Waiting times for M/G/1 queues with service-time or delay-dependent server vacations

This article shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one-at-a-time or exhaustive server vacations, depending on either service times or accrued workload. For the first type of dependence, each vacation time is a function of the immediately preceding service time or of whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. For the second type of dependence, the vacation time assigned to an arrival to follow its service is a function of the level of virtual wait reached. By this device, we can model situations in which vacations may be shortened whenever virtual delays have gotten excessive. The method of analysis employs level-crossing theory, and examples are given for various cases of service and vacation-time distributions. A closing discussion relates the new model class to standard M/G/1 queues where the service time is a sum of variables having complex dependencies. © 1992 John Wiley & Sons, Inc.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Bayesian inference of survival curve from record-breaking observations: Estimation and asymptotic results

In a variety of industrial situations experimental outcomes are only record-breaking observations. The data available may be represented as X₁, K_1., X₂, K₂,…, where X₁, X₂,… are the successive minima and K₁, K₂, … are the number of trials needed to obtain new records. Samaniego and Whitaker [11, 12] discussed the problem of estimating the survival function in both parametric and nonparametric setups when the data consisted of record-breaking observations. In this article we derive nonparametric Bayes and empirical Bayes estimators of the survival function for such data under a Dirichlet process prior and squared error loss. Furthermore, under the assumptions that the process of observing random records can be replicated, the weak convergence of the Bayes estimator is studied as the number of replications grows large. The calculations involved are illustrated by adopting Proschan's [9] data on successive failure times of air conditioning units on Boeing aircraft, for our purpose. The nonparametric maximum likelihood estimators of the survival function for different choices of the prior are displayed for comparison purposes.     

Parallel machine replacement

We consider the parallel replacement problem in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance costs motivate replacements, and the fixed replacement cost provides incentive for replacing machines of different ages together in “clusters.” We prove two intuitive results for this problem. First, it is never optimal to split a cluster of like-aged machines, and second, it is never optimal to replace newer clusters before older clusters. By incorporating these two results into an algorithmic approach, we vastly reduce the amount of computation required to identify an optimal replacement policy.     

CON/SLK due date assignment and scheduling on a single machine with two agents

We consider scheduling problems involving two agents (agents A and B), each having a set of jobs that compete for the use of a common machine to process their respective jobs. The due dates of the A‐jobs are decision variables, which are determined by using the common (CON) or slack (SLK) due date assignment methods. Each agent wants to minimize a certain performance criterion depending on the completion times of its jobs only. Under each due date assignment method, the criterion of agent A is always the same, namely an integrated criterion consisting of the due date assignment cost and the weighted number of tardy jobs. Several different criteria are considered for agent B, including the maxima of regular functions (associated with each job), the total (weighted) completion time, and the weighted number of tardy jobs. The overall objective is to minimize the performance criterion of agent A, while keeping the objective value of agent B no greater than a given limit. We analyze the computational complexity, and devise polynomial or pseudo‐polynomial dynamic programming algorithms for the considered problems. We also convert, if viable, any of the devised pseudopolynomial dynamic programming algorithms into a fully polynomial‐time approximation scheme. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 416–429, 2016     

Two heuristics for the economic lot scheduling problem: An experimental study

In this article we present and test two heuristics for the economic lot scheduling problem. The first heuristic was developed by one of us (P.C. Geng) during Ph.D. research, while the other is a convergent implementation of an algorithm due to Doll and Whybark. We study the performance of these heuristics on a large set of test problems constructed using a new form of problem generation that yields random problems within an experimental design.     

A graphical aid for sensitivity analysis of estimated regression coefficients

A problem often arising in applied linear regression modeling is determining the appropriate weight to attach to each observation. In the extreme, the problem extends to the deletion of observations from a data base. Since the choice of weights, fitting criteria, and estimation procedure depend on the specific objectives of the modeling, universally applicable guidelines are virtually nonexistent. However, the sensitivity of analytic conclusions to weights assigned to “suspect” observations can be conveniently assessed using a graphical display. This report develops such a display based on a modeling of outliers which leads naturally to estimators based on a weighted least-squares criterion, and a data-analytic method for determining how much downweighting to impose on a specific subset of observations. This technique is illustrated with several examples, including one relating air pollution to human mortality.     

无摩擦的空气轴承技术对超精密加工机床进给驱动系统的控制需…

加工过程中随着对精密度和加工环境的要求的不断提高,越来越需要在机床的结构和控制器原理这两者之间进行特殊的组合。近年来,为了补偿进给驱动系统的直接导轨的摩擦造成的影响,人们发明了大量的控制决策,例如［１］－［３］。他们虽然提供了各式各样的功能强大的非线性的机构,但通常又使用相当复杂的计算机算法来耗费系统资源。借助于先进的空气静压轴承技术（ＦＶＭ－空气－轴承）摩擦可以被彻底消除,因而直线导轨也就不存在     

基于神经网络的超精密机床伺服进给非线性模型辨识

以双轴Ｔ型结构的超精密金刚石车床的伺服进给系统为研究对象,采用自构造神经网络技术,建立了系统的非线性动态数学模型,为系统非线性控制与补偿提供参考模型