In paper, a scheduling model is considered for multiple Map Reduce jobs. The goal in is to design an automatic job scheduler that minimizes the make span of such a set of Map Reduce jobs. In this work, we find that there is a key assumption in which leads to the violation of the conditions for classical Johnson's algorithm and a suboptimal job scheduling for minimizing total make span. By considering a better strategy and implementation, we can still meet the conditions of classical Johnson's algorithm. Then we can still use Johnson's algorithm for an optimal solution. As for Balanced Pools algorithm proposed in paper, under our proposed new strategy, it is possible to solve it exactly in linear time, but not NP-hard as suggested in the proof is provided. With the new strategy, results obtained in need reevaluating
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