Scheduling a batch processing facility

A method for batching jobs within a class in advance of sequencing is presented. It is shown that under certain simplifying assumptions, optimal batch composition can be obtained independent of the sequencing problem. This composition is determined by assigning parts to batches according to an earliest due date (EDD) rule. An efficient methodology for sequencing the batches based on the Lagrangian relaxation technique is presented. The solution to the Lagrangian relaxation dual problem is a lower bound on the cost of the optimal schedule. If the assumptions are relaxed, the EDD rule becomes a heuristic for solving the batch composition problem, and the same batch sequencing algorithm can be used to obtain a schedule. In that case, the dual cost is a lower bound on the cost of all possible sequences with the same batch composition. Preliminary results show that good schedules can be efficiently obtained