Related Machine Scheduling with Machine Speeds Satisfying Linear Constraints
We propose a related machine scheduling problem in which the speeds of machines are variables and must satisfy a system of linear constraints, and the processing times of jobs are given and known. The objective is to decide the speeds of machines and minimize the makespan of the schedule among all the feasible choices. The problem is motivated by some practical application scenarios. This problem is strongly NP-hard in general, and we discuss various cases of it. In particular, we obtain a polynomial time algorithm when there is one linear constraint. If the number of constraints is more than one and the number of machines is a fixed constant, then we give a \((2+\epsilon )\)-approximation algorithm. For the case where the number of machines is an input of the problem instance, we propose several approximation algorithms, and obtain a PTAS when the number of distinct machine speeds is a fixed constant.
KeywordsRelated machine scheduling Linear programming Approximation algorithm
This work has been supported by NSFC No. 11801589, No. 11771245 and No. 11371216. We also thank Tianning Shi for helpful discussions on this work.
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