• Industrial Engineering and Management Systems
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• 제8권3호
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• pp.155-161
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• 2009

We focus on discrete event systems with a structure of parallel processing, synchronization, and no-concurrency. We use max-plus algebra, which is an effective approach for controller design for this type of system, for modeling and formulation. Since a typical feature of this type of system is that the initial schedule is frequently changed due to unpredictable disturbances, we use a simple model and numerical examples to examine the possibility of applying the concepts of the feeding buffer and the project buffer of critical chain project management (CCPM) on max-plus linear discrete event systems in order to control the occurrence of an undesirable state change. The application of a CCPM-based framework on a max-plus linear discrete event system was proven to be effective.

• Industrial Engineering and Management Systems
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• 제7권1호
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• pp.23-33
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• 2008

This paper proposes an approach to monitoring and scheduling methods for repetitive MIMO-FIFO DESs. We use max-plus algebra for modeling and formulation, known as an effective approach for controller design for this type of system. Because a certain type of linear equations in max-plus algebra can represent the system's behavior, the principal concerns in past researches were how to solve the equations. However, the researches focused mainly on analyses of the relation between inputs and outputs of the system, which implies that the changes or the slacks of internal states were not clarified well. We first examine several properties of the corresponding state variables, which contribute to finding and tracing the float times in each process. Moreover, we provide a rescheduling method that can take into account delays or changes of the internal states. These methods would be useful in schedule control or progress management.

• 한국철도학회논문집
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• 제12권2호
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• pp.267-275
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• 2009

Max-Plus 대수란, 선형 대수(linear algebra)에서의 더하기(addition) 연산과 곱하기(multiplication)연산을 최대값(maximization), 더하기(addition)로 각각 대체한 비선형 시스템을 말한다. Max-Plus 대수는 전통적인 의미의 선형 대수에서 다뤄지는 고유값(eigenvalue), 고유벡터(eigenvector), 안전성(stability) 등의 개념이 Max-Plus 대수에서도 그대로 적용되고, 그것의 의미 또한 실제 시스템의 다양한 해석을 가능케 하고 있어, 최대값 연산과 더하기 연산으로 이루어진 이산 사건 시스템(discrete event system)을 분석할 수 있는 유용한 도구가 된다. 이러한 이산 사건 시스템의 대표적인 예가 바로 환승을 고려한 열차 스케줄이다. 현재 수도권에는 1호선${\sim}$8호선, 인천 1호선, 분당선, 중앙선 등 11개 노선의 도시 철도가 운영되고 있다. 각 노선들은 서울 Metro, 서울도시철도공사, KORAIL 등 서로 다른 운영사에 의해 운영되고 있어서 각 노선의 스케줄 또한 노선간의 환승을 고려하지 않은 채 독립적으로 작성되고 있는 실정이다. 이러한 독립적인 열차 스케줄은 승객들의 긴 환승시간으로 이어진다. 본 연구에서는 Max-flus대수 방법론에 대한 자세한 설명을 기초로 1호선과 2호선, 4호선의 주요 환승역인 사당역과 신도림역, 시청역, 동대문역을 중심으로 Max-Plus 대수 방법론의 적용 가능성을 검토해 보았다.

• Industrial Engineering and Management Systems
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• 제10권4호
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• pp.279-287
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• 2011

This research develops a framework for resolving time and worker conflicts in the Critical Chain Project Management (CCPM) method, expressed in the form of a Max-Plus Linear (MPL) system. Our previous work proposed a method for resolving time conflicts. However, in practical cases, both time and worker conflicts may occur. Hence, we propose a method for resolving both time and worker conflicts for a single project. We first consider how to detect a resource conflict. Then, we define an adjacency matrix to resolve the detected conflicts. Using the proposed method, we confirm that the resource conflict can be resolved through a numerical example.

• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.1-9
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• 2002

Among the state-space description of discrete vent systems, the max-plus algebra is known as one of the effective approach. This paper proposes a model predictive control (MPC) design method based on the max-plus algebra. Several studies related to these topics have been done so far under the constraints that system parameters are constant. However, in practical systems such as production systems, it is common and sometimes inevitable that system parameters vary by each event. Therefore, it is of worth to design a new MPC controller taking account of adjustable system parameters. In this paper, we formulate system parameters as adjustable ones, and they are solved by a linear programing method. Since MPC determines optimal control input considering future reference signals, the controller can be more robust and the operation cost can be reduced. Finally, the proposed method is applied to a production system with three machines, and the effectiveness of the proposed method is verified through a numerical simulation.

• 한국시뮬레이션학회논문지
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• 제21권4호
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• pp.11-24
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• 2012

이 연구는 상수 공정 시간을 갖는 라인생산시스템에서 CONWIP과 DBR이 각각 max-plus 선형시스템의 특수형태임을 밝히고 max-plus 대수에 기반한 안정대기시간 연구결과를 이용하여 CONWIP와 DBR의 성능을 비교 분석하였다. CONWIP의 경우, 생산시스템 내의 체류시간은 DBR의 경우보다 항상 짧다는 사실이 수학적으로 규명되었고 예제를 통해 계산, 비교되었다. 한편 두 경우에서 모두, 애로공정이후 노드에서의 대기시간은 유한버퍼의 크기와 공정의 순서에 무관함을 확인하였다. CONWIP에서는 시스템 내 평균 대기시간 또는 체류시간이 공정의 순서에 무관하지만, DBR에서는 애로공정이 뒤로 갈수록 감소함을 확인하였다.

• Industrial Engineering and Management Systems
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• 제11권4호
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• pp.397-405
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• 2012

This research proposes a framework of buffer management for multi-project systems in the critical chain project management (CCPM) method, expressed in the form of max-plus linear (MPL) representation. Since time buffers are inserted in the projects for absorbing uncertainties in task durations and protecting the completion times, the proposed method provides a procedure for frequently surveying the rates of consumed buffers and the rate of elapsed times. Their relation expresses the performance of the projects which is plotted on a chart through the completed processes. The chart presents the current performance of the projects and their interaction, which alerts managers to make necessary decisions at the right time for managing each project and the entire multi-project system. The proposed framework can analyze the complex system readily, and it enables managers to make an effective decision on scheduling. The effectiveness of the framework is demonstrated through a numerical example.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2000년도 추계학술대회 및 정기총회
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• pp.161-164
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• 2000

A cyclic shop is a production system that repeatedly produces identical sets of jobs, called minimal part sets, in the same loading and processing sequence. We consider a version of cyclic shop where the operations are processed and unloaded within time limits, so called a time window. We model the shop using an event graph model, a class of Petri nets. To represent the time window constraint, we introduce places with negative time delays. From the shop modeling graph, we develop a linear system model based on the max- plus algebra and characterize the conditions on the existence of a stable schedule.

• ETRI Journal
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• 제36권4호
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• pp.609-616
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• 2014

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transform-free) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ${\rho}$, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector $D_n$ are available.

• Journal of Advanced Marine Engineering and Technology
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• 제39권5호
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• pp.563-569
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• 2015

A chemical reaction occurring in CSTR (Continuous Stirred Tank Reactor) is significantly affected by the concentration, temperature, pressure, and reacting time of materials, and thus it has strong nonlinear and time-varying characteristics. Also, when an existing linear PID controller with fixed gain is used, the performance could deteriorate or could be unstable if the system parameters change due to the change in the operating point of CSTR. In this study, a technique for the design of a fuzzy PD plus I controller was proposed for the temperature control of a CSTR process. In the fuzzy PD plus I controller, a linear integral controller was added to a fuzzy PD controller in parallel, and the steady-state performance could be improved based on this. For the fuzzy membership function, a Gaussian type was used; for the fuzzy inference, the Max-Min method of Mamdani was used; and for the defuzzification, the center of gravity method was used. In addition, the saturation state of the actuator was also considered during controller design. The validity of the proposed method was examined by comparing the set-point tracking performance and the robustness to the parameter change with those of an adaptive controller and a nonlinear proportional-integral-differential controller.