We study the scheduling problem of minimizing total load on a proportionate flowshop. We consider position-dependent job processing times in the most general way. We show that this problem is solved in O(n4) time, where n is the number of jobs. We then extend the setting to allow job-rejection, where the scheduler may decide to process only a subset of the jobs, and the rejected jobs are penalized. This extension is shown to be solved in O(n5) time.
Bibliographical noteFunding Information:
This research was supported by the Israel Science Foundation (grant No. 1286/14 ). The second author was supported in part by the Recanati Fund of The School of Business Administration , and by Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem , Israel.
- Position-dependent processing times
- Proportionate flowshop
- Total load