• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.3
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• pp.95-104
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• 2001

In this paper, we consider a maximin version of the linear programming knapsack problem with extended generalized upper bound (GUB) constraints. We solve the problem efficiently by exploiting its special structure without transforming it into a standard linear programming problem. We present an O(n$^3$) algorithm for deriving the optimal solution where n is the total number of problem variables. We illustrate a numerical example.

• Knowledge Management Research
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• v.20 no.3
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• pp.39-47
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• 2019

Response surface methodology (RSM) is a group of statistical modeling and optimization methods to improve the quality of design systematically in the quality engineering field. Its final goal is to identify the optimal setting of input variables optimizing a response. RSM is a kind of knowledge management tool since it studies a manufacturing or service process and extracts an important knowledge about it. In a real problem of RSM, it is a quite frequent situation that considers multiple responses simultaneously. To date, many approaches are proposed for solving (i.e., optimizing) a multi-response problem: process capability function approach, desirability function approach, loss function approach, and so on. The process capability function approach first estimates the mean and standard deviation models of each response. Then, it derives an individual process capability function for each response. The overall process capability function is obtained by aggregating the individual process capability function. The optimal setting is given by maximizing the overall process capability function. The existing process capability function methods usually use the arithmetic mean or geometric mean as an aggregation operator. However, these operators do not guarantee the Pareto optimality of their solution. Moreover, they may bring out an unacceptable result in terms of individual process capability function values. In this paper, we propose a maximin-based process capability function method which uses a maximin criterion as an aggregation operator. The proposed method is illustrated through a well-known multiresponse problem.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.145-152
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• 1997

We present a continuous resource allocation problem with maximin objective functions under the generalized lower bound(GLB) and generalized upper bound(GUB) constraints. This problem is an extension for the problems of previous studies. An efficient algorithm is developed by exploiting extended structural properties, where n is the total number of variables. The worst computational complexity of the proposed algorithm is O(nlogn).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.501-505
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• 1998

In this paper, an LP problem with convex polyhedral objective coefficients is treated. In the problem, the interactivities of the uncertain objective coefficients are represented by a bounded convex polyhedron (a convex polytope). We develop a computation algorithm of a maxmin achievement rate solution. To solve the problem, first, we introduce the relaxation procedure. In the algorithm, a sub-problem, a bilevel programing problem, should be solved. To solve the sub-problem, we develop a solution method based on a branch and bound method. As a result, it is shown that the problem can be solved by the repetitional use of the simplex method.

• Journal of Korean Society for Quality Management
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• v.17 no.2
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• pp.93-100
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• 1989

Nonlinear rank statistics for the simple tree alternatives problem are considered. Pitman efficiencies between several procedures are studied. A new maximin procedure is suggested and shown to have good efficiency properties. Additionally, it is desirable to terminate the experiment early comparing well known rank statistics or multiple comparison test statistics.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.4
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• pp.369-374
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• 2015

In order to efficiently optimize the problem involving complex computer codes or computationally expensive simulation, surrogate models are widely used. Because their accuracy significantly depends on sample points, many experimental designs have been proposed. One approach is the sequential design of experiments that consider existing information of responses. In earlier research, the correlation coefficients of the kriging surrogate model are introduced as weight parameters to define the scaled distance between sample points. However, if existing information is incorrect or lacking, new sample points can be misleading. Thus, our goal in this paper is to propose a weight function derived from correlation coefficients to generate new points robustly. To verify the performance of the proposed method, several existing sequential design methods are compared for use as mathematical examples.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.65-75
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• 2012

In setting an experimental design for the prediction outside the experimental region (extrapolation design), it is natural for the experimenter to be very careful about the validity of the model for the design because the experimenter is not certain whether the model can be extended beyond the design region or not. In this paper, a hybrid constrained type approach was adopted in dealing model uncertainty as well as the prediction error using the three basic principles available in literature, maxi-min, constrained, and compound design. Furthermore, the effect of the distance of the extrapolation design point from the design region is investigated. A search algorithm was used because the classical exchange algorithm was found to be complex due to the characteristic of the problem.

• Journal of the military operations research society of Korea
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• v.33 no.1
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• pp.59-74
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• 2007

Computer simulation models are in general quite complex and time-consuming to run, and therefore, a simpler meta-model is usually constructed for further analysis. In this paper, JANUS, a war-game simulator, is used to describe a certain tank combat situation. Then, second-order response surface and artificial neural network meta-models are developed using the data from eight different experimental designs. Relative performances of the developed meta-models are compared in terms of the mean squared error of prediction. Computational results indicate that, for the given problem, the second-order response surface meta-model generally performs better than the neural network, and the orthogonal array-based Latin hypercube design(LHD) or LHD using maximin distance criterion may be recommended.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.693-703
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• 2014

When setting up an experiment for extrapolation at multiple points outside the design space, we often face a difficulty in which point we should emphasize even if the polynomial model under consideration is given. In this paper we propose various methods under two possible scenarios that deal with extrapolations. One considered in this paper is the situation when the model assumed can be extended beyond the design space. In this setting, the many classical methods(including various approaches the authors proposed before) were revisited in the context of extrapolation. But the real problem arises when there is an uncertainty concerning the validity of the assumed model. Therefore, the second scenario is to develop an appropriate procedure when we have limited information about model. Consequently, a hybrid approach is suggested to deal with this issue of how to handle the multiple extrapolating under model uncertainty. A search algorithm was implemented because the classical exchange algorithm was found difficult to handle the complexity of the problem.