• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.169-180
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• 2015

Recently, scheduling problems with position-dependent processing times have received considerable attention in the literature, where the processing times of jobs are dependent on the processing sequences. However, they did not consider cases in which each processed job has different learning or aging ratios. This means that the actual processing time for a job can be determined not only by the processing sequence, but also by the learning/aging ratio, which can reflect the degree of processing difficulties in subsequent jobs. Motivated by these remarks, in this paper, we consider a two-agent single-machine scheduling problem with linear job-dependent position-based learning effects, where two agents compete to use a common single machine and each job has a different learning ratio. Specifically, we take into account two different objective functions for two agents: one agent minimizes the total weighted completion time, and the other restricts the makespan to less than an upper bound. After formally defining the problem by developing a mixed integer non-linear programming formulation, we devise a branch-and-bound (B&B) algorithm to give optimal solutions by developing four dominance properties based on a pairwise interchange comparison and four properties regarding the feasibility of a considered sequence. We suggest a lower bound to speed up the search procedure in the B&B algorithm by fathoming any non-prominent nodes. As this problem is at least NP-hard, we suggest efficient genetic algorithms using different methods to generate the initial population and two crossover operations. Computational results show that the proposed algorithms are efficient to obtain near-optimal solutions.

• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1624-1647
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• 2020

Vehicular network is one of the most important subjects for researchers in recent years. Anycast routing protocols have many applications in vehicular ad hoc networks. The aim of an anycast protocol is sending packets to at least one of the receivers among candidate receivers. Studies done on anycast protocols over vehicular networks, however, have capability of implementation on some applications; they are partial, and application specific. No need to say that the lack of a comprehensive study, having a strong analytical background, is felt. Mathematical modeling in vehicular networks is difficult because the topology of these networks is dynamic. In this paper, it has been demonstrated that vehicular networks can be modeled based on time-expanded networks. The focus of this article is on geographical anycast. Three different scenarios were proposed including sending geographic anycast packet to exactly-one-destination, to at-least-one-destination, and to K-anycast destination, which can cover important applications of geographical anycast routing protocols. As the proposed model is of MILP type, a decentralized heuristic algorithm was presented. The evaluation process of this study includes the production of numerical results by Branch and Bound algorithm in general algebraic modeling system (GAMS) software and simulation of the proposed protocol in OMNET++ simulator. The comprehension of the result of proposed protocol and model shows that the applicability of this proposed protocol and its reactive conformity with the presented models based on presented metrics.

• Journal of the Korea Society for Simulation
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• v.24 no.4
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• pp.77-88
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• 2015

In this paper, we consider a two-agent single-machine scheduling problem with exponential job-dependent position-based learning effects. The objective is to minimize the total weighted completion time of one agent with the restriction that the makespan of the other agent cannot exceed an upper bound. First, we propose a branch-and-bound algorithm by developing some dominance /feasibility properties and a lower bound to find an optimal solution. Second, we design an efficient simulated annealing (SA) algorithm to search a near optimal solution by considering six different SAs to generate initial solutions. We show the performance superiority of the suggested SA using a numerical experiment. Specifically, we verify that there is no significant difference in the performance of %errors between different considered SAs using the paired t-test. Furthermore, we testify that random generation method is better than the others for agent A, whereas the initial solution method for agent B did not affect the performance of %errors.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.1-13
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• 1998

The purpose of this paper is to formulate the three-dimensional loading problem and to develop an exact algorithm. The three-dimensional loading problem is not only to load as many boxes as possible, but also to ensure load stability. In this Paper, we propose formulation by zero-one integer programming. Further we propose as an algorithm the branch-and-bound enforced by efficient bounding criteria. As an upper bound, we use the solution of the Lagrangean relaxation problem which relaxes constraints of zero-one IP, and as a lower bound, we use a heuristic solution induced by the solution of the Lagrangean relaxation problem. Last, we show computational experiments on convergency of upper and lower bounds.

• Journal of the Korea Society of Computer and Information
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• v.3 no.4
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• pp.44-48
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• 1998

In this paper proposed Component Synthesis Algorithm(CSA) for mapping described HDL to RT component of given library. CSA transform I/O variables of HDL and relation of operators to control/data flow graph(CDFG) that consists of graph, reduce the size of graph, compute the cost, the bound, and the method that use compatibility graph(CG), and then mapping to component. Component synthesis used branch-and-bound algorithm. The result that synthesis using CSA algorithm was proved that this result and the cost of the manual were indentified.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.115-124
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• 1993

A structural system reliability analysis is studied for the safety assessment of midship section. Probabilistically dominant collapse modes are generated by Element Replacement Method and Incrimental Load Method. In order to avoid generating the same modes repeatedly, it is branched at final plastic hinge. Using first and second order bound methods, system failure probability of midship section is computed and compared with deterministic load factor method to show the usefulness of the proposed method.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.1
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• pp.1-8
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• 1985

By introducing the concept of reliability of parallel systems the set covering. A branch-and-bound algorithm is developed and illustrated by a numerical example. The procedure has been coded and its computational efficiency is studied.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.40
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• pp.137-142
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• 1996

An algorithm for solving the cardinality constrained linear programming knapsack problem is presented. The algorithm has a convenient structure for a branch-and-bound approach to the integer version, especially to the 0-1 collapsing knapsack problem. A numerical example is given.

• Korean Management Science Review
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• v.11 no.3
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• pp.55-65
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• 1994

Given the flow matrix, plant size and department sizes, the algorithms in this paper provide the layout with rectilinear distance. To construct automated facility design, cut tree approach is employed. A branch and bound computer code developed by Tillinghast is modifided to find the feasible fits of departments without shape distortion in the plant rectangle.