Operations and Shipment Scheduling of a Batch on a Felxible Machine

We consider processing and shipment scheduling of a batch of size M jobs on a flexible (multifunctional) machine. All jobs in the batch require the same sequence of N operations on the machine. Costs are incurred in the forms of holding costs of jobs waiting for the next operation, setup costs whenever the machine is set up for a new operation, and shipment cost whenever the whole batch or a part of it is shipped to the customer. Using a dynamic programming formulation of the problem, we first show how the problem size increases in M and N . Then, by focusing on the properties of some classes of batch-splitting policies, a heuristic algorithm is presented that generates suboptimal policies. Some numerical results are provided which show that the algorithm performs very well.