Optimal batch sizing in a multi-stage production system with rework consideration

In a production system, rework process plays an important role in eliminating waste and effectively controlling the cost of manufacturing. Determining the optimal batch size in a system that allows for rework is, therefore, a worthwhile objective to minimize the inventory cost of work-in-processes and the finished goods. In this paper, models for the optimum batch quantity in a multi-stage system with rework process have been developed for two different operational policies. Policy 1 deals with the rework within the same cycle with no shortage and policy 2 deals with the rework done after N cycles, incurring shortages in each cycle. The major components that play a role in minimizing this cost of the system are manufacturing setups, work-in-processes, storage of finished goods, rework processing, waiting-time, and penalty costs to discourage the generation of defectives. The mathematical structure of this rework processing model falls under a nonlinear convex programming problems for which a closed-form solution has been proposed and results are demonstrated through numerical examples, followed by sensitivity analyses of different important parameters. It is concluded that the total cost in policy 2 tends to be smaller than that in policy 1 at lower proportion of defectives if the in-process carrying cost is low. Policy 2 may be preferred when the work-in-process carrying cost is low and the penalty cost is negligible.     

Testing the structure of multistage stochastic programs

A fixed topology of stages and/or a fixed branching scheme are common assumptions for applications and numerical solution of scenario based multistage stochastic programs. Using contamination technique to test this structure, we extend the results of Dupačová (Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds) Prague stochastics. Matfyzpress, Praha, pp 91–101, 2006a) to stochastic programs with multistage polyhedral risk objectives. The ideas are exemplified by bond portfolio management problems and complemented by illustrative numerical results.     

具有急慢性阶段的MSIS流行病模型阈值和稳定性结果

系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.     

A stochastic model for the HIV epidemic in homosexual populations involving age and race

In this paper, we derive a stochastic model for the HIV epidemic in homosexual populations involving age and race. To account for effects of different mixing patterns, a low risk selection rule is introduced. The model is then formulated in terms of chain multinomial distributions by means of which the means are derived. Some simulation studies by computer indicate clearly that age and race have a significant impact on the HIV epidemic.     

Thermoluminescence in sediments and historical supernovae explosions

Summary Thermoluminescence from the different layers of a recent core drilled in the Tyrrhenian Sea has been measured. The sedimentation rate of 0.115 cm y⁻¹ previously determined by the²¹⁰Pb−²²⁶Ra method allows the profile of TL to be obtained in the last 1500 years. We notice that sharp peaks in the TL intensity appear during the years in which records of hystorical supernovae explosions are given. A working model of the process based on the irradiation of dust in the upper atmosphere by γ-rays produced in the SN burst allows a satisfactory energy estimate of the observations to be done. Moreover, the profile shows the modulation of the irradiations of the Earth environment produced by the Sun in the past.     

Nucleation and growth of Cu onto polycrystalline Pt electrode from acidic CuSO4 solution in the presence of H2SeO3

The early stages of Cu electrodeposition onto Pt(poly) have been investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] ≥ 2×10² using electrochemical and ex situ AFM techniques. The overpotential deposition of Cu has been performed onto a Pt surface precovered independently with Cu in amount close to an equivalent monolayer. Chronoamperometric results have been shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model. The values of diffusion coefficient D for Cu²⁺, number of nuclei N and average nuclei radius r _av have been calculated. In the local regions of the surface, the separate large agglomerates composed of the different diameter clusters have been revealed in both cases, but, in the presence of the H₂SeO₃, they attained a distinct chain-like configuration. Some morphological characteristics have been reported.     

不同发展阶段高中化学教师的PCK表征研究*——以“物质的量”主题为例

为探讨不同发展阶段的高中化学教师对于“物质的量”主题的认识,聚焦学科教学知识(PCK)的2个基本组成部分:(1)学生理解的知识,(2)教学策略和表征知识。基于PCK课堂观察量表和CoRe模型,对比分析新手、熟手、专家型教师关于“物质的量”主题的PCK表征。研究结果表明,不同发展阶段化学教师的PCK存在差异,教师对学生知识的理解影响了教学策略和表征方式的决策。     

具外来感染者和急慢性阶段流行病模型的周期解

建立和研究了一类具有外来感染者和急慢性阶段的流行病模型.我们假设单位时间内有常数量的外来感染者进入所研究地区,并且假设模型具有周期感染率.我们将利用重合度的延拓定理,导出模型周期解的存在性.     

滑坡预报的几个基本问题

在滑坡预报研究中，必须首先解决与预报密切相关的一些基本问题。否则，往往导致预报误差很大或者预报失败。根据作者的初步探索，本文重点讨论了滑坡预报的分类及定义、预报参数及其监测点的选取、变形突变现象的分析与处理以及斜坡变形阶段的定量判断等基本问题。