Multidimensional Dynamic Programming Algorithm for N-Level Batching with Hierarchical Clustering Structure

This study focuses on the N-level batching problem with a hierarchical clustering structure. Clustering is the task of grouping a set of item types in such a way that item types in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. In hierarch...

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Published in:	Mathematical problems in engineering Vol. 2017; no. 2017; pp. 1 - 12
Main Authors:	Lim, Seung-Kil, Kim, Jae-Gon, Bang, June-Young
Format:	Journal Article
Language:	English
Published:	Cairo, Egypt Hindawi Publishing Corporation 01.01.2017 Hindawi John Wiley & Sons, Inc
Subjects:	Algorithms Batch processing Cluster analysis Clustering Clusters Computer industry Costs Dynamic programming Hierarchies Integer programming Manufacturing Mathematical problems Tasks
ISSN:	1024-123X, 1563-5147
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Abstract	This study focuses on the N-level batching problem with a hierarchical clustering structure. Clustering is the task of grouping a set of item types in such a way that item types in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. In hierarchical clustering structure, more and more different item types are clustered together as the level of the hierarchy increases. N-level batching is the process by which items with different types are grouped into several batches passed from level 1 to level N sequentially for given hierarchical clustering structure such that batches in each level should satisfy the maximum and minimum batch size requirements of the level. We consider two types of processing costs of the batches: unit processing cost and batch processing cost. We formulate the N-level batching problem with a hierarchical clustering structure as a nonlinear integer programming model with the objective of minimizing the total processing cost. To solve the problem optimally, we propose a multidimensional dynamic programming algorithm with an example.
AbstractList	This study focuses on the N-level batching problem with a hierarchical clustering structure. Clustering is the task of grouping a set of item types in such a way that item types in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. In hierarchical clustering structure, more and more different item types are clustered together as the level of the hierarchy increases. N-level batching is the process by which items with different types are grouped into several batches passed from level 1 to level N sequentially for given hierarchical clustering structure such that batches in each level should satisfy the maximum and minimum batch size requirements of the level. We consider two types of processing costs of the batches: unit processing cost and batch processing cost. We formulate the N-level batching problem with a hierarchical clustering structure as a nonlinear integer programming model with the objective of minimizing the total processing cost. To solve the problem optimally, we propose a multidimensional dynamic programming algorithm with an example. This study focuses on the N ‐level batching problem with a hierarchical clustering structure. Clustering is the task of grouping a set of item types in such a way that item types in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. In hierarchical clustering structure, more and more different item types are clustered together as the level of the hierarchy increases. N ‐level batching is the process by which items with different types are grouped into several batches passed from level 1 to level N sequentially for given hierarchical clustering structure such that batches in each level should satisfy the maximum and minimum batch size requirements of the level. We consider two types of processing costs of the batches: unit processing cost and batch processing cost. We formulate the N ‐level batching problem with a hierarchical clustering structure as a nonlinear integer programming model with the objective of minimizing the total processing cost. To solve the problem optimally, we propose a multidimensional dynamic programming algorithm with an example.
Author	Lim, Seung-Kil Kim, Jae-Gon Bang, June-Young
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Cites_doi	10.1186/1471-2202-13-90 10.1093/molbev/mst028 10.1155/2014/202350 10.1016/j.eswa.2013.08.028 10.1093/bib/bbn058 10.1016/j.eswa.2014.09.054 10.1016/j.tre.2011.11.003 10.1002/widm.53 10.1016/j.datak.2012.12.002 10.1016/j.procs.2015.09.027 10.1080/00207543.2010.512620 10.1371/journal.pone.0029847 10.1371/journal.pone.0071715 10.1016/j.patrec.2006.02.022 10.1016/0272-6963(95)00017-M 10.1111/tgis.12100 10.1057/jors.2014.68
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Copyright	Copyright © 2017 Seung-Kil Lim et al. Copyright © 2017 Seung-Kil Lim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright_xml	– notice: Copyright © 2017 Seung-Kil Lim et al. – notice: Copyright © 2017 Seung-Kil Lim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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SubjectTerms	Algorithms Batch processing Cluster analysis Clustering Clusters Computer industry Costs Dynamic programming Hierarchies Integer programming Manufacturing Mathematical problems Tasks
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