• 대한수학회지
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• 제40권6호
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• pp.943-950
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• 2003

The maximal column rank of an m by n matrix A over max algebra is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

• Industrial Engineering and Management Systems
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• 제3권1호
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• pp.1-11
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• 2004

This paper proposes a new algorithm for determining an optimal control input for production systems. In many production systems, completion time should be planned within the due dates by taking into account precedence constraints and processing times. To solve this problem, the max-plus algebra is an effective approach. The max-plus algebra is an algebraic system in which the max operation is addition and the plus operation is multiplication, and similar operation rules to conventional algebra are followed. Utilizing the max-plus algebra, constraints of the system are expressed in an analogous way to the state-space description in modern control theory. Nevertheless, the formulation of a system is currently performed manually, which is very inefficient when applied to practical systems. Hence, in this paper, we propose a new algorithm for deriving a state-space description and determining an optimal control input with several constraint matrices and parameter vectors. Furthermore, the effectiveness of this proposed algorithm is verified through execution examples.

• 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.

• 호남수학학술지
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• 제33권1호
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• pp.93-113
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• 2011

Let $a{\oplus}b$ = max(a, b), $a{\otimes}b$=a+b, a, $b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${\oplus},{\otimes}$) extended to matrices and vectors over $\mathbb{R}_{\varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\mathbb{R}_{\varepsilon}$.

• 한국정보통신학회논문지
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• 제12권10호
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• pp.1794-1800
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• 2008

본 논문에서는 PLA를 사용하여 디지털논리 스위칭함수를 효과적으로 구성하는 방법을 제안하였다. 제안한 방법은 먼저 포스트 대수를 기반으로 MIN 대수연산과 MAX 대수연산을 제안하였고, 이를 구현하기 위해 T-gate에 대해 논의하였다. 그리고 PLA의 기본 회로인 MIN 배열, MAX 배열과 리터럴에 대해 논의하였다. PLA를 사용하여 디지털논리스위칭함수를 설계하기 위해 변수분할, 모듈러 구조, 리터럴 생성기, 복호기와 인버터를 제안하였다. 제안한 방법은 좀 더 콤펙트하고 확장성이 용이하다.

• 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.

• 대한수학회논문집
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• 제30권4호
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• pp.385-402
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• 2015

In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of "$c_f$-Max X", we prove that every member of "$c_f$-Max X" is a prime ideal. Also we conclude some more related results.

• 경영과학
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• 제24권1호
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• pp.25-34
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• 2007

In this study, we consider stationary waiting times in finite-buffer 3-node single-server queues in series with a Poisson arrival process and with either constant or non-overlapping service times. We assume that each node has a finite buffer except for the first node. The explicit expressions of waiting times in all areas of the stochastic system were driven as functions of finite buffer capacities. These explicit forms show that a system sojourn time does not depend on the finite buffer sizes, and also allow one to compute and compare characteristics of stationary waiting times at all areas under two blocking rules communication and manufacturing blocking. The goal of this study is to apply these results to an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on stationary waiting times at all nodes. Numerical examples are also provided.

• 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.

• 한국수학사학회지
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• 제31권1호
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• pp.1-17
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• 2018

In this expository paper, we present an abridged report on the max-plus eigenspaces of max-plus matrices with its brief history. At the end of our work, a number of examples are presented with maple codes, and then we make a claim from the observation of these examples, which is on the euclidean dimension of the max-plus eigenspaces of strongly definite matrices.