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

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

• Korean Management Science Review
• /
• v.22 no.1
• /
• pp.167-178
• /
• 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
• /
• v.18 no.2
• /
• pp.19-22
• /
• 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.

• Proceedings of the Korean Information Science Society Conference
• /
• 2003.04d
• /
• pp.451-453
• /
• 2003

본 논문은 블루투스 MAC 계층에서의 패킷 스케줄링 성능의 개선을 목적으로 한다 현재 대부분의 많은 블루투스 MAC 계층 스케줄링 방식은 라운드로빈(RR)을 사용하고 있는데, 많은 슬롯과 시간을 낭비하게 되고 최적화된 업링크와 다운링크에 적합하지 않다. 한편, 블루투스의 마스터 노드에서 생기는 자원 낭비 문제를 해결하기 위한 몇 가지 MAC 스케줄링 알고리즘이 있다. 본 논문에서는 Bin-packing 과 DRR 을 이용하는 MAC 계층에서의 효과적인 패킷 스케줄링 알고리즘을 제안하고 시뮬레이션을 통해서 그 성능이 기존 방식에 비해 우월함을 보인다.

• Journal of Korean Institute of Industrial Engineers
• /
• v.34 no.4
• /
• pp.470-480
• /
• 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
• /
• v.7 no.2
• /
• pp.126-132
• /
• 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.

• The monthly packaging world
• /
• s.210
• /
• pp.44-51
• /
• 2010

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

• Journal of Korea Multimedia Society
• /
• v.14 no.9
• /
• pp.1165-1174
• /
• 2011

In data broadcasting systems, servers continuously disseminate data items through broadcast channels, and mobile client only needs to wait for the data of interest to present on a broadcast channel. However, because broadcast channels are shared by a large set of data items, the expected delay of receiving a desired data item may increase. This paper explores the issue of designing proper data allocation on multiple broadcast channels to minimize the average expected delay time of all data items, and proposes a new data allocation scheme named two level bin-packing(TLBP). This paper first introduces the theoretical lower-bound of the average expected delay, and determines the bin capacity based on this value. TLBP partitions all data items into a number of groups using bin-packing algorithm and allocates each group of data items on an individual channel. By employing bin-packing algorithm in two step, TLBP can reflect a variation of access probabilities among data items allocated on the same channel to the broadcast schedule, and thus enhance the performance. Simulation is performed to compare the performance of TLBP with three existing approaches. The simulation results show that TLBP outperforms others in terms of the average expected delay time at a reasonable execution overhead.