• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.3
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• pp.1-12
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• 2017

In this paper, we generalize lifted inequalities to a 0-1 mixed-integer bilinear covering set with linear terms. This work is motivated by the observation that Generalized Bilinear Inequality (GBI) occurs in the Branch and Bound process. We find some conditions and prove the subadditivity of lifting functions for lifting to be sequence-independent. Using the theoretical results, we develop facet-defining inequalities for a GBI-defined set through three steps of lifting.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.1-10
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• 1998

We consider the precedence-constrained knapsack problem. which is a knapsack problem with precedence constraints imposed on the set of variables. Especially, we focus on the case where the precedence constraints cir be represented as a bipartite graph, which occurs most frequently in applications. Based on the previous studios for the general case, we specialize the polyhedral results on the related polytope and derive stronger results on the facet-defining properties of the inequalities.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.59-80
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• 1997

Designing highly survivable interoffice telecommunication networks is considered. The problem is formulated as a minimum-cost network design problem with three node connectivity constraints. These valid and facet-defining inequalities for the convex hull of the solution are presented. A branch and cut algorithm is proposed based on the inequalities to obtain the optimal solution. With the lower bound by the cutting plane algorithm, a delete-ink heuristic is proposed to otain a good upper bound in the branch and bound procedure. The effeciveness of the branch and cut algorithm is demonstrated with computational results for a variety of problem sets : different lower bounds, two types of link costs and large number of links. The cutting plane procedure based on the three inequalities provides excellent lower bounds to the optimal solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.2
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• pp.103-109
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• 2017

Metal 3D printing, which is an additive metal manufacturing (AMM) process, enables the development of full-density metallic tools and parts using metal powders that are precisely delivered and controlled for deposition with no powder bed. However, some unknown geometric defects and irregular geometric features on an STL model can possibly result in incorrect metal part fabrication after the build. This study first proposes a methodical approach for verifying the build part, including the missing facet problems in an STL model, by defining some irregular features that possibly exist on the part. Second, 2D tool paths on each build layer were investigated for detecting any singular region inside the layer. The method was implemented for building two sample STL models using a direct energy deposition process, and finally, it was visually simulated for diagnosis.