• Industrial Engineering and Management Systems
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• v.8 no.3
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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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• v.7 no.1
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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.

• Industrial Engineering and Management Systems
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• v.10 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.603-613
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• 2013

In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Two new modified Gauss-Seidel methods for linear system with M-matrices, J. Comput. Appl. Math. 233 (2009), 922-930] considered the modified Gauss-Seidel method for solving M-matrix linear system with the preconditioner $P_{max}$. In this paper, we consider the modified Gauss-Seidel method for solving the linear system with the generalized preconditioner $P_{max}({\alpha})$, and study its convergent properties when the coefficient matrix is an H-matrix. Numerical experiments are performed with different examples, and the numerical results verify our theoretical analysis.

• Industrial Engineering and Management Systems
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• v.1 no.1
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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.

• Geomechanics and Engineering
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• v.16 no.4
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• pp.355-361
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• 2018

In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.1
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• pp.15-21
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• 2004

This paper deals with asymptotic stabilization problems for linear systems with time-varying input disturbances. In order to eliminate the influence of a disturbance on the system, a disturbance observer is designed and the time-varying disturbance can be rejected using its estimated value. Since the disturbance observer is kind of low-pass filter, it has inevitably estimation errors. To eliminate the inflences on the performance due to these errors, the additional control is designed based on these estimation errors using a well-known min-max control method. It is shown that the asymptotic stability of the closed-loop system is guaranteed. In general, the min-max control method requires the switching of control inputs and the switching magnitude of the control input is determined by the disturbance estimation error bounds. As the error bounds can be made arbitrarily small by choosing the high gain for the disturbance observer, the control method suggested in this paper can reduce the chattering phenomena as small as possible. Therefore, it has superior performance to the existing ones.

• Journal of the Korea Society for Simulation
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• v.21 no.4
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• pp.11-24
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• 2012

We compared a DBR(drum-buffer-rope) system with a CONWIP(constant work-in-process) system in a production line with constant processing times. Based on the observation that a WIP-controlled line production system such as DBR and CONWIP is equivalent to a m-node tandem queue with finite buffer, we applied a max-plus algebra based solution method for the tandem queue to evaluate the performance of two systems. Numerical examples with 6 workstations were also used to demonstrate the proposed analysis. The mathematical analyses support that CONWIP outperforms DBR in terms of expected waiting time and WIP. Unlike the CONWIP case, sequencing workstations in a DBR affects the performance of the system. Delaying a bottleneck station in a DBR reduces expected waiting time.

• Korean Management Science Review
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• v.24 no.1
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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.

• Journal of the Korean Society for Railway
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• v.12 no.2
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• pp.267-275
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• 2009

Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.