• Management Science and Financial Engineering
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• v.13 no.2
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• pp.47-77
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• 2007

This paper considers a scheduling problem where a customer orders multiple products(jobs) from a production facility. The objective is to minimize the sum of the order(batch) completion times. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. Although each job has a unique processing time, we consider the case where batch processing times are identical. This simplification allows us to develop heuristics with improved performance bounds. This problem was motivated by a real world problem encountered by foreign electronics manufacturers. We first establish the complexity of the problem. For the two parallel machine case, we introduce two simple but intuitive heuristics, and find their worst case relative error bounds. One bound is tight and the other bound goes to 1 as the number of orders goes to infinity. However, neither heuristic is superior for all instances. We extend one of the heuristics to an arbitrary number of parallel machines. For a fixed number of parallel machines, we find a worst case bound which goes to 1 as the number of orders goes to infinity. Then, a tighter bound is found for the three parallel machine case. Finally, the heuristics are empirically evaluated.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.345-356
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• 1995

The aim of this paper is to analyze the batch service queueing model M/M(a, b ; ${\mu}_k/1$) under general bulk service rule with mean service rate ${\mu}_k$ for a batch of k units, where $a{\leq}k{\leq}b$. This queueing model consists of the two-dimensional state space so that it is characterized by two-dimensional state Markov process. The steady-state solution and performane measure of this process are derived by using Matrix Geometric method. Meanwhile, a new approach is suggested to calculate the two-dimensional traffic density R which is used to obtain the steady-state solution. In addition, to determine the optimal service initiation threshold a, a decision model of this queueing system is developed evaluating cost of service per batch and cost of waiting per customer. In a job order production system, the decision-making procedure presented in this paper can be applicable to determining when production should be started.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.10a
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• pp.227-230
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• 2000

배치작업(Batch Job)이란 ERP 시스템에서 제공해야 하는 기능중의 하나로 스케쥴링하여 정해진 시간에 사용자의 interaction이 없이 오프라인(off-line)으로 서버에서 자동으로 실행시키는 작업을 말한다. ERP 시스템의 성능을 향상시키기 위해서는 기존의 사용자와 interactive한 오프라인작업을 효율적으로 운영하고 이를 모니터링/통제하는 기능에 더하여, 기업 업무를 오프라인으로 처리하는 시스템이 개발되어야 한다. 작업 부하가 많이 소요되는 작업이나 주기적으로 처리되는 작업은 작업부하가 상대적으로 낮은 시간을 택하여 수행하도록 하여 시스템의 부하를 경감시키고 작업 효율을 향상시킬 수 있다. 본 논문에서는 기존에 개발된 ERP 시스템에 오프라인처리를 위한 배치 작업 시스템 개발에 대해 연구하였다. 기존에 온라인 작업과는 독립적으로 작업을 오프라인으로 실행시킬 수 있도록 개발되어 시스템의 작업 부하를 경감시키고 시스템의 유휴시간을 활용하여 효율을 증가시킬 수 있어, 전체적인 시스템의 성능을 향상시킬 수 있다.

• Management Science and Financial Engineering
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• v.11 no.2
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• pp.19-43
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• 2005

This paper considers a variation of the customer order scheduling problem, and the variation is the case where the machine-job assignment is fixed. We examine the parallel machine environment, and the objective is to minimize the sum of the completion times of the batches. While a machine can process only one job at a time, different machines can simultaneously process different jobs in a batch. The recognition version of this problem is known to be NP-complete in the strong sense even if there exist only two parallel machines. When there are an arbitrary number of parallel machines, we establish three lower bounds and develop a dynamic programming (DP) algorithm which runs in exponential time on the number of batches. We present two simple but intuitive heuristics, SB and GR, and find some special cases where SB and GR generate an optimal schedule. We also find worst case upper bounds on the relative error. For the case of the two parallel machines, we show that GR generates an optimal schedule when processing times of all batches are equal. Finally, the heuristics and the lower bounds are empirically evaluated.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.23-32
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• 2020

Many small and medium-sized manufacturing companies process various product types to respond different customer orders in a single production line. To improve their productivity, they often apply batch processing while considering various product types, constraints on batch sizes and setups, and due date of each order. This study introduces a batch scheduling heuristic for a production line with multiple product types and different due dates of each order. As the process times vary due to the different batch sizes and product types, a recursive equation is developed based on a flow line model to obtain the upper bound on the completion times with less computational complexity than full computation. The batch scheduling algorithm combines and schedules the orders with same product types into a batch to improve productivity, but within the constraints to match the due dates of the orders. The algorithm incorporates simple and intuitive principles for the purpose of being applied to small and medium companies. To test the algorithm, two case studies are introduced; a high pressure coolant (HPC) manufacturing line and a press process at a plate-type heat exchanger manufacturer. From the case studies, the developed algorithm provides significant improvements in setup frequency and thus convenience of workers and productivity, without violating due dates of each order.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.1
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• pp.119-126
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• 1993

We study a manufacturing process that is quite common in semiconductor wafer fabrication of semiconductor chip production. A machine is used to process a job consisting of J wafers. Each job requires a setup, and the i$_{th}$ setup for a job is sucessful with probability P$_{i}$. The setup is prone to failure, which results in the loss of expensive wafers. Therefore, a tiral run is first conducted on a small batch. If the set up is successful, the test is passed and the balance of the job can be processed. If the setup is unsuccessful, the exposed wafers are lost to scrap and the mask is realigned. The process then repeats on the balance of the job. We call this as send-ahead policy and consider general policies in which the number of wafers that are sent shead depend on the cost of the raw wafer, the sequence of success probabilities, and the balance of the job. We model this process and determine the expected number of good wafers per job,the expected time to process a job, and the long run average throughput. An algorithm to minimize the cost per good wafer subject to a demand constraint is provided.d.d.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.1
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• pp.37-50
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• 2000

We are concerned with estimating the average performance of a re-entrant line with single-job machines and batch machines. The system has multiclass jobs, which will be processed in predetermined routes. An analytical approach may be intractable since the system would not be modeled by product form queueing networks due to the inclusion of batch machines and the consideraton of multiclass jobs which have different processing times. We propose an approximation method based on the Mean Value Analysis(MVA). Our method obtains the mean walting time in each buffer of a workstation and the mean cycle time using the MVA and heuristics. numerical experiments show that the errors of our method are within 5% compared with simulation.

• Korean Management Science Review
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• v.13 no.2
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• pp.25-48
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• 1996

Mixed Model Assembly Lines (MMALs) are increasingly used to produce differentiated products on a single assembly line without work-in-process storage, Usually, a typical MMAL consists of a number of (1) stations doing exactly the same operation on every job, (2) stations involving operations with different choices, and (3) stations offering operations that are not performed on every job, or that are performed on every job but with many options. For stations of the first type there is no sequencing problem at all. However, for the second type a set-up cost is incurred each time the operation switches from one choice to another. At the third type of stations, different models, requring different amounts and choices of assembly work, creates an uneven flow of work along the line and variations in the work load at these stations. When a subsequence of jobs requires more work load than the station can handle, it is necessary to help the operations at the station or to complete the work elsewhere. Therefore, a schedule which minimize the sum of set-up cost and utility work cost is desired. So this study has developed Fixed Random Ordering Rule (FROR), Fixed Ascending Ordering Rule (FAOR), Fixed Descending Ordering Rule, and Extended NHR (ENHR). ENHR is to choose optimal color ordering of each batch with NHR, and to decide job sequence of the batch with it, too. As the result of experiments, ENHR was the best heuristic algorithm. NHR is a new heuristic rule in which only the minimum addition of violations from both partial sequence and unassigned sequence at every branch could be considered. And this is a heuristic sequencing rule for the third type of stations at MMAL. This study developed one more heuristic algorithm to test the performance of NHR, which is named as Practical Heuristic Rule (PHR).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.5
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• pp.305-315
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• 2016

Due to the change from small volume production to small quantity batch production systems, individual companies have been attempting to produce a wide range of operating strategies, maximize their productivity, and minimize their WIP level by operating with the proper cycle time to defend their market share. In particular, using a complex workflow and process sequence in the manufacturing line has some drawbacks when it comes to designing the production strategy by applying analytical models, such as mathematical models and queueing theory. For this purpose, this paper uses three heuristic algorithms to solve the job release problem at the bottleneck workstation, product mix problem in multi-purpose machine(s), and batch size and sequence in batch machine(s). To verify the effectiveness of the proposed methods, a simulation analysis was performed. The experimental results demonstrated that the combined application of the proposed methods showed positive effects on the reduction of the cycle time and WIP level, and improvement of the throughput.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.692-699
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• 2008

Semiconductor research and development(R&D) fabs are very different than production fabs in many ways such as the scales of production, job priority, production methods, and performance measures. Efficient operations of R&D fabs are very important to the development of new product, process stability, high yield, and ultimately company competitiveness. This paper proposes the fab-wide scheduling method for operational optimization of the R&D fabs. Most scheduling systems of semiconductor fabs have only focused on maximizing throughput of each separated areas without considering WIP(works in process) flows of entire fab. In this paper, we proposes the a fab-wide scheduling system which schedules all lots to entire fab equipment at once. We develop the MIP(mixed integer programing) model which allocates the lots to production equipment considering many constraints of all processes and the CP(constraint programming) model which determines the sequences of the lots in the production equipment. The proposed FAB-wide scheduling model is applied to the newly constructed R&D fab. As a result, we have accomplished the system based automated job reservation, decrease of the hot lot delay, increase of the queue time satisfaction, the high throughput by maximizing the batch sizes, decrease of the WIP TAT(Turn Around Time).