초록
We consider the order consolidation problem that arises in production systems where customer orders are processed in batches. The problem involves maximizing the number of batches while satisfying the following conditions: (i) the total quantity processed in each batch must be above a prescribed level; (ii) the quantity in an order can be split and processed in more than one batches; (iii) each batch can include up to two different orders but can do so only when the two orders are compatible pair. This problem is known to be NP-hard and max-SNP hard. In this study, we develop an approximation algorithm with factor 1/3.