Approximation of a batch consolidation problem

In batch production systems, multiple items can be processed in the same batch if they share sufficiently similar production parameters. We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. This article focuses on the case in which only one or two items can be processed in a single batch. The problem is NP-hard and cannot be approximated within 1.0021 of the optimum under the premise, P = NP. However, the problem admits a 2 approximation. The idea is to decompose the demands of items so that a maximum matching in the graph on the vertices of the decomposed demands provides a well-consolidated batch set. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 000(00), 000–00