• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.248-256
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• 2005

In this paper, we compare two EOQ based inventory models under total cost minimization and profit maximization to investigate the difference in the optimal solutions. First of all, optimal solutions for both models through geometric programming (GP) techniques are found considering production (lot sizing) as well as marketing (pricing) decisions. An investigation of the effects of the changes in the optimal solutions according to varied parameters is performed by studying optimality conditions as well as by performing numerical analysis. We then conduct comparative analysis between the models to show the relationships between the optimal solutions of the models where certain conditions in the cost per unit and the demand per unit time are given. Several interesting economic implications and managerial insights are observed from this analysis.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.45-63
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• 2006

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.2
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• pp.173-182
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• 2001

Ascent trajectory optimization and optimal explicit guidance problems for a satellite launch vehicle in a 2-dimensional pitch plane are studied. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the pitch attitude control variable, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn are imposed. An optimal explicit guidance algorithm in the exoatmospheric phase is also presented, the guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. To verify the optimality and accuracy of the algorithm simulations are performed.

• Environmental and Resource Economics Review
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• v.11 no.2
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• pp.195-210
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• 2002

In this paper, we present a nonrenewable resource model including environmental pollution stock as a state variable to analyze the dynamic structure of environmental tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost for environmental pollution stock is the same as that of the costate variable for environmental pollution stock. We did this by applying the theorem, Continuous Dependence on Initial Conditions (Coddington and Levinston, 1985, pp. 22~27), to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of environmental tax to be imposed over time. In addition, we also identified that the costate variable for environmental pollution stock is solely due to the disutility effect.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.5
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• pp.526-532
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• 2014

In this paper, we present and analyze a LQ (Linear Quadratic) inverse optimal state-consensus protocol for continuous-time multi-agent systems with undirected graph topology. By Lyapunov analysis of the state-consensus error dynamics, we show the sufficient conditions on the algebraic connectivity of the graph to guarantee LQ inverse optimality and closed-loop stability. A more relaxed stability condition is also provided in terms of the algebraic connectivity. Finally, a formation control protocol for multiple mobile robots is proposed based on the target LQ inverse optimal consensus protocol, and the simulation results are provided to verify the performance of the proposed LQ inverse formation control method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.636-647
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• 2004

The objective of this paper is to provide an improved reorder decision policy for general multi-echelon distribution systems utilizing the shared stock information. It has been known that traditional reorder policies sometimes show poor performance in distribution systems. Thus, in our previous research we introduced the order risk policy which utilizes the shared stock information more accurately for the 2-echelon distribution system and proved the optimality. However, since the real world supply chain is generally composed with more than 2 echelons, we extend the order risk policy for the general multi-echelon systems. Since the calculation of the exact order risk value for general multi-echelon systems is very complex, we provide two approximation methods for the real-time calculation. Through the computational experiment comparing the order risk policy with the existing policies under various conditions, we show the performance of the order risk policy and analyze the value of the shared stock information varying with the characteristics of the supply chain.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.4
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• pp.15-25
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• 2000

In this paper, we introduce a point-to-multipoint minimum cost flow problem with convex and demand splitting. A source node transmits the traffic along the tree that includes members of the point-to-multipoint connection. The traffic is replicated by the nodes only at branch points of the tree. In order to minimize the sum of arc costs, we assume that the traffic demand can be splitted and transmitted to destination nodes along different trees. If arc cost is linear, the problem would be a Steiner tree problem in networks eve though demand splitting is permitted. The problem would be applied in transmitting large volume of traffic from a serve to clients in Internet environments. Optimality conditions of the problem are presented in terms of fair tree routing. The proposed algorithm is a finite terminating algorithm for $\varepsilon$-optimal solution. convergence of the algorithm is obtained under monotonic condition and strict convexity of the cost function. Computational experiences are included.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.11a
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• pp.159-165
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• 2003

The objective of this paper is to provide an improved reorder decision policy for general multi-echelon distribution systems utilizing the shared stock information. Since it has been known that traditional reorder policies sometimes show poor performance in distribution systems, in our previous research we introduced the order risk policy which utilizes the shared stock information more accurately f3r the 2-echelon distribution system and proved the optimality. However, since the real world supply chain is generally composed with more than 2 echelons, we extend the order risk policy for the general multi-echelon systems. Since the calculation of the exact order risk value fur general multi-echelon systems is very complex, we provide two approximation methods. Through the computational experiment comparing the order risk policy with the existing policies under various conditions, we show the performance of the order risk policy and analyze the value of the shared stock information varying with the characteristics of the supply chain.

• IE interfaces
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• v.17 no.3
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• pp.359-374
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• 2004

The objective of this paper is to provide an improved reorder decision policy for general multi-echelon distribution systems utilizing the shared stock information. It has been known that traditional reorder policies sometimes show poor performance in distribution systems. Thus, in our previous research we introduced the order risk policy which utilizes the shared stock information more accurately for the 2- echelon distribution system and proved the optimality. However, since the real world supply chain is generally composed with more than 2 echelons, we extend the order risk policy for the general multi-echelon systems. Since the calculation of the exact order risk value for general multi-echelon systems is very complex, we provide two approximation methods for the real-time calculation. Through the computational experiment comparing the order risk policy with the existing policies under various conditions, we show the performance of the order risk policy and analyze the value of the shared stock information varying with the characteristics of the supply chain.