Sequential batching with minimum quantity commitment in N-level non-exclusive agglomerative hierarchical clustering structures

Abstract

This study considers a sequential batching problem with a minimum quantity commitment (MQC) constraint in N-level non-exclusive agglomerative hierarchical clustering structures (AHCSs). In this problem, batches are created for item types included in clusters according to the sequence of the levels in a given AHCS such that the MQC constraint as well as the maximum and minimum batch size requirements are satisfied, simultaneously. The MQC constraint ensures that more items than a committed minimum quantity must be batched at a level before items not batched at the level are sent to the next level. We apply the MQC constraint to control effectively the degree of heterogeneity (DoH) in the batching results. We developed a sequential batching algorithm for minimizing the total processing cost of items using properties identified to find better solutions of large-sized practical problems. Results of computational experiments showed that the developed algorithm found very good solutions quickly and the heuristic algorithm could be used in various practical sequential batching problems with the MQC constraint such as input lot formations in semiconductor wafer fabrication facilities, determination of truckloads in delivery service industry, etc. Also, we found some meaningful insights that dense cluster, small batch size, and tight MQC constraint are effective in reducing the total processing cost. Additionally, small batch size with loose MQC constraint seem to be helpful to reduce the DoH in the batching results. Finally, we suggested that the density of cluster, batch size, and MQC tightness should be determined simultaneously because of interactions among these factors. (C) 2020 by the authors; licensee Growing Science, Canada