This paper deals with a scheduling problem at a bottleneck common facility for n subsequent production lines, each of which is dedicated to produce a family of products. The common facility represents the bottleneck, since its capacity is less than the sum of the capacities of the n production lines. The components supplied by the bottleneck for the n lines are not exactly the same, and hence a non-productive change-over (or setup) time for the bottleneck is incurred when jobs switch between families. As such, it is desirable to make as few change-overs as possible to save the expensive setup time. However, if the bottleneck continues processing jobs for a given line, not only will the inventory at the line build up but also other lines will become idle. Thus, a scheduling scheme must be developed for finding a schedule that keeps all the production lines busy with few change-overs for the bottleneck. This objective can be appropriately measured by minimization of the total production time. For the case of n=2, a solution procedure is developed in this paper to find the optimal schedule.
