Application of the Microsoft Excel Solver tool in the solution of optimization problems of heat exchanger network systems

Optimization of heat exchanger networks (HEN_S) is a field of interest in Chemical Engineering. The aim is to use the residual heat of process streams to raise the temperature of other process streams which are cold, thus minimizing the use of hot and cold utilities. The usual way to deal with this task is to pose a linear programming problem according to a transshipment model in order to minimize either the general services consumptions or the number of hot and cold stream matchings required. This optimization is subjected to several restrictions given by the energy balances corresponding to each heat exchange.The high number of variables and equations obliges the use of specific software to solve these problems, e.g. GAMS (General Algebraic Modelling System). However, this software is not intuitive and requires a long time of training and a certain level of practice for the students to adequately use it.This work describes the use of Microsoft Excel-Solver for the sequential solving of HEN_S optimization problems according to the transshipment model. Solver is a much simpler, intuitive and easily available tool for the students who, besides, usually learn how to use it in the first years of their degree, in Informatics or similar subjects. Thus, it is not necessary to spend extra time in the teaching of the software, time that may be devoted to other contents.This paper presents an example of HEN_S problem proposed in the subject Simulation and Optimization of Chemical Processes corresponding to the Joint Master in Chemical Engineering of the Rey Juan Carlos University and the Autónoma University of Madrid and solved by the students using Excel-Solver.     

On the effects of the packet size distribution on the packet loss process

Real-time multimedia applications have to use forward error correction (FEC) anderror concealment techniques to cope with losses in today’s best-effort Internet. The efficiency of these solutions is known however to depend on the correlation between losses in the media stream. In this paper we investigate how the packet size distribution affects the packet loss process, that is, the distribution of the number of lost packets in a block, the related FEC performance and the average loss run length. We present mathematical models for the loss process of the MMPP+M/D/1/K and the MMPP+M/M/1/K queues; we validate the models via simulations, and compare the results to simulation results with an MPEG-4 coded video trace. We conclude that the deterministic packet size distribution (PSD) not only results in lower stationary loss probability than the exponential one, but also gives a less correlated loss process, both at a particular average link load and at a particular stationary loss probability as seen by the media stream.Our results show that for applications that can only measure the packet loss probability, the effects of the PSD on FEC performance are higher in access networks, where a single multimedia stream might affect the multiplexing behavior. Our results show that the effects of the PSD on FEC performance are higher in access networks, where a single multimedia stream might affect the multiplexing behavior and thus can improve the queuing performance by decreasing the variance of its PSD.     

Damage Development in Gray Cast Iron under Static Deformation

The authors discuss the results of experimental investigation of structural degradation of gray cast iron at various stages of static tensile deformation. Analysis of the deformation process has revealed that damageability of a material under loading can be assessed by both a special strain parameter and scatter of hardness characteristics or a ratio of the modulus deviation to the current value of the elastic modulus. A correlation between these parameters has been established.     

Controlled linear system with delayed relay output under impulse random disturbances

The paper is devoted to the first order delayed linear system with relay output controlled by the proportional-integral (PI) regulator. The deterministic system exhibits stable oscillations, and, since the system itself is stable, it can be suitable to switch off the controller if there are no disturbances during a long time interval. In the present work, the random disturbances are modelled by a Poisson stream of impulses, and the goal is to determine the instants of switching on (off) of the PI controller. After several assumptions and quantization of the time axis, we construct the new optimal control problem which is successfully solved with the help of the dynamic programming approach.     

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.     

Different insights for improving part and system reliability obtained from exactly same DFOM “failure numbers”

Techniques for improving the reliability and maintainability of both nonrepairable and repairable items can be suggested by failure data analysis. It is shown that a given set of failure numbers leads to very different improvement strategies when the numbers are the times-between-successive-failures of one or more repairable items, rather than the times-to-failure of nonrepairable items. Since this should have been obvious more than 50 years ago, at the onset of formal reliability engineering activities, several reasons are proffered for the widespread and protracted misinterpretation of even the most basic—and simple!—conceptual and practical differences between nonrepairable and repairable items.     

Optimal production-inventory policy for make-to-order versus make-to-stock based on the M/Er/1 queuing model

This paper analyzes a multi-product production / inventory system where demands for each item arrive according to a Poisson process and the production time for each product has an Erlang distribution. The paper proposes an optimality condition that specifies whether each product should be produced make-to-stock or make-to-order. In the event a product should be produced make-to-stock, an approach for computing the optimal base-stock level is proposed. Numerical examples are given for illustrative purpose.     

La distribucion hipergeometrica como binomial de poisson

Resumen En este trabajo demostramos que toda distribución hipergeométricaH(N, X,n) puede ser descrita como suma de pruebas independientes con probabilidades de éxito distintas entre sí. Tal distribución recibe habitualmente el nombre de binomial de Poisson o binomial generalizada.      

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Parametric and nonparametric Bayesian model specification: A case study involving models for count data

In this paper we present the results of a simulation study to explore the ability of Bayesian parametric and nonparametric models to provide an adequate fit to count data of the type that would routinely be analyzed parametrically either through fixed-effects or random-effects Poisson models. The context of the study is a randomized controlled trial with two groups (treatment and control). Our nonparametric approach uses several modeling formulations based on Dirichlet process priors. We find that the nonparametric models are able to flexibly adapt to the data, to offer rich posterior inference, and to provide, in a variety of settings, more accurate predictive inference than parametric models.