Batching to Minimize Flow Times on Parallel Heterogeneous Machines

Traditional scheduling models have emphasized sequencing of tasks at machines. At multiple-machine work-centers mean flow times are affected by the allocation of work to machines, as well as the batch-sizes used for processing. An efficient algorithm for computing the optimal solution for the single product case is given. An approximate closed-form solution is available that could be used as a heuristic loading-rule in a dynamic environment. For the special case of equal setup times at machines, the optimal solution is given in closed form. Further, it is demonstrated that the optimal flow time for the work center depends only on the total processing rate at that center.