Focused Scheduling in Proportionate Flowshops

The proportionate flowshop is a special class of flowshops in which the operation times of jobs are proportionate, e.g., because of differences in the speeds of machines. In this paper, we make use of a special property of proportionate flowshops, namely that the bottleneck in the shop is almost always the one where job operations are proportionately longer than for any other operations (the slowest machine) to demonstrate a scheduling procedure that makes scheduling decisions by focusing on the information and consequences at the bottleneck resource. This is called the Focused Approach. The scheduling objective is to minimize the total tardiness cost of jobs, where each job may have a different tardiness cost. The decision rule used in this approach is the Idle Time Rule whose development is described in this paper. The approach was tested using approximately proportionate flowshops of different sizes. The results obtained for small 3-machine problems were compared against the optimal permutation schedules obtained using Branch-and-Bound and was found to be near-optimal. For larger problems using 4- and 8-machine flowshops, the results were compared to five other scheduling methods. The focused approach performed far better than those other scheduling methods not only in minimizing tardiness cost, but also minimizing the percentage of tardy jobs and the percentage of processing time to work-in-process time. Finally, the two-product shop where the bottleneck was dynamic was studied and, using a simple strategy to track bottlenecks, the focused approach was again found to perform well compared with other heuristic methods.