Parallel Machine Scheduling Problems

The objective of this paper is to minimize both the makespan and the total completion time. Since parallel-machine scheduling which contains the function constraint problem has been a new issue, this paper explored two parallel-machine scheduling problems with function constraint, which refers to the situation that the two machines have a same function but one of the machines has another. We pointed out that the function constraint occurs not only in the manufacturing system but also in the service system. For the makespan problem, we demonstrated that it is NP-hard in the ordinary sense. In addition, we presented a polynomial time heuristic for this problem and have proved its worst-case ratio is not greater than 5/4. Furthermore, we simulated the performance of the algorithm through computational testing. The overall mean percent error of the heuristic is 0.0565%. The results revealed that the proposed algorithm is quite efficient. For the total completion time problem, we have proved that it can be solved in On4 time.

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Comparative Analysis of Mixed Integer Programming Formulations for Single-Machine and Parallel-Machine Scheduling Problems

IEEE Access ◽

10.1109/access.2019.2947685 ◽

2019 ◽

Vol 7 ◽

pp. 152998-153011 ◽

Cited By ~ 2

Author(s):

Kuo-Ching Ying ◽

Chen-Yang Cheng ◽

Shih-Wei Lin ◽

Chia-Yang Hung

Keyword(s):

Comparative Analysis ◽

Integer Programming ◽

Mixed Integer Programming ◽

Single Machine ◽

Machine Scheduling ◽

Parallel Machine Scheduling ◽

Parallel Machine ◽

Mixed Integer ◽

Scheduling Problems ◽

Machine Scheduling Problems

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Modified Harris Hawks Optimizer for Solving Machine Scheduling Problems

Symmetry ◽

10.3390/sym12091460 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1460

Author(s):

Hamza Jouhari ◽

Deming Lei ◽

Mohammed A. A. Al-qaness ◽

Mohamed Abd Elaziz ◽

Robertas Damaševičius ◽

...

Keyword(s):

Computation Time ◽

Machine Scheduling ◽

Setup Time ◽

Parallel Machine Scheduling ◽

Parallel Machine ◽

Scheduling Problems ◽

Large Problem ◽

Unrelated Parallel Machine Scheduling ◽

Problem Instances ◽

Machine Scheduling Problems

Scheduling can be described as a decision-making process. It is applied in various applications, such as manufacturing, airports, and information processing systems. More so, the presence of symmetry is common in certain types of scheduling problems. There are three types of parallel machine scheduling problems (PMSP): uniform, identical, and unrelated parallel machine scheduling problems (UPMSPs). Recently, UPMSPs with setup time had attracted more attention due to its applications in different industries and services. In this study, we present an efficient method to address the UPMSPs while using a modified harris hawks optimizer (HHO). The new method, called MHHO, uses the salp swarm algorithm (SSA) as a local search for HHO in order to enhance its performance and to decrease its computation time. To test the performance of MHHO, several experiments are implemented using small and large problem instances. Moreover, the proposed method is compared to several state-of-art approaches used for UPMSPs. The MHHO shows better performance in both small and large problem cases.

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