Based on the MapReduce model, a two-phase parallel machine scheduling problem is studied. In the model, each job consists of two operations named Map and Reduce. The Map operation can be split and processed simultaneously, while the Reduce shall be processed on a single machine. Considering the arrival time, and due date of each job, we establish a mixed integer linear programming (MILP) model, aiming at minimizing the weighted makespan and total tardiness. An improved whale optimization algorithm (IWOA) is proposed, which uses differential perturbation and dimension-by-dimension Levy perturbation to obtain a near-optimal solution. The numerical results show that the IWOA outperforms both the particle swarm optimization and the whale optimization algorithms for the considered problem.