A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

Farm tractor models for research and development purposes

The modelling problems related to the simulation of the dynamics of farm tractors are dealt with. The aim is to develop reliable mathematical models to speed-up the research and development activities in which farm tractors and their sub-systems (driveline, steering and suspension system, etc.) are to be conceived and designed. Two models of farm tractors have been developed. The first model is based on a proprietary software, able to quickly simulate the motion of a vehicle on smooth or rough soil. The second model has been developed by the commercial software ADAMS/Car^®, which allows to model complicated transmission and suspension systems. In both of the two models, the tyres, the transmission system, the suspension system, the steering system, the engine and the body inertia are carefully described mathematically. Both of the two models are defined in a parametric way. Particular attention has been devoted to the measurements of the tyre characteristic and of the inertia parameters of the farm tractor body. For the measurement of tyre characteristics, a new instrumented wheel hub has been used. The accurate measurement of both the tyre characteristic and body inertia tensor has allowed a good agreement between measured and computed time histories referring to a number of validation manoeuvres performed either on-road or off-road. The derived farm tractor models could simulate the working conditions of a generic farm tractor while hauling a plough or while running at a relatively high speed on a rough soil or while steering on a sloped, soft surface.