It has been addressed in the existing literature that the volume–capacity (v/c) ratio on a private toll road is constant, regardless of the toll value and capacity set by the private companies for each toll road in the network. The previous derivation depends on the assumption that the user...

Conventional analysis of optimal congestion pricing relies on three primary elements, namely, the speed-flow relationship, the demand function, and the generalized cost. Analytical demand functions tailed for congestion pricing are, however, difficult to establish in practice even with advanced...

The classical Wardropian principle assumes that users minimize either individual travel cost or overall system cost. Unlike the pure Wardropian equilibrium, there might be in reality both competition and cooperation among users, typically when there exist oligopoly Cournot-Nash (CN) firms. In...

The continuous network design problem (CNDP) is generally formulated as a mathematical program with equilibrium constraints (MPEC). It aims to optimize the network performance via expansion of existing links subject to the Wardrop user equilibrium constraint. As one of the extremely challenging...

Reversing port rotation directions of ship routes is a practical alteration of container liner shipping networks. The port rotation directions of ship routes not only affect the transit time of containers, as has been recognized by the literature, but also the shipping capacity and transshipment...

This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper...

This paper deals with a tactical-level liner ship route schedule design problem which aims to determine the arrival time of a ship at each portcall on a ship route and the sailing speed function on each voyage leg by taking into account time uncertainties at sea and at port. It first derives the...

This paper develops a mathematical program with equilibrium constraints (MPEC) model for the intermodal hub-and-spoke network design (IHSND) problem with multiple stakeholders and multi-type containers. The model incorporates a parametric variational inequality (VI) that formulates the user...

This paper develops three game-theoretical models to analyze shipping competition between two carriers in a new emerging liner container shipping market. The behavior of each carrier is characterized by an optimization model with the objective to maximize his payoff by setting optimal freight...