• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.229-250
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• 2022

Since the publication of Markowitz's (1952) mean-variance portfolio model, research on portfolio optimization has been conducted in many fields. The existing mean-variance portfolio model forms a nonlinear convex problem. Applying Dantzig's linear programming method, it was converted to a linear form, which can effectively reduce the algorithm computation time. In this paper, we proposed a Dantzig perturbation portfolio model that can reduce management costs and transaction costs by constructing a portfolio with stable and small (sparse) assets. The average return and risk were adjusted according to the purpose by applying a perturbation method in which a certain part is invested in the existing benchmark and the rest is invested in the assets proposed as a portfolio optimization model. For a covariance estimation, we proposed a Gaussian kernel weight covariance that considers time-dependent weights by reflecting time-series data characteristics. The performance of the proposed model was evaluated by comparing it with the benchmark portfolio with 5 real data sets. Empirical results show that the proposed portfolios provide higher expected returns or lower risks than the benchmark. Further, sparse and stable asset selection was obtained in the proposed portfolios.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1988.10a
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• pp.18-18
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• 1988

• Journal of the Korean Society for Railway
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• v.15 no.2
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• pp.185-192
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• 2012

Line planning is to determine the frequency of trains on each line to satisfy origin-destination demand while minimizing total operation cost. However, different from the line planning in passenger transportation, it is more important at which intermediate stations each train should be stopped and shunted because the freight car handling works like drop-off or(and) pick-up can incur much time and high cost so that the delay deteriorates the quality of rail freight transportation service. We present an optimization model for constructing line plan in rail freight transportation to simultaneously minimize the train operation cost and total transportation time of freights. And we suggest a column generation approach for our problem, which can solve the real network instances in reasonable computation times.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.6
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• pp.209-220
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• 2014

Compressive Sensing (CS) is a new signal acquisition paradigm which enables sampling under Nyquist rate for a special kind of signal called sparse signal. There are plenty of CS recovery methods but their performance are still challenging, especially at a low sub-rate. For CS recovery of natural images, regularizations exploiting some prior information can be used in order to enhance CS performance. In this context, this paper addresses improving quality of reconstructed natural images based on Dantzig selector and smooth filters (i.e., Gaussian filter and nonlocal means filter) to generate a new regularization called smooth residual error regularization. Moreover, total variation has been proved for its success in preserving edge objects and boundary of reconstructed images. Therefore, effectiveness of the proposed regularization is verified by experimenting it using augmented Lagrangian total variation minimization. This framework is considered as a new CS recovery seeking smoothness in residual images. Experimental results demonstrate significant improvement of the proposed framework over some other CS recoveries both in subjective and objective qualities. In the best case, our algorithm gains up to 9.14 dB compared with the CS recovery using Bayesian framework.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-12
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• 1997

Complementaity problem theory developed by Lemke [10], Cottle and Dantzig [8] and others in the early 1960s and thereafter, has numerous applications in diverse fields of mathematical and engineering sciences. And it is closely related to variational inquality theory and fixed point theory. Recently, fixed point methods for the solving of nonlinear complementarity problems were considered by Noor et al. [11, 12]. Also complementarity problems related to variational inequality problems were investigated by Chang [1], Cottle [7] and others.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.3 no.3
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• pp.55-58
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• 1980

Today, L.P. model has often been used in solving economic and managemental phenomena. But in case of adopting L.P. model in dealing with practical economic and managemental problems there is a possibility that we have difficulties in solving these problems because of greatness of model size, cost for collecting data, cost for adjusting matrix, and etc. In this respect "Decomposition Algorithm for L.P." has been used in overcoming the difficulties above stated. In this paper therefore, I will try to introduce and them criticize Dantzig -Wolfe's "Decomposition Method" and Kornai - Liptak's "Two - Level Planning".ot;Two - Level Planning".uot;.

• Journal of the military operations research society of Korea
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• v.23 no.2
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• pp.155-170
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• 1997

Currently, increasing the number of artillery units requires more deployment space in FABA. However, available positions of artillery units in FEBA is limited due to mountainous terrains. Therefore, it is hard to find enough artillery position space in accordance with the field artillery mannual. This paper studies on determination of the size of battery position in order to maximize the firing-effectiveness and to minimize the enemy threat. Also, it studies the possibility of reducing the size of a battery position. The optimum size of a battery position id obtained by using Dantzig's model and Supper Quick II model which produces the probability of kill data with various input data. As a result, it shows that the size of battery position can be reduced without decreasing the firing-effectiveness.

• Management Science and Financial Engineering
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• v.7 no.2
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• pp.1-11
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• 2001

Gouveia and Pires (European Journal of Operations Research 112(1999) 134-146) have proposed four extended formulations having precedence variables as extra variables and characterized the projections of three of the four formulations into the natural variable space. In Gouveia and Pires (Discrete Applied Mathematics 112 (2001)), they also have introduced some other extended formulations with the same extra variables and conjectured that the projection of one of the proposed formulations is equivalent to the one proposed by Dantzig, Fulkerson, and Johnson (Operations Research 2(1954) 393-410). In this paper, we provide a unifying framework based on which we give alternative proofs on the projections of three extended formulations and new proofs on those of two formulations appeared in Gouveia and Pires(1999, 2001).

• Journal of the Korean Operations Research and Management Science Society
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• v.11 no.2
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• pp.37-50
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• 1986

In combining dispersed optimization models, either primal or dual(or both) decomposition method widely used as an organizing device. Interpreting the methods economically, the concepts of price and resource-directive coordination are generally well accepted. Most of deomposition/ integration methods utilize either primal information of dual information, not both, from subsystems, while some authors have developed mixed decomposition approaches employing two master problems dealing primal and dual proposals separately. In this paper a hybrid decomposition method is introduced, where one hybrid master problem utilizes the underlying relationships between primal and dual information from each subsystem. The suggested method is well justified with respect to the flexibility in information flow pattern choice (some prices and other quantities) and to the compatibility of subdivision's optimum to the systemwide optimum, that is often lacking in conventional decomposition methods such as Dantzig-Wolfe's. A numerical example is also presented to illustrate the suggested approach.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.16-22
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• 2019

After Dantzig and Rasmer introduced Vehicle Routing Problem in 1959, this field has been studied with numerous approaches so far. Classical Vehicle Routing Problem can be described as a problem of multiple number of homogeneous vehicles sharing a same starting node and having their own routes to meet the needs of demand nodes. After satisfying all the needs, they go back to the starting node. In order to apply the real world problem, this problem had been developed with additional constraints and pick up & delivery model is one of them. To enhance the effectiveness of pick up & delivery, hub became a popular concept, which often helps reducing the overall cost and improving the quality of service. Lots of studies have suggested heuristic methods to realize this problem because it often becomes a NP-hard problem. However, because of this characteristic, there are not many studies solving this problem optimally. If the problem can be solved in polynomial time, optimal solution is the best option. Therefore, this study proposes a new mathematical model to solve this problem optimally, verified by a real world problem. The main improvements of this study compared to real world case are firstly, make drivers visit every nodes once except hub, secondly, make drivers visit every nodes at the right time, and thirdly, make drivers start and end their journey at their own homes.