To split or not to split: Selecting the right server with batch arrivals

We consider a dispatching system, where jobs, arriving in batches, are assigned to single-server FCFS queues. Batches can be split to different queues on per job basis. However, the holding costs are batch-specific and incurred until the last member of the batch completes the service. By using the first policy improvement step of the MDP framework, we are able to derive robust dispatching policies, which split arriving batches only when deemed advantageous. The approach is also demonstrated in numerical examples.