Various Optimizers for Single-stage Production

The following note develops theorems which enable one to schedule operations on a single-stage production system so a s to minimize certain functions o r optimizers. It is shown that the maximum tardiness of job completion is minimized by ordering the jobs according to the date the job is due to be completed. The sum of t imes until eachjob is completed may be minimized under various conditions. If all jobs can be completed by their due dates, a weighted sum of completion t imes can be minimized, subject to all jobs being completed by their due dates. This is done by scheduling las t the jobs with the largest ratio of processing t ime to weighting factor among those jobs which will be completed on time i f scheduled las t ; the next to l a s t job is scheduled by applying the same rule to the remaining jobs, and so forth, until the complete ordering is obtained.