On-line batching problems

We introduce on-line batching problems as a new class of on-line combinatorial problems. In an on-line batching problem the task is to chop batches from a growing queue of objects, such that the cost is minimized, where the cost consists of setup cost for each batch, processing cost for each batch, and holding cost for each object that is not processed immediately. For on-line batching problems we propose a solution approach based on decomposing the chopping and the processing of the batches. The chopping problem is solved with statistical learning, whereas the processing of a batch is independent of other batches. In this article we only consider the case where processing a batch is equivalent to solving a combinatorial optimization problem. In order to generate learning examples we need partial solutions to infinite off-line batching problems. We show that these solutions can be obtained with a forward algorithm that solves a sequence of finite off-line batching problems using a dynamic programming formulation. On the basis of an empirical performance analysis, we conclude that our approach outperforms all classical approaches in terms of cost and applicability.