Scheduling products with subassemblies and changeover time

We revisit the problem, previously studied by Coffman et al, of scheduling products with two subassemblies on a common resource, where changeovers consume time, under the objective of flow-time minimization. We derive some previously unidentified structural properties that could be important to researchers working on similar batch scheduling problems. We show that there exists a series of base schedules from which optimal schedules can be easily derived. As these base schedules build on each other, they are easy to construct as well. We also show that the structure of these base schedules is such that batch sizes decrease over time in a well-defined manner. These insights about the general form of the schedules might also be important to practitioners wanting some intuition about the schedule structure that they are implementing.