Abstract
This study focuses on theN-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 levelNsequentially 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 theN-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.
Highlights
According to Wikipedia, clustering problem is the task of grouping a set of item types in such a way that item types in the same cluster are more similar to each other than to those in other clusters
We describe the N-level batching problem (NLBP) with agglomerative hierarchical clustering structure considered in this study
In the Nlevel batching problem, given items with different types can be grouped into several batches at each level and this batching process is performed from level 1 to level N sequentially in the given hierarchical clustering structure until all of given items are grouped
Summary
According to Wikipedia, clustering problem 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. Nunez-Iglesias et al [9] proposed an active machine learning approach for performing hierarchical agglomerative clustering from superpixels to improve segmentation of 2D and 3D images. Lim et al [15] studied the three-level presorting loading problem which occurs in the commercial bulk mail service They considered the problem as a three-level hierarchical clustering problem and proposed an optimal solution algorithm. We consider an N-level batching with agglomerative hierarchical clustering structure in which the highest possible level of the hierarchy is N. 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 a given hierarchical clustering structure such that batches in each level of the hierarchy should satisfy the maximum and minimum batch size requirements of the level. The objective of the problem is to minimize the total cost for processing all items
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