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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2017/6021708