We reconsider the pollution permit concept in a setting extended to include dynamics, spatially diversified firms, and an oligopoly in product markets. The firms can manage their pollution emissions or stocks by (1) buying pollution permits and emitting pollution, (2) shipping pollutants to...

In this paper, we consider dynamic congestion pricing in the presence of demand uncertainty. In particular, we apply a robust optimization (RO) approach based on a bi-level cellular particle swarm optimization (BCPSO) to optimal congestion pricing problems when flows correspond to dynamic user...

In this paper we present a continuous-time network loading procedure based on the Lighthill–Whitham–Richards model proposed by Lighthill and Whitham (1955) and Richards (1956). A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel...

The Vickrey model, originally introduced in Vickrey (1969), is one of the most widely used link-based models in the current literature in dynamic traffic assignment (DTA). One popular formulation of this model is an ordinary differential equation (ODE) that is discontinuous with respect to its...

This paper is concerned with the continuous-time Vickrey model, which was first introduced in Vickrey (1969). This model can be described by an ordinary differential equation (ODE) with a right-hand side which is discontinuous in the unknown variable. Such a formulation induces difficulties with...

This paper presents a model of the strategic behavior of firms operating in a spatial supply chain network. The manufacturing and retailing firms engage in an oligopolistic, noncooperative game by sharing customer demand such that a firm’s decisions impact the product prices, which in turn...

A direct approach to performing sensitivity analysis for a spatial price equilibrium problem with nonlinear transportation cost, commodity supply and commodity demand functions is presented. The first order derivatives of all decision variables with respect to parameter perturbations are shown...

This paper reviews the problems associated with application of the concept of consumers' surplus to the measurement of benefits derived from a transportation investment. This review is warranted since such measurement is very complicated when alternative modes or different paths are available to...

The task of predicting the short run equilibrium of a transportation market is central to the study of many transportation problems. In this paper we review the different approaches and methodologies that have been proposed to deal with the equilibrium problem in transportation markets. The...