Multidimensional Dynamic Programming Algorithm forN-Level Batching with Hierarchical Clustering Structure

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.