Approximations for the time spent in a dynamic job shop with applications to due-date assignment

In this paper we develop approximations for the distribution of the total time spent in a dynamic job shop. In particular, using an exponential limit theorem and an heuristic decomposition of open queueing networks, we show that for a large class of dynamic job shops, the total time spent in a dynamic job shop can be approximated by an exponential random variable with an appropriate mean. Approximations for job shops that do not belong to this class are also developed. Numerical results show that the proposed approximations are in general very good. Application of these approximations in the assignment of due-dates is also illustrated.     

Performance evaluation of flexible manufacturing systems with blocking

Analytical approximations for the performance of flexible manufacturing systems (FMS) with blocking of machines due to limited local buffers are presented. The approximations are based on a detailed analysis of FMS configurations used in industry. The method proposed uses informations generated by applying the classical closed queueing network (CQN) model to the FMS. The approximations developed are tested against simulation models for a wide variety of FMS configurations. The results presented show that the approximations are very good.     

A Queueing Model for A Technical Control Facility

In this paper we develop a queueing model for one possible operating rule for a technical control facility. As suggested in reference [1] a military technical control facility can be considered as a multi-server queueing system. One possible operating rule, the situation where one and only one of the servers may periodically leave the facility, has not been considered previously in the queueing theory literature. In this paper, we give an exact analysis, as well as presenting several approximations, to the steady state behavior.     

Decomposition without aggregation for performance approximation in queueing network models of semiconductor manufacturing

Accurate and speedy forecasts of production cycle time are key components that support the operation of modern semiconductor wafer fabricators. Estimates of cycle time can be obtained via simulation, but such an approach, though common, requires significant computational investment and model maintenance. Queueing network models and approximations for their performance can provide a viable alternative. As modern semiconductor manufacturing systems exhibit largely reentrant product routing, but contain essential probabilistic routes (for metrology and rework), prior mean cycle time approximation methods are not well suited to the system structure. In this paper, we extend the decomposition without aggregation (DWOA) approach – which is tailored to systems with deterministic routing – to allow for the existence of probabilistic paths. Numerical and simulation studies are conducted with numerous practically inspired datasets to assess the quality of the resulting mean cycle time approximations. The results reveal that our approach outperforms the existing mean cycle time approximations on datasets inspired by the semiconductor industry MIMAC benchmark datasets. For example, in MIMAC dataset 1, our mean cycle time approximations exhibit an average of 10.33% error compared to 18.82% error for existing approaches.     

基于排队论和数学规划的资源配置优化方法

为解决零件加工系统资源优化配置问题,提出一种计算方法.针对零件加工系统的特点,总结出串联、循环、选择3种基本结构.在零件加工时间服从指数分布的假设下,根据排队论求出零件在系统中平均排队时间.优化目标是零件在系统中平均排队时间最短.在资源数量约束下,依次让各工序资源数量增一,使零件在系统中平均排队时间减少最大的工序首先分配资源.在资金约束情况下,通过0-1规划方法,列出目标函数和约束方程并求解.最后通过一个实例说明如何综合利用这两种方法进行资源优化配置.     

Machining Parameter Selection for a Stochastic Flow System

This paper examines the foundation for economic analysis in unreliable metal cutting processes. Using queueing models, we present some observations on the effect of cutting speed upon tool life, rate of acceptance of work, and mean flow time in machining parameter optimization.     

An analysis of the ceiling height requirement for a large-scale semiconductor fab

This paper proposes the proposition that the fab ceiling height may become a bottleneck for throughput in a large-scale semiconductor fab. To justify the proposition, we propose a systematic approach for the design of the fab ceiling height. In this approach, we develop a queuing network model to evaluate the cycle time performance of a fab design under a target throughput. This queuing network model is adapted from Connor et al. [1996. A queueing network model for semiconductor manufacturing. IEEE Transactions on Semiconductor Manufacturing, 9 (3), 412–427] by additionally treating the transportation facilities as finite-capacity resources. Numerical experiments were carried out. The results indicate that a large-scale fab with an inappropriate ceiling height may limit the installation of transportation capacity, which, in turn, limits the utilisation of tool capacity, and thus lowers the fab throughput that can be achieved.     

On the approximations to the single server queue

In this article some approximations for the mean number in the single server queueing system are presented and compared. Based on numerical comparison a guide is provided to select the appropriate approximation(s) for different ranges, of the squared coefficient of variation of the inter-arrival and service time distributions. Two approximations for the distribution of the number in the system are given and the better is chosen.     

Generalized queueing network analysis of integrated supply chains

Supply chain networks are formed from complex interactions between several companies whose aim is to produce and deliver goods to the customers at specified times and places. Computing the total lead time for customer orders entering such a complex network of companies is an important exercise. In this paper we present analytical models for evaluating the average lead times of make-to-order supply chains. In particular, we illustrate the use of generalized queueing networks to compute the mean and variance of the lead time. We present four interesting examples and develop queueing network models for them. The first two examples consider pipeline supply chains and compute the variance of lead time using queueing network approximations available in the literature. This analysis indicates that for the same percentage increase in variance, an increase at the downstream facility has a far more disastrous effect than the same increase at an upstream facility. Through another example, we illustrate the point that coordinated improvements at all the facilities is important and improvements at individual facilities may not always lead to improvements in the supply chain performance. The existing literature on approximate methods of analysis of forkjoin queueing systems assumes heavy traffic and requires tedious computations. We present here two tractable approximate analytical methods for lead time computation in a class of fork-join queueing systems. Our method is based on the results presented by Clarke in 1961. For the case where the 'joining' servers of the queueing system are of the type D/N/1, we present an easy to use approximate method and illustrate its use in evaluating decisions regarding logistics (for instance, who should own the logistics fleet-the manufacturer or the vendor?) and computing simple upper bounds for delivery reliability, that is the probability that customer desired due dates are met.     

Lotsizing in Multi-Item Multi- Machine Job Shops

A great many manufacturing facilities can be described as closed job shops which process multiple items through multiple work centers for stock or for assembly. The performance of these shops is strongly dependent on the batching policies employed for work in the shop. In particular, waiting time in queue and total manufacturing lead time for batches are functions of lotsizes. In turn these affect work-in-process costs, safety stock requirements, schedule performance and part coordination for assembly. The relationship between lot-sizing and shop performance is represented using a queueing network model which is then embedded in an optimization routine that searches for optimal lot sizes.     

Lot size optimisation under pooled and unpooled scenarios in batch production system

The lot-sizing problem in batch manufacturing systems with capacity constraints is studied using queueing relationships and optimisation techniques. In this research, the effect of lot sizes when there are parallel machines and multiple part types is considered. Furthermore, the issue of whether or not to use pooled queues, based on part types, to feed the machines is examined. Different scenarios are evaluated using GI/G/n queueing approximations to predict performance and optimise lot sizes. Optimisation is based on minimising the mean flowtimes, which include queue and lot service times. The results show that if part types are very different, there are situations in which pooling is not advantageous.     

Structural optimization of uncertain dynamical systems considering mixed-design variables

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete-continuous sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal and quadratic approximations. The approximations are combined with an effective sensitivity analysis of the reliability constraints in order to generate explicit expressions of the constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. The optimization scheme exhibits monotonic convergence properties. Two numerical examples showing the effectiveness of the approach reported herein are presented.     

Influence of finite semiconductor thickness on thin film transistor characteristics

Through an exact numerical analysis of the electron charge in the conduction band as a function of the gate voltage, the influence of the finite thickness of the semiconductor channel on thin film transistor characteristics is investigated. It is shown that, in various experimentally interesting situations, sufficiently accurate approximations can be found which are much easier to calculate. However, if bulk trapping occurs in a heavily doped semiconductor, no such approximation can be found.     

一类一般化的排队网络族的全稳定性

本文对一类有两个工作站的一般化的排队网络族给出了其全稳定的一个充分条件。     

First and second order constraint approximations in structural optimization

The use of first order constraint approximations is now a common practice in structural optimization. Second order approximations have been avoided because of the perception that the required second derivatives are expensive to calculate. Recent developments that provide inexpensive second derivatives may justify the use of second-order approximations. The present paper compares two commonly used first order approximations to the corresponding second order approximations. Truss and laminated plate problems are used to compare the accuracy of the approximation and its effect on computational efficiency in structural optimization.     

Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper selectively surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates.     

An improved algorithm for optimizing a closed queueing network model of a flexible manufacturing system

Vinod and Solberg (1985) address an optimization problem within the framework of a closed queueing network model for a Flexible Manufacturing System (FMS). The above problem is referred to as the Optimal System Configuration Problem of an FMS. The optimization parameters in the problem are the number of machines at each workstation and the total number of jobs circulating in the system. In this paper we suggest a more efficient algorithm for the solution of the above-mentioned problem. Our algorithm is of an implicit enumeration nature and derives its efficiency from the exploitation of properties of the throughput function of a closed queueing network. The efficiency of the algorithm is demonstrated with the use of extensive computational results.     

Reducing cycle times in manufacturing and supply chains by input and service rate smoothing

A key performance parameter of a manufacturing network or supply chain is its cycle time; the time that a typical item spends in the network. A previous simulation study on a semiconductor assembly and test facility showed that cycle times could be reduced by having smooth input and service rates. This suggested that there is a “cycle time principle” that, for a system with a specified throughput or input rate, the shortest cycle times are obtained when the input and service rates do not vary over time. We prove that this principle is true for the M/G/1 and M/M/s queueing systems and Jackson networks. The analysis involves establishing several results on the concavity of waiting time probabilities and the convexity of expected waiting times and queue lengths, as functions of input and service rates. These results also have natural uses in other optimization problems.     

Optimal design of stochastic production lines: a dynamic programming approach

We consider the problem of choosing the number and type of machines for each station in a new production line where the sequence of processes (i.e., manufacturing recipe) has already been established. We formulate a model to minimize cost (investment plus operating) subject to constraints on throughput and cycle time. Using queueing network approximations within a dynamic programming framework, we develop a line design algorithm that works in station-wise fashion. For computational tractability, we must discretize a continuous state space. However, we are able to compute bounds on the error in the cost function as a guide to the appropriate choice of grid size. We conclude by applying our algorithm to an industrial problem that motivated this work.