Scheduling a Production Shop. Midwest Parts Supply (MPS) is a fabricator of small steel parts that are sold as components to manufacturers of electronic appliances and medical equipment. In the MPS fabrication department, steel sheets are subjected to a series of three main operations—cutting, trimming, and polishing—which must be completed in this order. Each machine processes the jobs in the same order, so it is sufficient to specify a single job sequence in order to describe a schedule. No machine can process more than one job at a time. This morning, ten jobs have been released to the shop by the ERP system, and the production manager is interested in minimizing the time it takes to complete the entire schedule, usually referred to as the schedule makespan. The following table gives the number of hours required for each operation.
What sequence achieves the minimum makespan and what is the minimum length of a schedule?