The max Problem of Scheduling Multiple Groups of Jobs on Multiple Processors at Different Speeds

We mainly study the max problem of scheduling n groups of jobs on n special-purpose processors and m general-purpose processors at different speeds provided that the setup time of each job is less than times of its processing time. We first propose an improved LS algorithm. Then, by applying this new algorithm, we obtain two bounds for the ratio of the approximate solution LS to the optimal solution T* under two different conditions