Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

On a Question of Phillips

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *? of the ring ? of integers by using a linear mod 1 function h : F ?, where F is the α-dimensional vector space over ? when α is the cardinality of *?. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.     

The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences

Recently, Fishbum and Lavalle (1995) and Lefèvre and Utev (1996) have considered some stochastic order relations specific for arithmetic random variables. The present work is concerned with these orderings, together with two other classes of stochastic order relations closely related. First, attention is paid to characterizations and various properties of all these orderings. Then, sufficient conditions of crossing-type for the two new classes of orderings are derived and extrema among discrete random variables are deduced. This is applied in actuarial sciences to obtain new bounds for the classical single life premiums as well as for the probability of ruin in the compound binomial risk model.     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...     

产品定级中挑选专家的数学模型

在工农业产品评定级别中，专家组的水平是至关重要的。文中给出一个挑选专家组成员的数学模型，可以检验专家对参评产品的决策水平，为评价所评结论的可信度提供参考依据。     

第I类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ｉ类非自共轭锥上．作为其应用，显式给出了以这些锥为底的管状域（或第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ Ｓｚｅｇ¨ｏ核和形式Ｐｏｉｓｏｎ核．     

n进制中非零数字之积函数的均值公式

设 N =a1nk1+ a2 nk2 +… + asnks( 1 aik2 >… >ks 0 ) ,a( N,n) =a1a2 … as,本文给出了均值 Ar( N ,n) =∑m相似文献   

Gamma-ray spectroscopy of the neutron-rich Ni region through heavy-ion deep-inelastic collisions

Nuclei in the neutron-rich Ni region have been studied by γ-ray spectroscopy. Gamma-rays emitted from isomers, with T _1/2 > 1 ns, produced in heavy-ion deep-inelastic collisions were measured with an isomer-scope. The nuclear structure of the doubly magic ⁶⁸Ni and its neighbor ^69,71Cu is discussed on the basis of the shell model. Future experiments for more neutron-rich Ni nuclei are also viewed. Received: 1 May 2001 / Accepted: 4 December 2001