Production lot size problem with failure in repair and backlogging derived without derivatives

Conventional approaches for solving the production lot size problems are by using the differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. This note presents a simple algebraic method to replace the use of calculus for determining the optimal lot size. This study refers to the approach used by Grubbström and Erdem [Grubbström, R.W., Erdem, A., 1999. The EOQ with backlogging derived without derivatives, International Journal of Production Economics 59, 529–530] and extends it to the model examined by Chiu and Chiu [Chiu, S.W., Chiu, Y.-S.P., 2006. Mathematical modelling for production system with backlogging and failure in repair. Journal of Scientific and Industrial Research 65(6), 499–506]. This paper demonstrates that the lot size solution and the optimal production-inventory cost of an imperfect EMQ model can be derived without derivatives. As a result, the practitioners or students with little or no knowledge of calculus may be able to manage or understand with ease the realistic production systems.     

A Subgrid-Scale Stabilized Finite Element Method for Multicomponent Reactive Transport through Porous Media

Standard Galerkin finite element methods (GFEM) lack stability in solving advection-dominated solute transport in porous media. They usually require prohibitively fine grids and extremely small time steps to solve for advection-dominated problems. The algebraic subgrid-scale stabilized (ASGS) finite element method has been proved to overcome such problems for single-species reactive transport. Its potential for dealing with multicomponent reactive transport has not yet been explored. Here we present a numerical formulation of ASGS for steady and transient multicomponent reactive transport. Subgrid-scale transport equations are solved first by using an ASGS approximation and their solutions are substituted back into the grid-scale equations. A sequential iteration approach (SIA) is used to solve for coupled transport and chemical equations. Coupling of ASGS and SIA, ASGS+SIA, has been implemented in a reactive transport code, CORE^2D V4, and verified for conservative solute transport. ASGS+SIA has been tested for a wide range of 1-D transient multicomponent reactive transport problems involving different types of chemical reactions such as: (1) Kinetically controlled aqueous species degradation, (2) Kinetic mineral dissolution, (3) Serial-parallel decay networks, and (4) Cation exchange and pyrite oxidation at local equilibrium. ASGS+SIA always provides accurate solutions and therefore offers an efficient option to solve for advection-dominated multicomponent reactive transport problems.     

e~(At)四种计算方法的比较

状态转移矩阵eAt在现代控制理论与工程技术以及常系数微分方程组理论中有着非常重要的应用.通过一个实例,给出计算状态转移矩阵eAt的四种不同的方法:矩阵指数函数展开法,Jordan标准形法,待定系数法,Laplace变换法.笔者论述了各种计算方法的基本步骤及计算的难点与要点,经过分析对比,最后给出最优选择.     

Towards “Ideal Multistart”. A stochastic approach for locating the minima of a continuous function inside a bounded domain

A stochastic global optimization method based on Multistart is presented. In this, the local search is conditionally applied with a probability that takes in account the topology of the objective function at the detail offered by the current status of exploration. As a result, the number of unnecessary local searches is drastically limited, yielding an efficient method. Results of its application on a set of common test functions are reported, along with a performance comparison against other established methods of similar nature.     

Photon transport with a localized source in locally convex spaces

This paper deals with the study of a mathematical model of photon transport in an interstellar cloud where a localized source is present. The source is represented by a Dirac delta functional. The problem is studied in the setting of locally convex spaces. By means of the theory of semigroups on locally convex spaces and the adjoint approach, we prove existence and uniqueness of the solution. Copyright © 2006 John Wiley & Sons, Ltd.     

The Uniqueness of the World

We follow some wild speculations in trying to understand the uniqueness of our physical world, from the field concept to F-TheoryDedicated to Emilio Santos on his 70th birthday. I have enjoyed discussions with Emilio on physics for the last 40 years; in spite of disagreements on many issues, I have an everlasting admiration for him and for his approach to science     

Some Latin American experiences concerning teaching of chemical metrology

In this paper, 15 years of the experiences acquired concerning the teaching of chemical metrology in Latin America are presented. These include postgraduate and undergraduate activities developed in eight countries. The combination of theoretic and practical activities and the sequence of learning from metrological, statistical, and chemometrical backgrounds up to practical activities in personal computers are basic and motivate the learning process. Care is taken to promote the metrological approach and thinking in analytical chemistry. The learning of computing techniques plays an important role, combining graphic and numerical techniques for data analysis. The role of examples during the teaching process is analyzed and recognized. The introduction of a general model of errors permits one to approach different topics on a metrological basis. The metrological approach of uncertainty based on the theory of errors permits one to develop the topic. Undergraduate students acquire a basic metrological knowledge and other experiences are also presented. Recommendations for undergraduate and postgraduate programs are pointed out.     

Experience with in-house PT-schemes in the chemical industry

There are many different means of demonstrating the quality of performance of an analytical laboratory. Proficiency testing (PT) is just one! As in other analytical fields, interlaboratory comparisons play an important role in the chemical industry. Collaborative trials or method performance studies do have a long tradition in this field. Sometimes they were designed as laboratory performance studies with the clear aim of making analytical results comparable, e.g. petrol, coal, gas, noble metals analyses – not to mention the biggest PT scheme run on a daily world-wide basis – trade itself. All this is an ongoing process, which started long before the idea of assessing and accrediting the performance of analytical laboratories was born. However, when striving for accreditation in 1996, the analytical production laboratories of the Chemicals Business Unit of the Bayer AG in Germany implemented another facet of PT schemes. In-house-PT schemes are performed regularly and turned out to be useful in evaluating, monitoring, and thus improving, the quality of routine analytical work. Received: 5 December 2000 Accepted: 15 January 2001     

An evolutionary approach to rehabilitation patient scheduling: A case study

Focusing on real settings, this study aimed to develop an evolutionary approach based on genetic algorithm for solving the problem of rehabilitation patient scheduling to increase service quality by reducing patient waiting time and improve operation efficiency by increasing the therapy equipment utilization. Indeed, due to partial precedence constraints of rehabilitation therapies, the problem can be structured as a hybrid shop scheduling problem that has received little attention to date. In addition, a mixed integer programming model was also constructed as a benchmark to validate the solution quality with small problems. Based on empirical data from a Medical Center in Taiwan, several experiments were conducted to estimate the validity of the proposed algorithm. The results showed that the proposed algorithm can reduce patient waiting time and enhance resource utilization and thus demonstrated the practicality of the proposed algorithm. Indeed, a decision support system embedded with the developed algorithm has been implemented in this medical center.