A decision theory approach for scheduling jobs with unequal ready times and incompatible families on a single batch processing machine

We present a method to solve a scheduling problem with incompatible job families and unequal ready times of the jobs for a single batch processing machine. Problems of this type arise, for example, in the diffusion process in semiconductor manufacturing. We are interested in minimizing the performance measure total weighted tardiness (TWT). We extend the decision theory approach of Kanet and Zhou to the present situation. By introducing an appropriate time window, we first form a potential batch from the jobs that are ready within the time window. We then evaluate this decision by considering the TWT value of the remaining jobs. In order to calculate the TWT of these jobs we have to estimate the completion times of the jobs. We use a simple average completion time estimate and more sophisticated completion time estimate by a deterministic forward simulation using a variant of the Apparent Tardiness Cost Dispatching rule. We report on computational experiments based on generated test data.