable CO₂ emission models along with a fixed cost per vehicle-km for accidents can increase the optimal toll by 44% while increasing the true welfare gained by only 8%. The results clearly demonstrate that model assumptions for externalities can have a significant impact on the resulting policies and in the case of accidents the policies can be reversed.

Estimation of a time‐dependent origin‐destination matrix for congested highway networks

This paper presents a time‐dependent origin‐destination (O‐D) matrix estimation procedure embedded with a dynamic traffic assignment model, in which the predictive dynamic user optimal conditions in congested networks are maintained. Two solution algorithms are proposed, namely: an iterative (ITR) scheme and a method of successive averages (MSA) scheme. It is found that the MSA scheme outperforms the ITR scheme. As a prior O‐D matrix is an important input for the problem, its quality is essential for the reliability of the matrix estimation procedure. Empirical constraints are set in relation to the quality of the prior O‐D matrix for the estimation procedure. Numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types

This research investigates freeway-flow impacts of different traveler types by specifying and applying a latent-segmentation model of congested and uncongested driving behaviors. Drivers in uncongested conditions are assumed to drive at self-chosen speeds, while drivers in congested conditions are assumed to take speed as given and choose a spacing (between their vehicle and the previous vehicle). Several classes of driver-vehicle combinations are distinguished in a data set based on double-loop-detector pulses and a household travel survey. These classifications are made on the basis of vehicle type and gender, leading to class estimates of speeds and spacings. The segmentation model is specified as a logit function of density, weather, and vehicle type, leading to estimates of congested-condition probabilities. Unobserved heterogeneity is incorporated in all models via common error assumptions.Results indicate that segmentation models are promising tools for traffic data analysis and that information on travelers, their vehicles, and weather conditions explains significant variation in flow data. By clarifying a greater understanding of traffic conditions and traveler behavior explains much scatter in the fundamental relation between flow, speed, and density, can assist regions in their traffic-management efforts and engineers in their design of roadway facilities. Ultimately, such improvements to travel networks should enhance quality of life.     

Future use of stage bus services

The reasons underlying the decline of stage bus services in the U.K. over the past 30 years seem to be well understood, and the probable future trends have been projected using a quantitative forecasting model. The model considers U.K. bus services at a very aggregate level, but it breaks the demand into specific user groups: work trips, children's travel, travel by the elderly, and all other travel, and separately for households with and without a private car. Forecasts depend very sensitively on the level of economic growth assumed, since this governs the two major factors which determine public transport use — car ownership and the cost of operating the services. If the economy could recover its historic growth rates, a further substantial decline in bus use seems inevitable under most realistic assumptions. However, with the present economic outlook, a lower growth rate seems likely to persist for some time, and in this case public transport use will become much more stable in the 1990's; a tendency which would be helped if there were large increases in fuel prices. Many of the Metropolitan Counties have adopted policies of strongly restraining future rises in fares, in some cases to the extent of freezing fares in monetary terms. The effects of such policies on both patronage and subsidies are considered here, and although much of the current political attention is focussed on controlling fares, the question of balance between fares and service levels is also discussed. Lastly, it must be admitted that these predictions are based on knowledge which is largely restricted to the short-term effects of transport policies. The nature of our uncertainty about longer-term effects, and the possible size of them, is considered in terms of sensitivity-testing of the prediction model.     

Location planning for transit-based evacuation under the risk of service disruptions

The effectiveness of transit-based emergency evacuation highly depends on the location of pick-up facilities, resource allocation, and management. These facilities themselves are often subject to service disruptions during or after the emergency. This paper proposes a reliable emergency facility location model that determines both pre-emergency facility location planning and the evacuation operations afterwards, while facilities are subject to the risk of disruptions. We analyze how evacuation resource availability leverages individual evacuees’ response to service disruptions, and show how equilibrium of the evacuee arrival process could be reached at a functioning pick-up facility. Based on this equilibrium, an optimal resource allocation strategy is found to balance the tradeoff between the evacuees’ risks and the evacuation agency’s operation costs. This leads to the development of a compact polynomial-size linear integer programming formulation that minimizes the total expected system cost from both pre-emergency planning (e.g., facility set-up) and the evacuation operations (e.g., fleet management, transportation, and exposure to hazardous surroundings) across an exponential number of possible disruption scenarios. We also show how the model can be flexibly used to plan not only pre-disaster evacuation but also post-disaster rescue actions. Numerical experiments and an empirical case study for three coastal cities in the State of Mississippi (Biloxi, Gulfport, and D’lberville) are conducted to study the performance of the proposed models and to draw managerial insights.     

A combined land use-transportation model when zonal travel demand is endogenously determined

A combined transportation-land use model is proposed in this paper. Unlike other existing urban land use and transportation planning models in which a “fixed demand” for services is assumed to be known at the zonal level of an urban area, zonal travel demand is endogenously determined together with link congestion costs, optimal amounts of production and resulting efficient densities of land uses, once the transportation network is given. Some characteristics of alternative solutions are demonstrated. The proposed model represents progress over previous efforts in combining land use-transportation problems since the travel choice as to origin, destination and routes as well as amounts of goods to be produced at the optimal density of land uses are integrated into a consistent mathematical programming framework.     

A multi-objective optimization model for sustainable logistics facility location

This paper offers an exploratory study of sustainable facility location. The methodology, based on the classical uncapacitated facility location problem, provides decision makers with a multi-objective optimization model to determine the trade-off among economic, service and environmental considerations. Our results indicate that it may be desirable to open more facilities than optimal from a narrow economic perspective to reduce the carbon dioxide emissions of transport and to improve service reliability.     

Risk-based maintenance and rehabilitation decisions for transportation infrastructure networks

A method for determining optimal risk-based maintenance and rehabilitation (M&R) policies for transportation infrastructure is presented. The proposed policies guarantee a certain performance level across the network under a predefined level of risk. The long-term model is formulated in the Markov Decision Process framework with risk-averse actions and transitional probabilities describing the uncertainty in the deterioration process. The well known Conditional Value at Risk (CVaR) is used as the measure of risk. The steady-state risk-averse M&R policies are modeled assuming no budget restriction. To address the short-term resource allocation problem, two linear programming models are presented to generate network-level polices with different objectives. While the proposed methodology is general and can be used with any performance indicator, pavement roughness is used for numerical studies and an analytical expression for computing CVaR is derived.