Discrete time model for two-machine one-buffer transfer lines with restart policy

The paper deals with analytical modeling of transfer lines consisting of two machines decoupled by one finite buffer. In particular, the case in which a control policy (referred as “restart policy”) aiming to reduce the blocking frequency of the first machine is addressed. Such a policy consists of forcing the first machine to remain idle (it cannot process parts) each time the buffer gets full until it empties again. This specific behavior can be found in a number of industrial production systems, especially when some machines are affected by outage costs when stops occur. The two-machine one-buffer line is here modeled as a discrete time Markov process and the two machines are characterized by the same operation time. The analytical solution of the model is obtained and mathematical expressions of the most important performance measures are provided. Some significant remarks about the effect of the proposed restart policy on the behavior of the system are also pointed out.     

Performance evaluation of transfer lines with general repair times and multiple failure modes

The paper proposes a decomposition method for evaluating the performance of transfer lines where machines can fail in multiple modes and can be repaired with non-exponential times. Indeed, while times to machine failure can be often modeled using exponential distributions with acceptable accuracy, times to repair are very rarely observed to be exponentially distributed in actual systems. This feature limits the applicability of existing approximate analytical methods to real production lines. In this paper, the discrete acyclic phase-type distribution is used to model the repair process, for each failure mode of the machines composing the system. The exact analysis of the two-machine system is used as a building block for the decomposition method, proposed to study multi-stage lines. Numerical results show the high accuracy of the developed method in estimating the average throughput and buffer levels.     

A new method to mitigate data fluctuations for time series prediction

Although the classic exponential-smoothing models and grey prediction models have been widely used in time series forecasting, this paper shows that they are susceptible to fluctuations in samples. A new fractional bidirectional weakening buffer operator for time series prediction is proposed in this paper. This new operator can effectively reduce the negative impact of unavoidable sample fluctuations. It overcomes limitations of existing weakening buffer operators, and permits better control of fluctuations from the entire sample period. Due to its good performance in improving stability of the series smoothness, the new operator can better capture the real developing trend in raw data and improve forecast accuracy. The paper then proposes a novel methodology that combines the new bidirectional weakening buffer operator and the classic grey prediction model. Through a number of case studies, this method is compared with several classic models, such as the exponential smoothing model and the autoregressive integrated moving average model, etc. Values of three error measures show that the new method outperforms other methods, especially when there are data fluctuations near the forecasting horizon. The relative advantages of the new method on small sample predictions are further investigated. Results demonstrate that model based on the proposed fractional bidirectional weakening buffer operator has higher forecasting accuracy.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

Support vector machines maximizing geometric margins for multi-class classification

Machine learning is a very interesting and important branch of artificial intelligence. Among many learning models, the support vector machine is a popular model with high classification ability which can be trained by mathematical programming methods. Since the model was originally formulated for binary classification, various kinds of extensions have been investigated for multi-class classification. In this paper, we review some existing models, and introduce new models which we recently proposed. The models are derived from the viewpoint of multi-objective maximization of geometric margins for a discriminant function, and each model can be trained by solving a second-order cone programming problem. We show that discriminant functions with high generalization ability can be obtained by these models through some numerical experiments.     

Stochastic models of space priority mechanisms with Markovian arrival processes

In this paper, we study a single-server queue with finite capacity in which several space priority mechanisms are implemented. The arrival process is the general Markovian arrival process (MAP) which has been used to model the bursty arrival processes commonly arising in communication applications. The service times are generally distributed. These buffer mechanisms enable the Asynchronous Transfer Mode (ATM) layer to adapt the quality of the cell transfer to the quality of service requirements of the specific broadband ISDN services and to improve the utilization of the network resources. This is done by a selective discarding of cells according to the class they belong to. Computable expressions for various performance parameters are obtained. Numerical results are given for the case of a two-state Markov-modulated Poisson process (MMPP) and deterministic service times. The values derived can be used to evaluate the benefits of using priorities in an ATM network when the traffic is bursty and to make a comparative study of the buffer mechanisms. These results extend the models previously developed, which were limited to Poisson arrivals.     

一类可靠性模型的适定性

研究由一个可靠机器，一个不可靠机器和一个缓冲库构成的生产线．首先对应于此系统的数学模型化为抽象Cauchy问题，然后运用C0-半群理论证明此模型存在唯一的非负解。     

Optimal maintenance of two stochastically deteriorating machines with an intermediate buffer

We consider a manufacturing system in which an input generating installation transfers a raw material to a subsequent production unit. Both machines deteriorate stochastically with usage and may fail. For each machine the deteriorating process is described by some known transition probabilities between different degrees of deterioration. A buffer has been built between the two machines in order to cope with unexpected failures of the installation. A discrete-time Markov decision model is formulated for the optimal preventive maintenance of both machines. The maintenance times are geometrically distributed and the cost structure includes operating costs, storage costs, maintenance costs and costs due to the lost production. It is proved that for fixed buffer content and for fixed deterioration degree of one machine, the average-cost optimal policy initiates a preventive maintenance of the other machine if and only if its degree of deterioration exceeds some critical level. We study, by means of numerical results, the effect of the variation of some parameters on the optimal policy and on the minimum average cost. For the case in which the maintenance times follow continuous distributions, an approximate discrete-time Markov decision model is proposed.     

Representation and analysis of transfer lines with machines that have different processing rates

A transfer line is a tandem production system, i.e. a series of machines separated by buffers. Material flows from outside the system to the first machine, then to the first buffer, then to the second machine, the second buffer, and so forth. In some earlier models, buffers are finite, machines are unreliable, and the times that parts spend being processed at machines are equal at all machines. In this paper, a method is provided to extend a decomposition method to large systems in which machines are allowed to take different lengths of time performing operations on parts. Numerical and simulation results are provided.     

On the Mean Production-rate Analysis of a Two-stage Production System with End Buffer and Random Demand

This paper deals with the transient fluctuations of the mean production rate of a two-stage production system subject to interstage and end inspections and end buffer. The interstage and end inspections are instantaneous, and the end buffer is with finite capacity of size N. A stochastic model is developed to describe the system, and analytical expressions to evaluate the mean production rate (MPR) of machine j (=I, II) in [0, t] with arbitrary distributions of processing times at the stages of production and exponential supply and demand pattern have been obtained by using the state-space method and the regeneration-point technique. A particular case is investigated, and numerical results are presented.     

A review of open queueing network models of manufacturing systems

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.     

基于一般学习效应下的单机排序问题

近来具有学习效应的机器排序问题收到广泛的关注.对于机器排序中工件的实际加工来说,与工件加工位置有关的学习模型更具有现实性.本文研究了工件加工位置和与已经加工过的工件之和有关的一般学习效应模型.首先证明文献中与位置和已经加工过的工件加工时间之和有关的学习模型是本模型的特殊情形.其次对于单机排序问题我们提出一般解法.     

Development of a model for a two-station serial transfer line subject to machine and buffer failure

In modern automated production lines, it is common to connect pairs of machines with mechanical storage devices in order to provide buffering between processing stations. Since these devices are mechanical, they are prone to failure. Previous research concerning the analytical modeling of a class of production lines, the serial transfer line, assumes that these buffers are completely reliable. The concept of an unreliable buffer is introduced and an analytic model of a two machine line with an unreliable buffer is developed. It is proposed that this model will form the foundation for an analytic model of the more complex K > 2 machine serial transfer line with unreliable buffers.     

Evaluation of rejected cases in an acceptance system with data envelopment analysis and goal programming

Some DEA models have been proposed for acceptance or rejection based on a set of cases that have been previously classified. Also, a modified DEA-type linear programming model has been proposed to determine whether a new case must be accepted or rejected, depending on its location on, above, or below the sample frontier. However, these models assume that all attributes that characterize a case are discretionary. This paper extends these results by proposing a model that includes discretionary and non-discretionary attributes (inputs), and more important, a goal program which resembles a modified additive model to determine which characteristics must be changed (and by how much) in order to accept an initially rejected case. A real application is provided to illustrate the potential of the proposed ideas.     

Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.     

Exact model matching of generalized state space systems

The problem of exact model matching for generalized state space (GSS) systems via pure proportional state and output feedback is studied. The following two major issues are resolved here for the first time: The necessary and sufficient conditions for the problem to have a solution and the general analytical expressions for the exact modelmatching controller matrices. The important case of left invertible systems is treated separately wherein simple solutions are established for the above two major issues and results on structural properties of the closed-loop system are reported. Known results on model matching of regular systems are derived as a special case of the GSS systems results, thus unifying the solution of the exact model-matching problem of regular and singular systems.The work described in this paper has been partially funded by the General Secretariat for Research and Technology of the Greek Ministry of Industry, Research, and Technology and by the Heracles General Cement Company of Greece.     

Mathematical description of artificial sense-of-touch systems

The paper proposes a mathematical formalism for describing artificial sense-of-touch systems. Mathematical models for obtaining, processing, and interpreting tactile information are provided. Problems of encoding and reproducing tactile information are formulated and algorithms for solving these problems are proposed. The problem of interpreting tactile information is considered, and the corresponding simple mathematical model is studied. Within the framework of this simple model, an exact solution of the interpretation problem is obtained for the case of finite deformations, and the insufficiency of the linear method (Hooke’s law) for describing problems of interpreting tactile data is shown. The presentation of mathematical models for the theory of artificial sense-of-touch systems in this paper is the first such detailed presentation in the Russian literature. These models are of interest to mathematicians, mechanicians, physicians, and engineers who construct or use artificial sense-of-touch systems.     

Sourcing decision under disruption risk with supply and demand uncertainty: A newsvendor approach

Multi-sourcing is considered as a common practice to hedge against supply disruption risk. In this context, this paper proposes two models for optimal order allocation in newsvendor setting, where both supply and demand are uncertain. The first model considers a risk neutral decision maker who maximizes the total expected profit under disruption risk. The second one is for a risk averse decision maker who does so under service level constraints. Analytical closed form solutions for both the models are derived. To overcome the computational complexity of the exact optimal solution, two algorithms are developed to generate optimal order quantity and the corresponding set of suppliers. The solutions with exact optimization algorithms and the proposed ones are illustrated and compared with numerical examples. The results show that the proposed algorithms give the exact optimal solution while being tractable. Finally, a case study is used to illustrate the applicability of the proposed model.     

基于改进支持向量机的高端装备制造业供应商分类研究

针对现有供应商分类方法应用于高端装备制造业供应商所存在的局限性,从相互依赖视角构建了高端装备制造业供应商分类指标体系,提出了基于改进支持向量机的高端装备制造业供应商分类模型。该模型根据供应商误分代价不同,设计代价敏感支持向量机分类器,利用粒子群算法优化分类器的参数,并采用概率输出方法对多个优化的二类分类器的结果进行组合以实现多类分类。实验结果表明,该模型提高了现有方法的分类效果,可以降低总体误分代价,有效识别出对高端装备制造企业具有重大影响的供应商,为高端装备制造企业实施供应商分类管理提供了依据。     

M/C2/c/K queuing model and optimization for a geriatric care center

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi‐server and finite‐buffer queues with general service time distribution is unknown. However, the phase‐type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase‐type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times. The research focus is twofold. First, a theoretical structure of a multi‐server and finite‐buffer queuing system in which the service time is modeled by the two‐phase Cox distribution is studied. It is focused on finding an efficient solution to the stationary probabilities using the matrix‐geometric method. It is shown that the stationary probability vector can be obtained with the matrix‐geometric method by using level‐dependent rate matrices, and the mean queue length is computed. Second, an empirical analysis of the model is presented. The proposed methodology is applied in a case study concerning the geriatric patients. Some numerical calculations and optimizations are performed by using geriatric data. Copyright © 2015 John Wiley & Sons, Ltd.