A Monte Carlo simulation based heuristic procedure for solving dynamic line layout problems for facilities using conventional material handling devices

A simple procedure is proposed to identify line layout solutions when a production facility with work centres of unequal size uses conventional material handling devices and operates under stochastic demand scenarios. The procedure uses Monte Carlo simulation (MCS) to empirically search for robust solutions defined as those that simultaneously meet minimum material handling cost performance levels across all demand scenarios. The results reported in this study suggest that ‘robust’ line layout solutions can be identified using a modest volume of random sampling. The procedure and results are demonstrated through a series of sample problems.     

A methodology for solving the unequal area facility layout problem using distance and shape-based measures

This paper presents a methodology for solving the unequal area facility layout problem commonly encountered in industry practice. A mixed-binary nonlinear-programming model is formulated to capture the operational issues encountered on the shop floor. In particular, in addition to the distance measure that is typically used to quantify the material handling costs, the impact of geometry or the shape of the departments is quantified in the formulation of the model. A higher-level heuristic solution algorithm, based on a concept known as ‘tabu search’, is proposed to efficiently solve industry-relevant problems. The methodology not only considers the impact of both distance and shape-based measures simultaneously in the proposed initial solution finding mechanism, but also in the evaluation of the objective function during the entire search procedure, in the hope that it will lead to identifying a better final solution. Taking into consideration fixed and variable tabu list sizes, along with long-term memory with maximum and minimum frequencies, has led to developing six different heuristics for the solution algorithm. A single factor experiment based on randomized block design has been used to compare the performances of the six different heuristics on three different problem structures—small, medium, and large—using the total cost as the criterion. Based on this experiment, the characterizations of search procedures have been recommended to facilitate identifying the best solution for each problem structure. The proposed method is also compared with those in the published literature by solving fairly well known unequal area facility layout problems. When an improvement is observed, the comparison has led to identifying a percentage improvement in total cost of approximately 2.8% to 11.8%, thus demonstrating the effectiveness of the model and the algorithm.     

Monte Carlo simulation of a transition radiation detector

This paper employs Monte Carlo simulations of the performance of a transition radiation detector (TRD). The program has been written for the TRD in the ZEUS spectrometer, which separates electrons from hadrons in the momentum range between 1 and 30 GeV/c. Both, total charge method and cluster counting method were simulated taking into account various experimental parameters. In particular, it was found that the cluster counting method relies on a quantitative understanding of the background originating from the production of δ-electrons by charged particles. The results of the Monte Carlo calculations are in agreement with experimental data obtained with prototypes within a systematic uncertainty of 20%. We applied our Monte Carlo program to studies in order to find an optimum layout for the TRD within available space in the ZEUS spectrometer. In this context, the performance of TRD layouts with different geometries and materials has been evaluated comprehensively. The geometry found by optimization promises an improvement on hadron suppression by a factor of about two for both methods compared with present results from test measurements. Applying algorithms for a detailed analysis of the energy and space distributions of the clusters in the TRD, hadrons in the momentum range from 1 to 30 GeV/c can be suppressed to a level of less than 2%. This method of cluster analysing improves the suppression of hadrons by a factor of about two compared to the total charge method.     

Mechanical fragmentation,Voronoi polyhedra and the theory of information

Objects which can undergo mechanical fragmentation are composed of all kinds of materials and comprise the entire span of sizes from celestial bodies to particles with initial sizes of a few mm. The problem has been treated theoretically by Mott, by a Monte Carlo simulation of the Voronoi diagram by Kiang, and also experimentally. Taking an essential element from the Mott formalism, we use the theory of information to derive an equation for the distribution of fragment masses. The result is equivalent to a distribution which follows from Mott's work. In contrast to earlier work, the relation is general since no specific assumptions have been made as to the nature of the fragmented material or with respect to its ductility (or lack of it). Reasons why the Monte Carlo results differ from the present ones are explained.     

A Monte Carlo simulation model for stationary non-Gaussian processes

A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second order correlation functions than translation processes. The paper also develops an algorithm for generating samples of any non-Gaussian process in the class of mixtures of translation processes. The algorithm is based on the sampling representation theorem for stochastic processes and properties of the conditional distributions. Examples are presented to illustrate the proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes.     

Calculation of eigenfunction fluxes in nuclear systems

A new Monte Carlo method is being developed to calculate eigenfunction fluxes in critical or near-critical nuclear systems. The correct estimation of fluxes is essential for radiation protection and shielding near these systems, in addition to isotope production, isotope depletion, nuclear criticality and other applications. The proposed method applies to Monte Carlo criticality eigenvalue calculations in which the fission sites in one generation are used as fission sources in subsequent generations. The usual Monte Carlo power iteration method for such problems often calculates fluxes (eigenfunctions) that are inaccurate and very different in symmetric parts of a problem geometry. The proposed method calculates flux distributions by estimating an approximate fission matrix. The way the fission matrix is estimated and used differs from other recent works. Preliminary results are promising.     

Stochastic elastic–viscoplastic analysis for discontinuous rock masses

Both the first-order second moment method and the Monte–Carlo method are introduced to elastic–viscoplastic block theory in this paper. The safety index of blocks, block combinations and the whole rock–block system can be obtained by establishing adequate limit state equation. Some slope safety problems have been studied with the proposed methods.     

Solving nonlinear aerodynamic problems on digital computers

An engineering method for solving nonlinear aerodynamic problems of plane and axisymmetric steady flows is proposed. The method is a modification of the Monte Carlo method.     

Hybrid finite element-Monte Carlo method for coupled conduction and gas radiation enclosure heat transport

A hybrid two-dimensional finite element-Monte Carlo numerical solution method has been developed for solving complex transient non-linear gas radiation enclosure problems. Solid conducting media are coupled to conducting gaseous or particulate participating media and both may be internally energy generating. Bilinear isoparametric elements are used, allowing geometrically complex enclosures with internal objects to be present. Radiative energy transport within the gaseous enclosures is accounted for using a Monte Carlo method which permits a broad range of complexities. Included here are: diffuse-grey and specularly reflecting walls with temperature and spectrally dependent, and non-homogeneous emissivities or absorptivities; absorbing/emitting gases with temperature and spectrally dependent, and non-homogeneous emissivities or absorptivities; and isotropic or anisotropic scattering gases or particles. This method was verified by solving several standard steady state problems and comparing the solutions to those found using the conventional finite element, the P–N and the exchange factor methods. Solution times are comparable to those of the finite element method. A more complex transient problem solution is then given to demonstrate the versatility and power of the method.     

基于蒙特卡洛方法的触发器聚类布局算法

针对触发器聚类的布局问题,提出了一种基于蒙特卡洛方法的触发器聚类布局算法。该方法的核心思想为设计合理的评分函数,并通过蒙特卡洛方法模拟触发器聚类在版图上的随机游走过程,获取样本,再通过评分函数评价样本质量,逐步地在可行域中搜索最优解。实验结果表明,相较于现有的方法,该方法在总线长与时序性能两方面,分别得到平均约9%与17%的改善与提升。此外,该方法具有较强的健壮性,适用于复杂度较高或者版图利用率较高的设计,并能够快速收敛,以较小的时间代价完成优化。     

Polarization structure of lidar signals reflected from ice crystal clouds

Polarization characteristics of signals of a monostatic lidar intended for sensing of homogeneous ice crystal clouds are calculated by the Monte Carlo method. Clouds are modeled as monodisperse ensembles of randomly oriented hexagonal ice crystals. The polarization state of multiply scattered lidar signal components is analyzed for different scattering orders depending on the crystal shapes and sizes as well as on the optical and geometrical conditions of observation. Light-scattering phase matrices (SPMs), calculated by the beam splitting method (BSM), are used as input data for solving the vector radiative transfer equation. The principles of the BSM method are briefly described, and the SPM components are given for hexagonal ice plates and columns of different sizes and linearly polarized incident radiation with the wavelength lambda = 0.55 microm.     

An improved monte carlo technique for radiation shield design

Reduction of statistical error in Monte Carlo shielding calculations is achieved by using antithetic variates with geometrical surface splitting while solving the radiation transport problems. Numerical results are presented for sample calculations for slab shields of different dimensions. The present method shows great improvement in efficiency for thick slabs and therefore is useful for practical shielding calculations.     

Developing exact and Tabu search algorithms for simultaneously determining AGV loop and P/D stations in single loop systems

There are some issues which have to be addressed when designing an automated guided vehicles system (AGVS) such as flow-path layout, traffic management, the number and the location of pick up and delivery points, vehicle routing and so on. One of the AGVS guide path configurations discussed in the previous researches includes a single-loop which is the subject of this paper. In unidirectional single loop systems, determining the loop for the motion of an AGV, and the location of pick up and delivery (P/D) stations in the cells, are prominent points which, when considered simultaneously, lead to better results than determining each one independently. However, in the literature it is proved that the problem of separately determining the shortest feasible loop is a NP-complete problem. In this paper, by considering a from-to chart and a block layout as the input of problem, we try to determine: (1) a single loop, with at least one shared edge with each cell, (2) the direction of the flow and (3) the location of P/D stations on the loop, all at the same time, in a way that the total travel distance on the loop be minimised. In this regard, first a new exact algorithm is presented and then three heuristic algorithms are developed utilising a Tabu search (TS) method. Solving randomly generated test problems shows that our exact algorithm is capable of solving small size problems; also all three TS algorithms work efficiently in solving problems that could not be solved by exact algorithms.     

Moments-based clustering techniques for manufacturing cell formation

Clustering and data organization algorithms and array sorting methods are most widely used in solving machine-part grouping problems in Group Technology (GT). One of the most recent search algorithms for part-family identification is the close-neighbour search algorithm. However the method does not suggest a solution that tries to eliminate exceptional elements after the block diagonal structure is produced. This paper presents a Method of Moments approach such as Weighted Moment, End Load Ratio and Differential Moment Methods to solve this problem. The effectiveness of these algorithms is tested against sixteen problems from the literature. The results show that the algorithms are very efficient and reliable.     

Response of LiF:Mg,Ti to low energy carbon and oxygen ions

The extended track interaction model (ETIM) has been formulated to explain the TL-fluence response for peak 5 to heavy ions using radial dose distributions produced by the ions in LiF and their luminescent centre occupation probability distributions. In this work, an experimental study of the TLD-100 fluence response to carbon and oxygen ions and its interpretation in terms of a Monte Carlo simulation of ETIM applied to peak 5 are presented. Irradiations were performed with 7.34 and 10.3 MeV 12C and 8.34 MeV 16O ions in the fluence interval between 2 x 10(7) and 2 x 10(11) cm(-2). Individual glow curve responses show the expected increase of supralinearity as the peak temperature increases. Data for peak 5 show a weak dependence with energy. These latter results are difficult to understand when one considers the differences in the expected radial occupancies for different ion energies.     

Monte carlo methods in reliability engineering

The potential of the Monte Carlo method as a common place tool for a broad range of reliability and logistic problems is discussed. The mathematical features of the method are illustrated and biasing methods aimed at reducing the cost of the calculation are described. These methods combine efficiency with simplicity of implementation in multipurpose computer codes. A multipurpose computer code package developed on the basis of the Monte Carlo method is described.     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

Dielectric investigations and theoretical calculations of size effect in lead titanate nanocrystals

The dielectric properties of nanograin ferroelectric lead titanate crystals are presented. The PbTiO3 samples were prepared by pressing nanopowders into plates and were studied experimentally by dielectric permittivity measurements in a wide frequency and temperature range. The TC dependence obtained showed a critical change of behavior with increasing mean nanoparticle size in the 9-nm region. The theoretical calculations based on Monte Carlo simulation were performed to describe the behavior of this material. It was shown that the distribution of nanoparticle sizes in the sample taken into account with the Monte Carlo method describes the dielectric properties of PbTiO3 nanocrystals quite well.     

联合分布函数蒙特卡罗模拟及结构可靠度分析

针对复杂极限状态方程可靠度计算问题,提出了基于理论联合分布函数以及2 种近似联合分布函数的结构失效概率蒙特卡罗模拟方法,并给出了计算流程图.采用2 个算例证明了所提方法的有效性.结果表明:所提的失效概率模拟方法的计算精度很高,尤其适用于复杂极限状态方程的可靠度计算问题.2 种联合分布函数近似构造方法得到的失效概率精度相当,近似方法与精确方法结果的差异随失效概率的减小而增大,而且随着变量间相关性的增加而增加.当失效概率小于10-3时,近似方法的失效概率误差较大.     

Evaluating Uncertainties in Interpolations Between Calibration Data for Thermocouples

Two methods for evaluating thermocouple calibration uncertainty over the temperature range of the calibration are presented, when the thermocouple is calibrated at only a few temperatures. The evaluation of the uncertainty at fixed-point temperatures is well established, but it is often not clear how the uncertainty arising from interpolation between fixed points can be determined. We present a conventional method, based on that described in the “Guide to the expression of uncertainty in measurement” (GUM), and a numerically-based Monte Carlo method, for quantifying the calibration uncertainty arising from the use of an interpolating polynomial defined by calibration data. The two methods are compared and found to be in excellent agreement, but the Monte Carlo method is, in general, more flexible, e.g., when measurements are described by non-normal distributions.