Pavement rehabilitation scheduling and toll pricing under different regulatory regimes

This paper addresses the highway pavement rehabilitation scheduling and toll pricing issues over a planning horizon. In the highway system concerned, two types of agents are considered, namely highway operator and road users. Two models, which account for different highway regulatory regimes (i.e. public and private), are proposed. In the public regulatory model, the government aims to maximize total discounted social welfare of the transportation system over the planning horizon by determining the optimal pavement rehabilitation schedule and toll level. In the private regulatory regime, a profit-driven private operator seeks to optimize the pavement rehabilitation schedule and toll level to maximize its own discounted net profit over the planning horizon. The proposed models treat the interactions between the highway operator and the road users in the system as a bi-level hierarchical problem in which the upper level is a multi-period pavement rehabilitation scheduling and toll pricing problem, while the lower level is a multi-period route choice equilibrium problem. A heuristic solution algorithm that combines a greedy approach and a sensitivity analysis based approach is developed to solve the proposed bi-level multi-period optimization models. An illustrative example is used to show the applications of the proposed models. The findings show that the highway regulatory regime, pavement deterioration parameter and the roughness-induced vehicle operating cost can significantly affect the pavement rehabilitation schedules and the toll level as well as the performance of transportation system in terms of total life-cycle travel demand, net profit and social welfare.     

Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction

This study deals with the lead time and ordering cost reduction problem in the single-vendor single-buyer integrated inventory model. We consider that buyer lead time can be shortened at an extra crashing cost which depends on the lead time length to be reduced and the ordering lot size. Additionally, buyer ordering cost can be reduced through further investment. Two models are presented in this study. The first model assumes that the ordering cost reduction has no relation to lead time crashing. The second model assumes that the lead time and ordering cost reduction are interacted. An iterative procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.     

Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Despite the simplicity and practicality of (deterministic) fundamental diagram models in highway traffic flow theory, the wide scattering effect observed in empirical data remains highly controversial, particularly for explaining traffic state variations. Owing to the analytical properties of the fundamental diagram modeling approach, in this study, we proposed an analytical and quantitative method for analyzing traffic state variations. We investigated the scattering effect in the fundamental diagram and proposed two stochastic fundamental diagram (SFD) models with lognormal and skew-normal distributions to explain the variations in traffic states. The first SFD model assumes that the scattering effect results from stochasticity in both the free-flow speed and the speed at critical density. Both random variables were assumed to follow the lognormal distribution. In the second SFD model, an integrated error term that was assumed to follow the skew-normal distribution over different density ranges was appended to the deterministic fundamental diagram. The properties of these two SFD models were analyzed and compared, and the parameters in these SFD models were calibrated using real-world loop detector data. The observed scatters from the empirical data were reproduced well by the simulated fundamental diagram model, indicating the validity of the proposed SFD models for explaining traffic state variations. Using these two analytical SFD models, we can analyze the stochastic capacity of freeways with closed forms. More importantly, the sources of stochasticity in freeway capacity can be traced in terms of randomly distributed parameters in fundamental diagram models.     

Implementación eficiente de una formulación semirrecursiva para la dinámica de sistemas multicuerpo de gran tamaño

This article shows an efficient implementation of a dynamic semi-recursive formulation for large and complex multibody system simulations, with interesting applications in the automotive field and especially with industrial vehicles. These systems tend to have a huge amount of kinematic constraints, becoming usual the presence of redundant but compatible systems of equations. The maths involved in the solution of these problems have a high computational cost, making very challenging to achieve real-time simulations.In this article, two implementations to increase the efficiency of these computations will be shown. The difference between them is the way they consider the Jacobian matrix of the constraint equations. The first one treats this matrix as a dense one, using the BLAS functions to solve the system of equations. The second one takes into account the sparse pattern of the Jacobian matrix, introducing the sparse function MA48 from Harwell.Both methodologies have been applied on two multibody system models with different sizes. The first model is a vehicle IVECO DAILY 35C15 with 17 degrees of freedom. The second one is a semi-trailer truck with 40 degrees of freedom. Taking as a reference the standard C/C + + implementation, the efficiency improvements that have been achieved using dense matrices (BLAS) have been of 15% and 50% respectively. The results in the first model have not improved significantly by using sparse matrices, but in the second one, the times with sparse matrices have been reduced 8% with respect to the BLAS ones.     

Balanced vehicular traffic at a bottleneck

The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or off-ramps. The coupling conditions for the Riemann problem of the system are applied in order to treat the interface between different road sections consistently. Our numerical simulations show the appearance of synchronized flow at highway bottlenecks.     

Collective risk models with dependence

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such risk models in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.     

基于独立分量分析——最小二乘支持向量机的公路建设项目投资估算新模型

为快速、准确地进行公路建设项目投资估算,提出了一种新型的公路建设项目投资估算模型.该模型首先基于独立分量分析技术,根据最小互信息原理,有效分离出公路建设项目投资估算的独立影响因素源.然后,将这些独立影响因素源用于最小二乘支持向量机的训练,从而建立了基于独立分量分析技术—最小二乘支持向量机的公路建设项目投资估算模型.该模型将独立分量分析技术的盲信号分离能力与最小二乘支持向量机处理有限样本条件下非线性回归问题的优势有机结合,提高了模型预测的准确性.     

Endogenous formation of networks for local public goods

The paper studies a situation in which agents can make a binding agreement both on the amount of local public goods and on the structure of networks through which they share the benefits of public goods. An agent enjoys the benefit of public goods produced by other agents who are (directly or indirectly) connected to him. There is a cost to maintain a link as well as to produce a public good. Because agents can choose the amount of public goods, the value of a link is endogenously determined. We consider two different models of sequential bargaining games through which a contract on allocations is established. In the first model, we allow agents to propose a pure allocation and show that there is no symmetric stationary perfect equilibrium for sufficiently patient agents. In the second model, agents are allowed to propose a distribution on allocations. As a result, we find a symmetric stationary perfect equilibrium in which probabilistic choices are made on an equivalent class of allocations. Subsequently, we characterize core allocations, which consist of a minimally connected network and an effort profile, in which at most one agent does not produce the maximum amount of public good.     

Construction of a real-world bilevel linear programming model of the highway network design problem

The formulation of the highway network design problem (NDP) as a bilevel linear program (BLP) allows more realistic solutions taking into account the reaction of users to improvements made by the system. In this paper, a conceptual framework for the optimization of investments in inter-regional highway networks in developing countries is proposed. The model is applied to the Tunisian network using actual data. Considerable effort was expended to make the implementation as realistic as possible, taking into consideration travel times, operating costs, accident costs, improvement costs, conservation laws, and effects of intra-regional flows. A new formulation allowing the incorporation of any improvement cost functions, including non-convex and non-concave functions, is introduced.     

A model of a general parimutuel system: Characterizations and equilibrium selection

We formulate a model of a parimutuel system which considers a horse race with two horses. In our model, the raceholder offers a rate of his total betting revenue in the first stage. In the second stage each bettor simultaneously decides whether he bets one unit of money on one horse or he withdraws, according to his win predictions for each horse. We assume that all bettor's predictions are different and are common knowledge. We define some types of equilibria in the second stage game and give necessary and sufficient conditions for their existence. One equilibrium is a selected as a solution for the second stage game. We also define a solution for the whole game by using this result. Finally, we analyze the relation between the solution and variance for the bettor predictions.We thank to Prof. Okada, A. and Ikebe, Y. for helpful discussions. Special thanks are due to an anonymous referee for very grateful comments.     

Time and inventory dependent optimal maintenance policies for single machine workstations: An MDP approach

In this work the problem of obtaining an optimal maintenance policy for a single-machine, single-product workstation that deteriorates over time is addressed, using Markov Decision Process (MDP) models. Two models are proposed. The decision criteria for the first model is based on the cost of performing maintenance, the cost of repairing a failed machine and the cost of holding inventory while the machine is not available for production. For the second model the cost of holding inventory is replaced by the cost of not satisfying the demand. The processing time of jobs, inter-arrival times of jobs or units of demand, and the failure times are assumed to be random. The results show that in order to make better maintenance decisions the interaction between the inventory (whether in process or final), and the number of shifts that the machine has been working without restoration, has to be taken into account. If this interaction is considered, the long-run operational costs are reduced significantly. Moreover, structural properties of the optimal policies of the models are obtained after imposing conditions on the parameters of the models and on the distribution of the lifetime of a recently restored machine.     

A Quasi Fixed-Point Theorem for a Product of u.s.c. or o.l.s. Correspondences with an Economic Application

In the first place, we present a quasi fixed-point theorem for a correspondence defined on some infinite-dimensional locally convex topological vector space such that some variables have open lower sections and the other ones are upper semicontinuous.In the second place, we propose a direct application of the quasi fixed-point result in an economic model. More precisely, we prove a nonemptiness result of the core of an exchange economy with asymmetric information, a continuum of states and a finite number of commodities.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.     

Valuing flexibility: an impulse control framework

This paper presents a general framework for modeling and evaluating investments which involve flexibility to switch between alternative states of operation (for example, different sets of production inputs and outputs). The model employs a contingent claims pricing approach and encompasses previous real option models as special cases. We discuss practical solution techniques for the valuation problem under different assumptions regarding the cost and frequency of switching.     

Numerical analysis of chip formation during machining for different value of failure strain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the papers [1, 2] the thermo-mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object. The influence of failure strain ε_f on states of strain and stress in surface layer during machining is explained. The phenomena on a typical incremental step were described using step-by-step incremental procedure, with updated Lagrangian formulation. Then, the Finite Element Method (FEM) and Dynamic Explicit Method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena: states of displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone through the introduction of finite elements of TARGET and CONTACT types, without the necessity to introduce boundary conditions. This model includes variational equations of the object's motion and deformation. Examples of calculations for the displacement, strain and stress field in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Joint optimization of process improvement investments for supplier–buyer cooperative commerce

This research focuses on supporting the formation of strategic alliances through the concept of cooperative commerce, where suppliers and buyers work together to jointly optimize their business. The general goal of this research is to examine existing cooperative commerce models for obstacles that would hinder their successful implementation into modern industrial applications and to address those shortcomings. Total annual cost equations are formulated to capture the joint total relevant cost of cooperative commerce business relationships. These total joint relevant cost models will include terms that capture the ordering cost, holding cost, and cost of quality, as well as any applicable investment cost for process improvements, consistent with traditional economic order quantity and economic production quantity theory. This research corrects a modelling/computational error found in the literature that led to underestimation of the effectiveness of process improvements in joint economic lot size models by 5–12%. In addition, the models are expanded to accommodate a full range of product quality inspection policies, from 0 to 100% product inspections. Furthermore, the models are modified to account for the cost of scrap generation, as well as the effects of accepting non-conforming product and rejecting conforming product during quality inspections. Once the total cost models are expanded to account for these neglected costs, the joint total relevant cost equations are minimized to find the optimal batch sizes, and the effects of each model extension on the model solution are studied. Results indicate that these extensions have a significant impact on the model results, such as reduced optimal batch sizes and increased optimal fraction conforming product.     

Production planning via scenario modelling

Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed. In contrast to traditional mathematical programming approaches, we use scenarios to characterize the uncertainty in demand. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield a nonanticipative or implementable policy. Such an approach makes it possible to model nonstationarity in demand as well as a variety of recourse decision types. Two scenario-based models for formalizing implementable policies are presented. The first model is a LP model for multi-product, multi-period, single-level production planning to determine the production volume and product inventory for each period, such that the expected cost of holding inventory and lost demand is minimized. The second model is a MIP model for multi-product, multi-period, single-level production planning to help in sourcing decisions for raw materials supply. Although these formulations lead to very large scale mathematical programming problems, our computational experience with LP models for real-life instances is very encouraging.     

Cost optimal periodic train scheduling

For real world railroad networks, we consider minimizing operational cost of train schedules which depend on choosing different train types of diverse speed and cost. We develop a mixed integer linear programming model for this train scheduling problem. For practical problem sizes, it seems to be impossible to directly solve the model within a reasonable amount of time. However, suitable decomposition leads to much better performance. In the first part of the decomposition, only the train type related constraints stay active. In the second part, using an optimal solution of this relaxation, we select and fix train types and try to generate a train schedule satisfying the remaining constraints. This decomposition idea provides the cornerstone for an algorithm integrating cutting planes and branch-and-bound. We present computational results for railroad networks from Germany and the Netherlands.     

A Branch and Price algorithm for the k-splittable maximum flow problem

The Maximum Flow Problem with flow width constraints is an NP-hard problem. Two models are proposed: the first model is a compact node-arc model using two flow conservation blocks per path. For each path, one block defines the path while the other one sends the right amount of flow on it. The second model is an extended arc-path model, obtained from the first model after a Dantzig–Wolfe reformulation. It is an extended model as it relies on the set of all the paths between the source and the sink nodes. Some symmetry breaking constraints are used to improve the model. A Branch and Price algorithm is proposed to solve the problem. The column generation procedure reduces to the computation of a shortest path whose cost depends on weights on the arcs and on the path capacity. A polynomial-time algorithm is proposed to solve this subproblem. Computational results are shown on a set of medium-sized instances to show the effectiveness of our approach.     

Empirical validation of a queueing approach to uninterrupted traffic flows

In this paper, the use of queueing theory for modeling uninterrupted traffic flows is evaluated. Empirical data on speeds and flows are used to evaluate speeds generated by the different queueing models. Using the Theil inequality coefficient as evaluation criterion, the speeds generated by the queueing models are compared to the empirical speeds. Queueing models that best fit the observed speeds are obtained. It appears that traffic flow on a highway during non-congested hours is best described using a M/G/1 queueing model. During the congested hours however, the state dependent queueing GI/G/z models are more realistic. Because the queueing models describe the empirical data well, they can also be used to evaluate potential improvements in existing traffic conditions. Received: April 2005 / Revised version: June 2005 AMS classification: 60K30, 68M20