A note on the structural stability of the equilibrium manifold

In a smooth pure exchange economy with fixed total resources we investigate whether the smooth selection property holds when endowments are redistributed across consumers through a continuous (non local) redistribution policy. We show that if the policy is regular then there exists a unique continuous path of equilibrium prices which support it. If singular economies are involved in the redistribution, then an analogous result can be obtained if the singular policy is the projection of a path transversal to the set of critical equilibria.Equilibrium manifold, regular equilibria, catastrophes, structural stability, smooth selection of prices

Evolution paths on the equilibrium manifold

In a pure exchange smooth economy with fixed total resources, we de- fine the length between two regular equilibria belonging to the equilibrium manifold as the number of intersection points of the evolution path connecting them with the set of critical equilibria. We show that there exists a minimal path according to this definition of length.Equilibrium manifold; regular economies; critical equilibria; catastrophes; Jordan-Brouwer separation theorem

Energy saving policies for a machine tool with warm-up, stochastic arrivals and buffer information

One of the measures for saving energy in manufacturing is the implementation of control strategies that reduces energy consumption during the machine idle periods. Specifically, the paper proposes a framework that integrates different control policies for switching the machine off when the production is not critical, and on either when the part flow has to be resumed or the queue has accumulated to a certain level. A general policy is formalized by modeling explicitly the power consumed in each machine state. A threshold policy is analyzed and the optimal parameter is provided for an M/M/1/K system. Numerical results are based on data acquired with dedicated experimental measurements on a real machining centre, and a comparison with common practices in manufacturing is also reported

Minimality and uniqueness of equilibrium

In this paper we propose the following conjecture: the equilibrium manifold E(r) ⊂ RLM−1, where L is the number of goods and M the number of consumers, is a minimal submanifold if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and for an arbitrary number of consumers and two goods under the assumption that the normal vector field of E(r) is constant outside a compact subset

Energy efficient control strategy for machine tools with stochastic arrivals and time dependent warm-up

Energy efficiency in manufacturing is becoming a challenging goal due to the demand of this sector in the worldwide scenario. One of the measures for saving energy is the implementation of control strategies that reduce machine energy consumption during the machine idle periods. This paper extends a threshold policy, that switches off the machine during interruptions of part flow, by modelling explicitly the warm-up time as dependent on the time period the machine stays in low power consumption state. The optimal policy parameter is provided numerically for general distributions of the part arrival time and general functions modelling the warm-up time. Numerical results are based on data acquired with dedicated experimental measurements on a real machining center

Endowments, patience types, and uniqueness in two-good HARA utility economies

This paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of $\gamma$ in the HARA utility function $\frac{\gamma}{1-\gamma}\left(b+\frac{a}{\gamma}x\right)^{1-\gamma}$. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in [4].Comment: 6 page

Endowments, patience types, and uniqueness in two-good HARA utility economies

This paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of γ in the HARA utility function γ 1−γ b+ a γx 1−γ. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in Loi and Matta (2022)

Energy Saving Opportunities and Value of Information: A Trade-off in a Production Line

A general framework for switching the machine off/on has been recently proposed in literature for single machines. However, the amount of information available along the production system is often limited and it might be not trivial to understand which information provides more benefits. This paper studies the performance of a production line when several control policies are applied at machine level. The amount of information at machine level varies and the trade-off with energy reduction is investigated. The considered performance measures are the energy consumed per part and the system throughput. Numerical results are based on discrete event simulation

Automated Generation of Digital Models for Production Lines through State Reconstruction

Thanks to the rapid advances in information technologies, digital twins have been widely adopted in the manufacturing industry to support production planning and control. At the core of a digital twin is a digital model that mirrors the physical system in a virtual space. It is inefficient to develop digital twins by modeling the considered systems manually. Although significant research effort has been made to automate the generation of digital models, most approaches so far impose strong assumptions on the available data or cannot precisely capture the behavior of the physical system. Noticing the current gap, we propose in this paper a novel approach for automatically generating a graph representation of a production line from an event log through state reconstruction. The feasibility of the proposed approach has been demonstrated on three simulated instances

A New Learning Factory Experience Exploiting LEGO For Teaching Manufacturing Systems Integration

Involving and stimulating students through intensive work in computer laboratories and simulation projects might be a challenging task, often due to the lack of the real manufacturing system that must be modeled and improved. Indeed, studying a manufacturing system that cannot be observed represents a real obstacle for student effective learning. In this paper, we describe the "LEGO FACTORY" initiative, an extra-curricular experience within the Master Degree Study Program in Mechanical Engineering of Politecnico di Milano. The initiative is open to students from any study course of the university. The goal is to exploit learning-by-playing principles to offer scholars the possibility to understand the most common issues in the design and management of manufacturing systems, with a focus on system integration. A miniaturized production system made with LEGO® MINDSTORMS® is provided to students who are asked to accomplish a project aiming at the improvement of the system performances. The participants work in teams and must introduce design modifications and develop technical solutions to address the requirements. The experience is described with the hope that the approach can be replicated in other environments