Batch-scheduling problems to minimize actual flow times of parts through the shop under JIT environment

The authors propose a performance measure called actual flow time for scheduling problems under JIT environment requiring that input material should arrive in the shop at the right times in the right quantities and that the completed parts should be delivered at their due dates. They also address batch-scheduling problems, i.e., to determine batch sizes and to schedule the resulting batches so as to minimize the actual flow times of parts through the shop. Optimal algorithms solving the problems on a single machine and heterogeneous machines with a common due date are developed, and an algorithm taking advantage of the optimal algorithms is proposed for solving the problems with multi-due-date. Proof of the optimality is not given for the later algorithm but numerical experience shows that it is very efficient. Numerical experience that shows the characteristics of the problems is also presented.