Numerical schemes for the optimal input flow of a supply-chain

An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation law for the density of processed parts coupled to an ODE for the queue buffer occupancy. The control problem is stated as the minimization of a cost functional J measuring the queue size and the quadratic difference between the outflow and the expected one. The main novelty is the extensive use of generalized tangent vectors to a piecewise constant control, which represent time shifts of discontinuity points. Such method allows convergence results and error estimates for an Upwind- Euler steepest descent algorithm, which is also tested by numerical simulations

On Optimization of a Highly Re-Entrant Production System

We discuss the optimal control problem stated as the minimization in the $L^2$-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the switch dispatch point (SDP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a quasi-pull policy. The main question we discuss in this paper is about the optimal choice of the input in-flux, push and quasi-pull constituents, and the position of SDP

Spatial behaviour of the states of bending in microstrech elastic plates

In this paper we study the spatial behavior of the states of bending in a microstretch elastic plate. We show that, for fixed time t, in that part of the plate where the distance to the support of data is greater tha ct (c is a material constant), the state of bending is vanishing. While for the part of the plate where the distance to the support is less than ct an appropriate measure associate with the state of bending decays exponentially with that distance. As a consequence, a uniqueness theorem is presented for an infinite plate with no apriori conditions at infinity

Problemi di Omogeneizzazione: Formule di Rappresentazione, Domini Perforati.

Sunto della tesi di dottorato di Ricerca in Analisi Matematica e Calcolo delle Probabilit

On Saint-Venant's principle in a poroelastic arch-like region

In this paper we consider the state of plane strain in an elastic material with voids occupying a curvilinear strip as an arch-like region described by R:a<r<b,0<h<x, where r and θ are polar coordinates and a, b, and ɷ (<2π) are prescribed positive constants. Such a curvilinear strip is maintained in equilibrium under self-equilibrated traction and equilibrated force applied on one of the edges, whereas the other three edges are traction free and subjected to zero volumetric fraction or zero equilibrated force. In fact, we study the case when one right or curved edge is loaded. Our aim is to derive some explicit spatial estimates describing how some appropriate measures of a specific Airy stress function and volume fraction evolve with respect to the distance to the loaded edge. The results of the present paper prove how the spatial decay rate varies with the constitutive profile. For the problem corresponding to a loaded right edge, we are able to establish an exponential decay estimate with respect to the angle θ. Whereas for the problem corresponding to a loaded curved edge, we establish an algebraical spatial decay with respect to the polar distance r, provided the angle ɷ is lower than the critical value π√2. The intended applications of these results concern various branches of medicine as for example the bone implants

Spatial behaviour for the harmonic vibrations in plates of Kirchoff type

In this paper the spatial behaviour of the steady-state solutions for an equation of Kirchhoff type describing the motion of thin plates is investigated. Growth and decay estimates are established associating some appropriate cross-sectional line and area integral measures with the amplitude of the harmonic vibrations, provided the excited frequency is lower than a certain critical value. The method of proof is based on a second–order differential inequality leading to an alternative of Phragmèn–Lindelöf type in terms of an area measure of the amplitude in question. The critical frequency is individuated by using some Wirtinger and Knowles inequalities

Analysis of urban traffic using queueing networks

A simulative traffic model of urban networks based on queueing theory is proposed. The urban network can be represented with an oriented graph: the edges model the roads and the nodes the connection roads. Once the graph modeling the urban section is outlined, some queueing systems are assiociated with the graph in such way to obtain a queueing network which can be investigated with analytical tools or by means of simulations. An example of application of the simulator based on the described model is presented

On Saint's Venant principle for a linear poroelastic material in plane strain

In this paper we consider the state of plane strain in an elastic material with voids occupying a rectangular strip. Such a strip is maintained in equilibrium under selfequilibrated traction and equilibrated force applied on one of the edges, while the other three edges are traction-free and subjected to zero volumetric fraction or zero equilibrated force. Our aim is to derive some explicit spatial estimates describing how some appropriate measures of a specific Airy stress function and volume fraction evolve with respect to the distance to the loaded edge. The both cases of homogeneous and inhomogeneous poroelastic materials are considered. The results of the present paper prove how the spatial-decay rate varies with the constitutive profile