• Journal of Korean Society of Industrial and Systems Engineering
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• v.26 no.3
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• pp.58-66
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• 2003

The cut tree approach of Montreuil and Ratliff [16] and eigenvector approach [10] are used to automatically draw a feasible facility layout with aisle structure. The department arrangement can minimize an aisle distance criterion considering door locations and dimension constraints. The aisle distance is measured by the door to door distance between departments. An eigenvector and cut tree approaches [1] are implemented based on the branch and bound technique in Kim et al. [2] in order to obtain feasible layouts. Then, the algorithm to fix the door location of each department is developed. After the door locations are determined, the factory layout is evaluated in terms of aisle distance. The aisle structure is obtained by expanding the original layout. The solution is kept until we will find better factory layout. The proposed approach based on the branch and bound technique, in theory, will provide the optimal solution. If the runs are time and/or node limited, the proposed method is a strong heuristic. The technique is made further practical by the fact that the solution is constrained such that the rectangular shape dimensions length(l) and width(w) are fixed and a perfect fit is generated if a fit is possible.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10a
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• pp.636-638
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• 1998

WDM망을 구성하는데 있어서 광학적 파장은 가장 중요한 자원의 하나이다. 그러나 주어진 통신 요구를 모두 수용하면서 동시에 최소한의 파장만을 사용하는 WDM망의 설계 문제는 이미 NP-complete 계열의 문제인 것으로 밝혀졌으며 많은 휴리스틱 알고리즘들이 제안되었다. 본 논문에서는 임의의 물리적 망 위상(topology)과 완전 연결(full connection)형태의 통신 요구가 주어질 경우, 요구되는 파장 경로(Wavelength Path, lightpath)를 확립하기 위한 방법으로써 각 노드 사이의 최단 거리 경로를 기반으로 하여 탐색 공간을 만들고 구성된 탐색 공간 내에서 Branch-and-bound 탐색방식을 수행하는 파장 경로 설정 알고리즘을 제안한다. Branch-and-bound탐색방식은 초기에 좋은 bound조건을 가질 경우 주어진 시간 안에 보다 넓은 탐색 공간을 검색할 수 있으므로 최초의 탐색에서 가능한 좋은 성능의 파장 경로 설정을 발견할 수 있어야한다. 시뮬레이션 실험을 통하여 최초의 탐색에서 발견한 파장 경로 설정과 구성된 탐색 공간내의 최적해를 얻고, cut-set를이용하여 요구 파장 개수의 하위 한계값을 계산한후, 이를 상호 비교하여 제안된 알고리즘의 성능을 평가한다.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.661-667
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• 1997

We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.10a
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• pp.10-10
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• 1993

본 연구에서는 다품종(multiple products) 다단계(multi-stage) 흐름 생산시스템에서의 제품별 로트 투입순서결정무제를 다루었다. 다단계 흐름 생산시스템의 투입순서 결정문제에 대한 기존연구는 각 단계의 기계대수가 1대인 경우에 관한 것이 대부분이지만, 본 연구에서는 각 단계의 기계대수가 복수이고 각 제품의 생산량이 로트로 주어지며, 또한 각 단계마다의 이송이 로트로 이루어지는 것이 아니라 1단위로 이루어지는 생산시스템을 대상으로 하였다. 그리고 각 제품의 생산준비기간은 투입순서와 관계 없이 일정하며 앞 단계에서 제품이 도착하지 않더라도 생산준비는 먼저 수행될 수 있다고 가정하였다. 제품별 로트 투입순서 결정문제에서 사용된 성능평가기준(performance measure)은 총작업소요시간(makespan)이며 순열투입순서(permutation schedule)만을 대상으로 하였다. 결정기법으로는 투입순서 결정문제에서 효율적인 것으로 알려져 있는 분지한계법(Branch & Bound)이 사용되었으며 분지한계법에서 이용되는 부분투입순서(partial sequence)에 대한 하한값(lower bound)을 제시하였다. 제시된 기법을 사용하면 현실적인 크기의 제품별 로트 투입순서 결정문제를 적당한 시간내에 충분히 해결할 수 있을 것으로 보인다. 제시된 해법으로 해결된 수치예제가 주어져 있다.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.202-210
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• 1995

Given a tree T with a root node 0 having the capacity H and a profit $c_{v}$ and a demand $d_{v}$ on each node v of T, the capacitated subtree of a tree problem(CSTP) is to find a subtree of T containing the root that has the maximum total profit, the sum of profits over the subtree, and also satisfies the constraint of which the sum of demands over the subtree must be less than or equal to H. We first define the so-called critical item for CSTP and find an upper bound on the linear programming relaxation of CSTP. We then present our branch and bound algorithm for solving CSTP and finally report the computational results on a set of randomly generated test problems.s.s.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.138-141
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• 2006

This paper considers a two-machine flow-shop scheduling problem for minimizing mean flow time. Each job has three non-preemptive operations, where the first and third operations must be Processed on the first and second machines, respectively, but the second operation can be processed on either machine. A lower bound based on SPT rule is derived, which is then used to develop a branch-and-bound algorithm. Also, an efficient simple heuristic algorithm is developed to generate a near-optimal schedule. Numerical experiments are performed to evaluate the performances of the proposed branch-and-bound and the heuristic algorithm

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.2
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• pp.80-93
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• 2008

This paper improves algorithms for an assembly-type flowshop scheduling problem in which each job is to assemble two types of components and makespan is the objective measure. For the assembly, one type of the components is outsourced with job-dependent lead time but the other type is fabricated in-house. When both components for a job are prepared, the assembly operation for the job can be started. This problem had been proved to be NP-Complete, so branch-and-bound (B&B) and heuristic algorithms have already been developed. In this paper, we suggest other dominance rules, lowerbound and heutistic algorithms. Also, we develop a new B&B algorithm using these improved bound and dominance rules. The suggested heuristics and B&B algorithm are compared with existing algorithms on randomly-generated test problems.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.417-429
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• 1998

This paper considers two-sided (left and right side) assembly lines which are often used, especially in assembling large-sized products such as trucks and buses. A large number of exact algorithms and heuristics have been proposed to balance one-sided lines. However, little attention has been paid to balancing two-sided assembly lines. We present an efficient algorithm based on a branch and bound for balancing two-sided assembly lines. The algorithm involves a procedure for generating an enumeration tree. To efficiently search for the near optimal solutions to the problem, assignment rules are used in the method. New and existing bound strategies and dominance rules are else employed. The proposed algorithm can find a near optimal solution by enumerating feasible solutions partially. Extensive computational experiments are carried out to make the performance comparison between the proposed algorithm and existing ones. The computational results show that our algorithm is promising and robust in solution quality.

• Journal of IKEEE
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• v.1 no.1 s.1
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• pp.31-46
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• 1997

In this paper, a parallel Optimal Best-First search Branch-and-Bound(B&B) algorithm(pobs) is designed and evaluated for MIN-based multiprocessor systems. The proposed algorithm decomposes a problem into G subproblems, where each subproblem is processed on a group of P processors. Each processor group uses tile sub-Global Best-First search technique to find a local solution. The local solutions are broadcasted through the network to compute the global solution. This broadcast provides not only the comparison of G local solutions but also the load balancing among the processor groups. A performance analysis is then conducted to estimate the speed-up of the proposed parallel B&B algorithm. The analytical model is developed based on the probabilistic properties of the B&B algorithm. It considers both the computation time and communication overheads to evaluate the realistic performance of the algorithm under the parallel processing environment. In order to validate the proposed evaluation model, the simulation of the parallel B&B algorithm on a MIN-based system is carried out at the same time. The results from both analysis and simulation match closely. It is also shown that the proposed Optimal Best-First search B&B algorithm performs better than other reported schemes with its various advantageous features such as: less subproblem evaluations, prefer load balancing, and limited scope of remote communication.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.86-102
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• 1991

The purpose of this paper is to present a branch and bound algorithm for the hierarchical transportation network design problem in 2-level directed networks. This problem is to find the least cost of hierarchical transportation networks which consist of a primary path and a secondary path. The primary path is a simple path from a prespecified orgin node to a prespecified terminal node. All nodes must be either a transsipment node on the primary path or connected to that path via secondary arcs. This problem is formulated to a 0-1 inter programming problem with assignment and illegal subtour elimination equations as constaints. We show that the subproblem relaxing subtour elimination constraints is transformed to a linear programming problem by means of the totally unimodularity. Optimal solutions of this subproblem are polynoially obtained by the assignment algorithm and complementary slackness conditions. Therefore, the optimal value of this subproblme is used as a lower bound. When an optimal solution of the subproblem has an illegal subtour, a better disjoint rule is adopted as the branching strategy for reducing the number of branched problems. The computational comparison between the least bound rule and the depth first rule for the search strategy is given.