We study the problem of minimizing total load on a proportionate openshop. The problem is proved to be NP-hard. A simple LPT (Longest Processing Time first)-based heuristic is proposed, and a bound on the worst-case relative error is introduced: (where m is the number of machines). The proposed bound is smaller than the classical bound on the relative error of LPT when minimizing makespan on parallel identical machines. The algorithm is tested numerically and is shown to produce very close-to-optimal schedules.
Bibliographical noteFunding Information:
This paper was supported by the Israel Science Foundation (Grant No. 2505/19 ) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 452470135 .
- Proportionate openshop
- Total load
- Worst case bound