• 한국컴퓨터정보학회논문지
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• 제19권10호
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• pp.169-173
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• 2014

최적 해를 다항시간으로 얻을 수 있는 알고리즘이 알려져 있지 않은 NP-완전인 상자포장 문제의 일종인 바지선 적재 문제에 대해, Gu$\acute{e}$ret et al.은 $O(m^4)$ 수행 복잡도의 선형계획법으로 해를 얻고자 하였다. 반면에, 본 논문에서는 이득 우선순위로 적재하는 규칙인 O(m log m) 복잡도의 알고리즘을 제안하였다. 제안된 방법은 첫 번째로 이득 우선순위를 결정하였다. 다음으로, 이득 우선순위 물품들을 바지선에 적재하는 방법으로 초기 적재 결과를 얻었다. 마지막으로, 바지선 적재 용량을 미달하는 경우, 이전에 적재된 물품과 미선적된 물품을 상호 교환하여 바지선 적재용량을 충족시켰다. 실험 결과, 제안된 알고리즘은 NP-완전 문제인 바지선 적재 문제에 대해 선형계획법의 $O(m^4)$를 O(m log m)으로 단축시켰다.

• 산업공학
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• 제5권2호
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• pp.75-85
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• 1992

A common problem for manufacturing industries, especially consumer goods industries, is how to establish standardized procedures for loading finished goods onto pallets or containers for subsequent storage and distribution. Utilizing previous research results on the palletizing problem, this paper develops micro-computer based programs which generate an optimum loading pattern leading to the minimum amount of unused pallet or container space. Development of pallet layout chart is also included in the computer programs. The results are displayed by computer-graphic. For the users who are unfamiliar with pallet loading problem and computer system, pull-down menu and user-computer interactive data input procedures are adopted.

• 한국경영과학회지
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• 제26권4호
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• pp.99-108
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• 2001

In the ring loading problem with demand splitting, traffic demands are given for each pall of nodes in an undirected ring network and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the problem is to minimize the maximum load on the ring. The fastest a1gorithm to date is Myung, Kim and Tcha＇s a1gorithm that runs in Ο(n｜K｜) time where n is the number of nodes and K is the index set of the origin-destination pairs of nodes having flow traffic demands. Here we develop an a1gorithm for the ring loading problem with demand splitting that improves the rerouting step of Myung, Kim and Tcha＇s a1gorithm arid runs in Ο(min{n｜K｜, n$^2$}) time.

• 대한산업공학회지
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• 제23권1호
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• pp.55-76
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• 1997

This paper presents a heuristic solution for the three dimensional container loading problem with boxes which are different in size. The container loading problem is formulated as a zero-one mixed integer programming model whose objective is to maximize the container utilization. Due to its problem complexity, we propose a heuristic based on layered loading technique. Also, presented is a way to achieve the weighting balance of the stacked boxes. A micro-computer based program is developed which generates container loading pattern provided by the proposed heuristic. The results are displayed by computer-graphic. To evaluate the performance of the proposed heuristic, computational experiments are performed. The results indicate that in most of the cases the proposed heuristic performs better than an existing heuristic in terms of the container utilization.

• 산업경영시스템학회지
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• 제28권3호
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• pp.156-165
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• 2005

A new heuristic algorithm for the heterogeneous single container loading problem is proposed in this paper, This algorithm fills empty spaces with the homogeneous load-blocks of identically oriented boxes and splits residual space into three sub spaces starting with an empty container. An initial loading pattern is built by applying this approach recursively until all boxes are exhausted or no empty spaces are left. In order to generate alternative loading patterns, the load-blocks of pattern determining spaces are replaced with the alternatives that were generated on determining the load-blocks. An improvement algorithm compares these alternatives with the initial pattern to find improved one. Numerical experiments with 715 test cases show the good performance of this new algorithm, above all for problems with strongly heterogeneous boxes.

• 한국경영과학회지
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• 제23권3호
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• pp.49-62
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• 1998

In the ring loading problem, traffic demands are given for each pair of nodes in an undirected ring network with n nodes and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the Problem is to minimize the maximum load on the ring. In the ring loading problem with integer demand splitting, each demand can be split between the two directions and the flow routed in each direction is restricted to integers. Recently, Vachani et al. ［INFORMS J. Computing 8 (1996) 235-242］ have developed an Ο(n$^3$) algorithm for solving this integer version of the ring loading problem and independently, Schrijver et al. ［to appear in SIAM J. Disc. Math.］ have presented an algorithm which solves the problem with ｛0,1｝ demands in Ο（n$^2$｜K｜ ) time where K denotes the index set of the origin-desㅇtination pairs of nodes having flow demands. In this paper, we develop an algorithm which solves the problem in Ο(n ｜K｜) time.

• 한국컴퓨터정보학회논문지
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• 제20권2호
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• pp.131-136
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• 2015

화공약품 탱크 적재 문제는 다항시간으로 해를 찾을 수 있는 알고리즘이 알려져 있지 않아 NP-완전으로 분류된 난제이다. 화공약품 탱크 적재 문제는 상자 포장 문제의 일종으로, Gu$\acute{e}$ret et al.은 $O(m^4)$ 수행 복잡도의 선형계획법으로 해를 얻고자 하였다. 반면에, 본 논문에서는 최소 여유량을 가진 탱크에 적재하는 규칙인 O(m) 복잡도의 알고리즘을 제안하였다. 제안된 방법은 첫 번째로 잔여량이 있는 탱크에 해당 화공약품을 적재하였다. 다음으로, 남은 화공약품을 적재할 수 있는 최소 여유량을 가진 탱크에 해당 화공약품을 적재하였다. 실험 결과, 제안된 알고리즘은 NP-완전 문제인 화공약품 적재 문제에 대해 선형계획법의 $O(m^4)$를 O(m)으로 단축시켰다.

• Journal of Electrical Engineering and Technology
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• 제9권2호
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• pp.423-432
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• 2014

Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied for solving Combined Economic Emission Dispatch (CEED) problem with valve-point loading of thermal generators. This CEED problem with valve-point loading is a nonlinear, constrained multi-objective optimization problem, with power balance and generator capacity constraints. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a nonsmooth optimization problem. To validate its effectiveness of NSGA-II, two benchmark test systems, IEEE 30-bus and IEEE 118-bus systems are considered. To compare the Pareto-front obtained using NSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Comparison with other optimization techniques showed the superiority of the NSGA-II approach and confirmed its potential for solving the CEED problem. Numerical results show that NSGA-II algorithm can provide Pareto-front in a single run with good diversity and convergence. An approach based on Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) is applied on non-dominated solutions obtained to determine Best Compromise Solution (BCS).

• 산업경영시스템학회지
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• 제45권4호
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• pp.240-246
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• 2022

This paper introduces a container loading problem and proposes a theoretical approach that efficiently solves it. The problem is to determine a proper weight of products loaded on a container that is delivered by third party logistics (3PL) providers. When the company pre-loads products into a container, typically one or two days in advance of its delivery date, various truck weights of 3PL providers and unpredictability of the randomness make it difficult for the company to meet the total weight regulation. Such a randomness is mainly due to physical difference of trucks, fuel level, and personalized equipment/belongings, etc. This paper provides a theoretical methodology that uses historical shipping data to deal with the randomness. The problem is formulated as a stochastic optimization where the truck randomness is reflected by a theoretical distribution. The data analytics solution of the problem is derived, which can be easily applied in practice. Experiments using practical data reveal that the suggested approach results in a significant cost reduction, compared to a simple average heuristic method. This study provides new aspects of the container loading problem and the efficient solving approach, which can be widely applied in diverse industries using 3PL providers.

• Structural Engineering and Mechanics
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• 제11권1호
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• pp.1-16
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• 2001

This paper discusses the elastic stability of unbraced frames under non-proportional loading based on the concept of storey-based buckling. Unlike the case of proportional loading, in which the load pattern is predefined, load patterns for non-proportional loading are unknown, and there may be various load patterns that will correspond to different critical buckling loads of the frame. The problem of determining elastic critical loads of unbraced frames under non-proportional loading is expressed as the minimization and maximization problem with subject to stability constraints and is solved by a linear programming method. The minimum and maximum loads represent the lower and upper bounds of critical loads for unbraced frames and provide realistic estimation of stability capacities of the frame under extreme load cases. The proposed approach of evaluating the stability of unbraced frames under non-proportional loading has taken into account the variability of magnitudes and patterns of loads, therefore, it is recommended for the design practice.