Scheduling jobs on two uniform parallel machines to minimize the makespan

The problem of scheduling n independent jobs on m uniform parallel machines such that the total completion time is minimized is a NP-Hard problem. We propose several heuristic-based online algorithms for machines with different speeds called Q2||Cmax. To show the efficiency of the proposed online algorithms, we compute the optimal solution for Q2||Cmax using pseudo-polynomial algorithms based on dynamic programming method. The pseudo-polynomial algorithm has time complexity O (n T2) and can be run on reasonable time for small number of jobs and small processing times. This optimal offline algorithm is used to benchmark the efficiency of the proposed online algorithms