• Management Science and Financial Engineering
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• v.19 no.1
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• pp.25-28
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• 2013

Consider the inverse bin-packing number problem. Given a set of items and a prescribed number K of bins, the inverse bin-packing number problem, IBPN for short, is concerned with determining the minimum perturbation to the item-size vector so that all the items can be packed into K bins or less. It is known that this problem is NP-hard (Chung, 2012). In this paper, we investigate some special cases of IBPN that can be solved in polynomial time. We propose an optimal algorithm for solving the IBPN instances with two distinct item sizes and the instances with large items.

• Korean Management Science Review
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• v.22 no.1
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• pp.167-178
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• 2005

The 2DBPP(Two-Dimensional Bin Packing Problem) is a problem of packing each item into a bin so that no two items overlap and the number of required bins is minimized under the set of rectangular items which may not be rotated and an unlimited number of identical .rectangular bins. The 2DBPP is strongly NP-hard and finds many practical applications in industry. In this paper we discuss a tabu search approach which includes tabu list, intensifying and diversification Strategies. The HNFDH(Hybrid Next Fit Decreasing Height) algorithm is used as an internal algorithm. We find that use of the proper parameter and function such as maximum number of tabu list and space utilization function yields a good solution in a reduced time. We present a tabu search algorithm and its performance through extensive computational experiments.

• Management Science and Financial Engineering
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• v.18 no.2
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• pp.19-22
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• 2012

In the bin-packing problem, we deal with how to pack the items by using a minimum number of bins. In the inverse bin-packing number problem, IBPN for short, we are given a list of items and a fixed number of bins. The objective is to perturb at the minimum cost the item-size vector so that all items can be packed into the prescribed number of bins. We show that IBPN is NP-hard and provide an approximation algorithm. We also consider a variant of IBPN where the prescribed solution value should be returned by a pre-selected specific approximation algorithm.

• Journal of Korean Institute of Industrial Engineers
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• v.34 no.4
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• pp.470-480
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• 2008

Loading steel coil products on a specialized packing case called pallet can be represented as a bin-packing problem with the special constraint where objects should be loaded on designated positions of bins. In this paper, under assuming that there exist only two types of objects, we focus on finding the optimum number of positions in a bin which minimizes the number of bins needed for packing a collection of objects. Firstly, we propose a method to decide the number of positions and prove that the method is optimum. Finally, for the packing problem using bins designed by the method, we show that the well-known algorithm, First-Fit Decreasing(FFD), is the optimum algorithm.

• Industrial Engineering and Management Systems
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• v.7 no.2
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• pp.126-132
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• 2008

The bin packing problem (BPP) is an NP-Complete Problem. The problem can be described as there are $N=\{1,2,{\cdots},n\}$ which is a set of item indices and $L=\{s1,s2,{\cdots},sn\}$ be a set of item sizes sj, where $0<sj{\leq}1$, ${\forall}j{\in}N$. The objective is to minimize the number of bins used for packing items in N into a bin such that the total size of items in a bin does not exceed the bin capacity. Assume that the bins have capacity equal to one. In the past, many researchers put on effort to find the heuristic algorithms instead of solving the problem to optimality. Then, the quality of solution may be measured by the asymptotic worst-case ratio or the average-case ratio. The First Fit Decreasing (FFD) is one of the algorithms that its asymptotic worst-case ratio equals to 11/9. Many researchers prove the asymptotic worst-case ratio by using the weighting function and the proof is in a lengthy format. In this study, we found an easier way to prove that the asymptotic worst-case ratio of the First Fit Decreasing (FFD) is not more than 11/9. The proof comes from two ideas which are the occupied space in a bin is more than the size of the item and the occupied space in the optimal solution is less than occupied space in the FFD solution. The occupied space is later called the weighting function. The objective is to determine the maximum occupied space of the heuristics by using integer programming. The maximum value is the key to the asymptotic worst-case ratio.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.311-314
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• 2004

The 2 DBPP(Two-Dimensional Bin Packing Problem) is a problem of packing each item into a bin so that no two items overlap and the number of required bins is minimized under the set of rectangular items which may not be rotated and an unlimited number of identical rectangular bins. The 2 DBPP is strongly NP-hard and finds many practical applications in industry. In this paper we discuss a tabu search approach which includes tabu list, intensifying and diversification strategies. The HNFDH(Hybrid Next Fit Decreasing Height) algorithm is used as an internal algorithm. We find that use of the proper parameter and function such as maximum number of tabu list and space utilization function yields a good solution in a reduced time. We present a tabu search algorithm and its performance through extensive computational experiments.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.205-206
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• 2000

In this paper, we consider variable sized bin packing problem, where the objective is not to minimize the total space used in the packing but to minimize the total cost of the packing when the cost of unit size of each bin does not increase as the bin size increases. A heuristic algorithm is described, and analyzed in two special cases: 1) b$\sub$m/｜…｜b$_1$and w$\sub$n/｜…｜w$_1$, and 2) b$\sub$m/｜…｜b$_1$, where b$\sub$i/ denotes the size of i-th type of bin and w$\sub$j/ denotes the size of j-th item. In the case 1), the algorithm guarantees optimality, and in the case 2), it guarantees asymptotic worst-case performance bounds of l1/9.

• Journal of the Korea Society of Computer and Information
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• v.20 no.10
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• pp.61-68
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• 2015

This paper deals with the pre-marshalling problem that the containers of container yard at container terminal are relocated in consensus sequence of loading schedule of container vessel. This problem is essential to improvement of competitive power of terminal. This problem has to relocate the all of containers in a bay with minimum number of movement. There are various algorithms such as metaheuristic as genetic algorithm and heuristic algorithm in order to find the solution of this problem. Nevertheless, there is no unique general algorithm that is suitable for various many data. And the main drawback of metaheuristic methods are not the solution finding rule but can be find the approximated solution with many random trials and by coincidence. This paper can be obtain the solution with O(m) time complexity that this problem deals with bin packing problem for m stack bins with descending order of take out ranking. For various experimental data, the proposed algorithm can be obtain the optimal solutions for all of data. And to conclude, this algorithm can be show that most simple and general algorithm with simple optimal solution finding rule.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.3
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• pp.125-136
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• 2009

The container packing problem Is one of the traditional optimization problems, which is very related to the knapsack problem and the bin packing problem. In this paper, we deal with the quadratic multiple container picking problem (QMCPP) and it Is known as a NP-hard problem. Thus, It seems to be natural to use a heuristic approach such as evolutionary algorithms for solving the QMCPP. Until now, only a few researchers have studied on this problem and some evolutionary algorithms have been proposed. This paper introduces a new efficient evolutionary algorithm for the QMCPP. The proposed algorithm is devised by improving the original network random key method, which is employed as an encoding method in evolutionary algorithms. And we also propose local search algorithms and incorporate them with the proposed evolutionary algorithm. Finally we compare the proposed algorithm with the previous algorithms and show the proposed algorithm finds the new best results in most of the benchmark instances.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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• pp.47-55
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• 1999

This paper develops an efficient heuristic algorithm for scheduling workforce level that can accommodate all the requested maintenance jobs. Each job has its own release and due dates as well as man-day requirement, and must be scheduled in a non-interrupted time interval, namely, without preemption. Duration of each job is not fixed, but to be determined within given specific range. The objective is to minimize workforce level to complete all the requested maintenance jobs. We show that the problem can be seen as a variant of the two-dimensional bin-packing problem with some additional constraints. A non-linear mixed integer programming model for the problem is developed, and an efficient heuristic algorithm based on bin-packing algorithms is proposed. In order to evaluate goodness of the solution obtained from the proposed algorithm, a scheme for getting a good lower bound for the optimum solution is presented and analyzed. The computational experiment shows that the proposed algorithm performs quite satisfactorily.