• 한국경영과학회지
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• 제14권2호
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• pp.19-26
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• 1989

We in this paper have defined the concept of .epsilon.-symmetric relation between the Lagrangean relaxation and the Benders' decomposition. This links the solutions of the Lagrangean subproblems and those of the Benders' subproblems even under positive duality gaps. As an application we have discussed the reduction of the size for a special class of problems.

• Management Science and Financial Engineering
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• 제5권2호
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• pp.25-41
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• 1999

This paper generalizes the classic two-stage multicommodity distribution system design problem to the one that includes plant locations as well as distribution center locations. Accommodating plant location leads to subproblems which are mixed are mixed integer. Hence. no LP-type subproblems are avail-able, and therefore standard Benders decomposition no longer applies. We develop new solution method which combines an integer L-shaped method with Benders decomposition to suit the purpose, and pre-sent the test results.

• 경영과학
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• 제12권2호
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• pp.63-75
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• 1995

The uncapacitated facility location problem considered here is to determine facility location sites, minimizing the total cost of establishing facilities and serving customer demand points which require primary and back-up services. To solve this problem effectively, we propose two things in this study. First, we propose an idea of Benders' decomposition approach as a solution method of the problem. Second, we implement the problem on GAMS. Using GAMS (general Algebraic Modeling System) can utilize an mixed-integer programming solver such as ZOOM/XMP and provide a completely general automated implementation with a proposed solution method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 추계학술대회 논문집 학회본부 A
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• pp.184-186
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• 1999

This paper presents a method for security constrained optimal reactive power planning in electric power systems. This method deals with corrective mode optimal reactive power dispatch in each (n-1)contingency system state and determination of the location and amount of reactive sources in preventive mode. In this paper the proposed scheme uses Benders decomposition method to determine the proper amount and location of reactive support in order to maintain a proper voltage profile and minimize active power transmission losses. This method is tested on IEEE 30 bus test system to prove effectiveness.

• 한국경영과학회지
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• 제15권1호
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• pp.23-35
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• 1990

A mathematical model for a dynamic capacitate facility location problem is formulated by a mixed integer problem. The objective of the model is to minimize total discounted costs that include fixed charges and distributed costs. The Cross Decomposition method of Van Roy is extended and applied to solve the dynamic capacitated facility location problem. The method unifies Benders Decomposition and Lagrangean relaxation into a single framework. It successively solves a transportation problem and a dynamic uncapacitated facility location problem as two subproblems. Computational results are compared with those of general mixed integer programming.

• Journal of Electrical Engineering and Technology
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• 제12권6호
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• pp.2196-2207
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• 2017

This paper presents a two-stage market auction model in a pool-based electricity market, which explicitly takes into account the system network security. The security network-constrained market auction model considers the use of corrective control to yield economically efficient actions in the post-contingency state, while ensuring a certain security level. Under this framework, the proposed model shows not only for quantifying the correlation between secure system operation and efficient market operation, but also for providing transparent information on the pricing system security for market participants. The two-stage market auction procedure is formulated using Benders decomposition (BD). In the first stage, the market participants bid in the market for maximizing their profit, and the independent system operator (ISO) clears the market based on social welfare maximization. System network constraints incorporating post-contingency control actions are described in the second stage of the market auction procedure. The market solutions, along with the BD, yield nodal spot prices (NSPs) and nodal congestion prices (NCPs) as byproducts of the proposed two-stage market auction model. Two benchmark systems are used to test and demonstrate the effectiveness of the proposed model.

• Journal of Electrical Engineering and Technology
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• 제10권3호
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• pp.709-718
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• 2015

Traditional transmission planning usually caters for rated wind power output. Due to the low occurrence probability of nominal capacity of wind power and huge investment in transmission, these planning methods will leads to low utilization rates of transmission lines and poor economic efficiency. This paper provides a novel transmission expansion planning method for integrating large-scale wind power. The wind power distribution characteristics of large-scale wind power output and its impact on transmission planning are analyzed. Based on the wind power distribution characteristics, this paper proposes a flexible and economic transmission planning model which saves substantial transmission investment through spilling a small amount of peak output of wind power. A methodology based on Benders decomposition is used to solve the model. The applicability and effectiveness of the model and algorithm are verified through a numerical case.

• Journal of Electrical Engineering and Technology
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• 제3권2호
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• pp.199-206
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• 2008

The introduction of competition in electricity markets emphasizes the importance of sufficient transmission capacities to guarantee effective power transactions. Therefore, for the economic and stable electric power system operation, transmission security constrains should be incorporated into the dispatch scheduling problem. With the intent to solve this problem, we decompose a dispatch scheduling problem into a master problem(MP) and several subproblems(SPs) using Benders decomposition. The MP solves a general optimal power flow(OPF) problem while the SPs inspect the feasibility of OPF solution under respective transmission line contingencies. If a dispatch scheduling solution given by the MP violates transmission security constraints, then additional constraints corresponding to the violations are imposed to the MP. Through this iterative process between the MP and SPs, we derive an optimal dispatch schedule incorporating the post-contingency corrective rescheduling. In addition, we consider interruptible loads as active control variables since the interruptible loads can participate as generators in competitive electricity markets. Numerical examples demonstrate the efficiency of the proposed algorithm.

• 한국경영과학회지
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• 제11권1호
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• pp.24-35
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• 1986

We investigate various methods of the Benders decoposition algorithm in its application to the simple plant location problem. We developed six variants. The master problem may be relaxed as an LP problem up to an appropriate point in time, or need not be solved to the optimality before a cut is added. Furthermore, since the subproblem is highly degenerated, we can generate more than one cuts at a time. The efficiency of the methods are examined using a sample problem. The result showed that the adding two-cut method was superior to the standard method. The LP relaxation and the non-optimization of the master program greatly improved the efficiency. Applying the LP relaxation method, we were able to reduce the computing time by two thirds of the time required by the standard method.

• 한국경영과학회지
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• 제9권2호
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• pp.3-8
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• 1984

This paper considers the intermediate warehouse location problem in a two stage distribution system where commodities are delivered from the given set of capacitated factories to customers via uncapacitated intermediate warehouses. In order to determine the subset of warehouses to open which minimizes the total distribution costs including the fixed costs associated with opening warehouses, the cross decomposition method for mixed integer programming recently developed by T.J. Van Roy is used. The cross decomposition unifies Benders decomposition and Lagrangean relaxation into a single framework that involves successive solutions to a primal subproblem and a dual subproblem. In our problem model, primal subproblem turns out to be a transshipment problem and dual subproblem turns out to be an intermediate warehouse location problem with uncapacitated factories.