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Performance evaluation of re-entrant lines with multi-class jobs and multi-server workstations
Production Planning & Control
Abstract and Figures
An approximation method is proposed for estimat-ing the performance measures of re-entrant lines with multi-server workstations based on the Mean Value Analysis (MVA) technique. The system of interest can be found in the semiconductor wafer fabrication line in which several circuit types are manufactured through re-entrant processes at both the single-job and the batch workstations. Each workstation may have several identical machines. Multi-class jobs are assumed to be processed in a predetermined routing, in which some processes may utilize the same workstation several times in the re-entrant fashion. The performance measures of interest are the steady-state average of the cycle time of each job class, the queue length of each bu er, and the throughput of the system. The system may not be modelled by a product form queueing network due to the inclusion of batch machines, multi-class jobs with di erent processing times, and multi-server workstations. Thus, a methodology is proposed for analysing such a re-entrant line approximately using the iterative procedures based upon the MVA and some heuristic adjustments. Results of numerical tests are provided to show the performance of the proposed approach against the simulation results.
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... Park et al. [4,5] extended the approach and solved the case of multi-class jobs and mixture of both single-job and batch machines. Park et al. [6] also extended their work to consider the multi-server workstation case. We further extend the previous work to consider the case of production loss due to machine failures and job yield. ...
... The major aspects that must be considered in modeling were: Re-entrant nature of the wafer flow visiting key machines between 20 and 30 times, mixture of the single-and batch-machines, the random machine failures and the yield losses. Park's earlier works addressed the first two key issues [4,5] and the multi-class issues [6], and finally this paper completes the methodology by adding the final issue of the random losses. The reason why the random loss issue is considered as the last item in the agenda is obvious. ...
... Some adjustments of the MVA procedure were proposed in our earlier works [4][5][6]. In this study, without detailed justification for them, we adopt the previous adjustment methods to enhance the accuracy of the MVA approach. ...
This paper proposes an approximation method based on mean value analysis (MVA) technique for estimating the performance measures of re-entrant manufacturing system with production loss. The model is an extension of the one proposed by Park et al. (Comput. Oper. Res. 29 (2002) 1009). A unique feature in the extended model is that random production losses due to machine failures and yields are considered. Considering such losses is critical in performance evaluation, because it may often cause significant errors in the results compared to the real values if the analysis does not explicitly consider them. However, such random losses substantially increase the complexity of the analysis, due to the fact that even through simulation it requires not only extra modeling efforts, but also a number of replications. As a result, it requires bigger efforts and data, and significantly longer computational times. For an analytical approach, such random losses also prohibit exact analysis of the system. Therefore, a methodology for analyzing the system approximately is proposed using the iterative procedures based upon the MVA and some heuristic adjustments. The performance measures of interest are the steady-state average of the cycle time of each job class, the queue length of each buffer, and the throughput of the system. Numerical tests are presented to show the performance of the proposed approach against the simulation results. Also, the comparisons with the earlier test results summarize the insights from the overall research thus far.
... One shortcoming of their approach was the need to treat each machine as a unique family, so they couldn't take advantage of situations in which some machines were identical. To address the more general case, Park, Kim, and Jun (2002) considered a facility that processed multiple products using multi-servers, where each server consisted of one or more identical machines. Choi, Kim, and Lee (2011) proposed a decision tree-based real-time scheduling mechanism for the reentrant hybrid flow shop scheduling problem. ...
... One shortcoming of their approach was the need to treat each machine as a unique family, so they couldn't take advantage of situations in which some machines were identical. To address the more general case, Park, Kim, and Jun (2002) considered a facility that processed multiple products using multi-server workstations, where each workstation consisted of one or more identical machines. MVA was also the primary analytic tool. ...
In semiconductor manufacturing, wafers are grouped into lots and sent to a separate facility for assembly and test before being shipped to the customer. This paper investigates the daily scheduling of such lots in a re-entrant flow environment where it is necessary to plan for several passes of the same lot through the system. Up to a dozen operations are required during assembly and test and many are performed by the same equipment. Work in process lots that have more than a single step remaining in their route are referred to as multi-pass lots. The scheduling problem is to determine machine setups, lot assignments, and lot sequences to achieve optimal output, as measured by four objectives related to key device shortages, throughput, machine utilisation, and makespan, in that order. When more than a single pass is considered, it is not possible to develop an efficient mathematical model to represent the decision process. To find solutions, we take a multi-stage approach, first applying a reactive greedy randomised search procedure (GRASP) to develop a schedule for the current lots waiting to be processed, and then using a similar procedure to schedule additional passes and changeovers. The performance of the methodology is evaluated using data provided by a leading semiconductor manufacturer for instances with up to 36 machines, 284 tooling pieces from six families, and 1036 lots. The results indicate that, on average, multi-pass scheduling improves the weighted sum of lots processed by 40% and machine utilisation by 11% compared to the results obtained with the single-pass algorithm.
... These results are an extension of the ideas first proposed by Narahari and Khan [28] who used MVA to approximate performance measures of re-entrant manufacturing systems. Youngshin Park, et al. [30] later extend their previous research [29] to include the case of re-entrant lines with multi-class jobs and multi-server workstations. In this article, a queueing network with both batch machines and single-server machines is analyzed using an MVA approach. ...
Typescript. Thesis (M.S.)--Air Force Institute of Technology, 2003. Includes bibliographical references. AFIT/GOR/ENS/03-09.
Semiconductor wafer fabrications are modeled as a re-entrant flow shop problem, in which the processing order of each lot is given, but each lot may enter a production line many times. Hence, a re-entrant flow shop is a very complicated problem, which has a property similar to a job shop problem. In this paper, we consider a scheduling method for a whole production line of re-entrant flow shop. A real wafer fabrication line consists of several hundreds of processes and requires re-scheduling many often. So we propose local search methods instead of seeking exact solutions. Some numerical results indicate that the proposed methods obtain good solutions in a short time.
Keywords re-entrantow shop, single-job machine, batch machine, mean value analysis. Abstract. We propose an approximate method based on the mean value analysis for estimating the average performance of re-entrantow shop with single-job machines and batch machines. The main focus is on the steady-state averages of the cycle time and the throughput of the system. Characteristics of the re-entrantow and inclusion of the batch machines com- plicate the exact analysis of the system. Thus, we propose an approximate analytic method for obtaining the mean waiting time at each buÄ er of the workstation and a heuristic method to improve the result of the analytic method. We compare the
Material flow in a semiconductor manufacturing system has the marked property of reentrancy. This property leads to interesting problems of machine scheduling. This property also introduces the non-product-form features into the corresponding queueing model of the semiconductor manufacturing system, and thus making it extremely difficult to exactly analyze the model, and evaluate the performance of the system. In this paper we present an efficient analytical technique for predicting the performance of a semiconductor manufacturing system, employing any fixed buffer machine scheduling policy. The method is based on mean value analysis (MVA), a well known queueing theory based technique for analyzing queueing networks. Computationally the method is overwhelmingly efficient compared simulation. The method also facilitates explicit modeling of scheduling policies used in multiclass manufacturing systems.
In a queuing process, let 1/λ be the mean time between the arrivals of two consecutive units, L be the mean number of units in the system, and W be the mean time spent by a unit in the system. It is shown that, if the three means are finite and the corresponding stochastic processes strictly stationary, and, if the arrival process is metrically transitive with nonzero mean, then L = λW.
Queueing networks are a useful class of models in many application domains, e.g., manufacturing systems, communication networks, and computer systems. Control is typically exercised over such systems by the use of scheduling policies. However, if one ventures outside a certain special class of systems for which the steady state distribution has a product form, very little is known concerning their performance or even stability. In the first half of this survey paper, we present new theoretical developments on stability analysis and performance evaluation for queueing networks and scheduling policies. We show how one may solve problems in stability and performance analysis by solving linear programs. In the second half, we address the problem of scheduling a class of queueing networks called re-entrant lines, which model semiconductor manufacturing plants. We propose a new class of scheduling policies based on smoothing all the flows in the system. We also report briefly from an extensive simulation study comparing the performance of the suggested scheduling policies with a range of other scheduling policies, for a variety of semiconductor manufacturing plant models.
Reentrant lines can be used to model complex manufacturing systems such as wafer fabrication facilities. As the first step to the optimal or near-optimal scheduling of such lines, we investigate their stability. In light of a recemt theorem of the first author [Ann. Appl. Probab. 5, No. 1, 49-77 (1995; Zbl 0822.60083 )] which states that a scheduling policy is stable if the corresponding fluid model is stable, we study the stability and instability of fluid models. To do this we utilize piecewise linear Lyapunov functions. We establish stability of first-buffer-first-served (FBFS) and last-buffer-first-served (LBFS) disciplines in all reentrant lines, and of all work-conserving disciplines in any three buffer reentrant lines. For the four buffer network of S. H. Lu and P. R. Kumar [IEEE Trans. Autom. Control 36, 1406-1416 (1994)] we characterize the stability region of the Lu and Kumar policy, and show that it is also the global stability region for this network. We also study stability and instability of Kelly-type networks. In particular, we show that not all work-conserving policies are stable for such networks; however, all work-conserving policies are stable in a ring network.
We present an algorithm for numerically finding the limiting distribution of the number in the system for the bulk-arrival, multiserver queueing system M X /D/c. Sample numerical results and graphs of various quantities of interest are also presented. In all cases, the proposed method is computationally efficient, accurate and reliable for both high and low values of the model parameters. The procedure is adaptable to other queueing models in discrete and continuous time, to problems in inventory control, the theory of dams, etc. Exact results found here will also be found useful by people dealing with inequalities, bounds, and approximations.
Traditionally, manufacturing systems have mainly been treated as either job shops or flow shops. In job shops, parts may arrive with random routes, with each route having a low volume. In flow shops, the routes are fixed and acyclic, as in assembly lines. With the advent of semiconductor manufacturing plants, and more recently, thin film lines, this dichotomy needs to be expanded to consider another class of systems, which we call re-entrant lines. The distinguishing feature of these manufacturing systems is that parts visit some machines more than once at different stages of processing.Scheduling problems arise because several parts at different stages of processing may be in contention with each other for service at the same machine. There may be uncertainties in the form of random service or set-up times, as well as random machine failures and repairs. The goal of scheduling is to improve performance measures such as mean sojourn time in the system, which is also known as the mean cycle-time, or the variance of the cycle-time.In this paper we provide a tutorial account of some recent results in this field. We describe several scheduling policies of interest, and provide some results concerning their stability and performance. Several open problems are suggested.