• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.261-275
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• 2003

In this paper we study two stage problems of stochastic convex programming. Solving the problems is very hard. A L-shaped method for it is given. The implement of the algorithm is simple, so less computation work is needed. The result of computation shows that the algorithm is effective.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.287-296
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• 1995

Wets ([4],[5],[6]) considered single objective linear two-stage programming problem under uncertainty with complete recourse. Artstein, Dupacova, Romisch, Schultz and Wets studied stability of this problem id depth. But in many real world problems to make best decision, we need multiple objective functions. So we consider the following multiple objective two-stage programming problems with complete fixed recourse.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.1
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• pp.9-13
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• 1985

This paper develops a decomposition method for stochastic programming with a block diagonal structure. Here we assume that the right-hand side random vector of each subproblem is differente each other. We first, transform this problem into a master problem, and subproblems in a similar way to Dantizig-Wolfe's Decomposition Princeple, and then solve this master problem by solving subproblems. When we solve a subproblem, we first transform this subproblem to a Deterministic Equivalent Programming (DEF). The form of DEF depends on the type of the random vector of the subproblem. We found the subproblem with finite discrete random vector can be transformed into alinear programming, that with continuous random vector into a convex quadratic programming, and that with random vector of unknown distribution and known mean and variance into a convex nonlinear programming, but the master problem is always a linear programming.

• Journal of Korea Water Resources Association
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• v.43 no.2
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• pp.131-138
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• 2010

Due to the increased water demand and severe drought as an effect of the global warming, the effluent from wastewater treatment plants becomes considered as an alternative water source to supply agricultural, industrial, and public (gardening) water demand. The effluent from the wastewater treatment plant is a sustainable water source because of its good quality and stable amount of water discharge. In this study, the water reuse system was developed to minimize total construction cost to cope with the uncertain water demand in future using two-stage stochastic linear programming with binary variables. The pipes in the water reuse network were constructed in two stages of which in the first stage, the water demands of users are assumed to be known, while the water demands in the second stage have uncertainty in the predicted value. However, the water reuse system has to be designed now when the future water demands are not known precisely. Therefore, the construction of a pipe parallel with the existing one was allowed to meet the increased water demands in the second stage. As a result, the trade-off of construction costs between a pipe with large diameter and two pipes having small diameters was evaluated and the optimal solution was found. Three scenarios for the future water demand were selected and a hypothetical water reuse network considering the uncertainties was optimized. The results provide the information about the economies of scale in the water reuse network and the long range water supply plan.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.1
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• pp.89-102
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• 2010

Future uncertainty on water demand caused by future climate condition and water consumption leads a difficulty to determine the reservoir operation rule for supplying sufficient water to users. It is, thus, important to operate reservoirs not only for distributing enough water to users using the limited water resources but also for preventing floods and drought under the unknown future condition. In this study, the reservoir storage is determined in the first stage when future condition is unknown, and then, water distribution to users and river stream is optimized using the available water resources from the first stage decision using 2-stage stochastic linear programming (2-SLP). The objective function is to minimize the difference between target and actual water storage in reservoirs and the water shortage in users and river stream. Hedging rule defined by a precaution against severe drought by restricting outflow when reservoir storage decreases below a target, is also applied in the reservoir operation rule for improving the model applicability to the real system. The developed model is applied in a system with five reservoirs in the Han River basin, Korea to optimize the multi-reservoir system under various future water demand scenarios. Three multi-purposed dams - Chungju, Hoengseong, and Soyanggang - are considered in the model. Gwangdong and Hwacheon dams are also considered in the system due to the large capacity of the reservoirs, but they are primarily for water supply and power generation, respectively. As a result, the water demand of users and river stream are satisfied in most cases. The reservoirs are operated successfully to store enough water during the wet season for preparing the coming drought and also for reducing downstream flood risk. The developed model can provide an effective guideline of multi-reservoir operation rules in the basin.

• Journal of the Korean Society for Railway
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• v.10 no.6
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• pp.742-750
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• 2007

This paper presents a mathematical model for a double-fleet operation in Korean high speed rail (HSR). KORAIL has a plan to launch new HSR units in 2010, which are composed of 10 railcars. The double-fleet operation assigns a single-unit or two-unit fleet to a segment, accommodating demand fluctuation. The proposed model assumes stochastic demand and uses chance-constrained constraints to assure a preset service level. It can be used in the tactical planning stage of the rail management as it includes several real-world conditions, such as the capacities of the infra-structures and operational procedures. In the solution approach, the expected revenue in the objective function is linearized by using expected marginal revenue, and the chance-constrained constraints are linearized by assuming that demands are normally distributed. Subsequently, the model can be solved by a mixed-integer linear programming solver fur small size problems. The test results of the model applied to Friday morning train schedules for one month sample data from KTX operation in 2004 shows that the proposed model could be utilized to determine the effectiveness of double-fleet operation, which could significantly increase the expected profit and seat utilization rates when properly maneuvered.