Under support of industry 4.0, researchers have shown an increased interest in MapReduce scheduling problems to process big data. However, very few studies investigate MapReduce scheduling problems under parallel batch machine environment, which is also common in practice. Motivated by this, we study a parallel batch machine scheduling problem in which all the jobs are belonging to MapReduce type. The objective of the considered problem is of minimizing the total weighted tardiness. For solving this problem, we first establish a mixed integer linear programming model, and then a rule-based genetic algorithm is developed to solve it. Numerical experiments are also conducted to demonstrate the effectiveness of the proposed method.

In this work, we incorporate human factors and real-life operations into newly proposed multitasking scheduling problems with periodic shift activities. It is motivated by personnel resource scheduling with periodic work shifts under the requirement of providing continuous service to customers. We model the problem as two identical parallel machine scheduling with complementary non-available time periods, and consider two models with the objectives of the makespan, i.e. the maximum completion time and respectively the total completion time. We then prove that the Greedy algorithm and SPT rule are of asymptotic and parametric approximation ratios for the two models, respectively.

Workload balance is significant in the manufacturing industry. However, on the one hand, some existing specific criteria cannot achieve the minimization workload imbalance of parallel machines. On the other hand, there are few algorithms in existing studies that can effectively solve the parallel machine scheduling problem with the objective of minimizing workload imbalance. Inspired by this, we investigate an identical parallel machine scheduling problem with the objective of the minimum workload smoothness index. We first establish a mathematical model for the considered problem and then linearize its objective function. We prove the NP-hardness of the problem by reducing the PARTITION problem to it, and we provide both the upper bound and lower bound of the studied problem. An efficient genetic algorithm and an improved list scheduling algorithm are also proposed to efficiently address the considered problem. The numerical results demonstrate the effectiveness of the proposed methods.