Question: A set of ten jobs must be scheduled at an integrated machining center that performs a number of metal-cutting operations on components for complex assemblies.

A set of ten jobs must be scheduled at an integrated machining center that performs a number of metal-cutting operations on components for complex assemblies. These jobs and their processing times (expressed in hours) are described in the following table. In addition, each job has a corresponding due date that has been calculated by the production-control system. As a result of the sequence chosen, each job will either be on time or else it will be late. If it is late, the amount of time by which it misses its due date is called its tardiness. The objective is to minimize the total tardiness in the schedule.

What is the minimum total tardiness and a sequence that achieves it?

2 3 4 Job 10 1 5 6 7 Processing time 9 8 12 3 2 5 17 5 25 15 Due date 44 50 20 24 20

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