Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

City logistics: trasporto merci in ambito urbano

Molteplici studi, portati a termine di recente in Europa ed oltreoceano, hanno focalizzato l’attenzione sulle problematiche indotte dal trasporto merci in ambito urbano e contribuito ad identificarne possibili soluzioni (city logistics). Le aree urbane, dovrebbero idealmente essere luoghi ove abitare, svolgere attività economiche, sociali e ricreative. Esse possono vedere compromessa la loro predisposizione a tali scopi anche a causa del crescente traffico delle merci, il cui trasporto è effettuato principalmente su gomma, per via delle brevi distanze da coprire e delle carenze infrastrutturali. I veicoli commerciali, ad eccezione di quelli di ultima generazione, incidono negativamente sulla qualità dell’ambiente urbano, generando inquinamento atmosferico e acustico. La politica del “just in time”, che prevede l’assenza di magazzini di stoccaggio delle merci, incrementa i movimenti commerciali. Nella presente tesi vengono trattati alcuni aspetti logistici di regolamentazione della sosta e degli accessi per i mezzi di trasporto merci, in grado di rendere più efficiente la distribuzione dei beni, mitigando le problematiche indotte dal traffico e, quindi, salvaguardando la qualità di vita nei centri cittadini.

Urban food planning, city logistics and sustainability: the role of the wholesale produce market. The cases of Parma and Bologna food hubs.

At global level, the population is increasingly concentrating in the cities. In Europe, around 75% of the population lives in urban areas and, according to the European Environmental Agency (2010), urban population is foreseen to increase up to 80 % by 2020. At the same time, the quality of life in the cities is declining and urban pollution keeps increasing in terms of carbon dioxide (CO2) emissions, waste, noise, and lack of greenery. Many of European cities struggle to cope with social, economic and environmental problems resulting from pressures such as overcrowding or decline, social inequity, health problems related to food security and pollution. Nowadays local authorities try to solve these problems related to the environmental sustainability through various urban logistics measures, which directly and indirectly affect the urban food supply system, thus an integrated approach including freight transport and food provisioning policies issues is needed. This research centres on the urban food transport system and its impact on the city environmental sustainability. The main question that drives the research analysis is "How the urban food distribution system affects the ecological sustainability in modern cities?" The research analyses the city logistics project for food transport implemented in Parma, Italy, by the wholesale produce market. The case study investigates the renewed role of the wholesale market in the urban food supply chain as commercial and logistic operator, referring to the concept of food hub. Then, a preliminary analysis on the urban food transport for the city of Bologna is presented. The research aims at suggesting a methodological framework to estimate the urban food demand, the urban food supply and to assess the urban food transport performance, in order to identify external costs indicators that help policymakers in evaluating the environmental sustainability of different logistics measures

Models and Algorihtm for the Optimization of Real-World Routing and Logistics Problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.