Abstract
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.
Highlights
Parallel machine in a production environment can be divided into three categories according to the nature of the machine: identical, uniform, and unrelated parallel machines
The parallel-machine production scheduling problem has been extensively studied under various classical scheduling performance measurement criteria. e makespan and total completion time are the two best important performance measurement criteria. e makespan is called the maximum completion time or the completion time of the last workpiece on the last machine. e makespan is usually used to measure the utilization of machinery and equipment
If one shortens the Discrete Dynamics in Nature and Society makespan and the machine utilization and production efficiency is improved, more flexible time can be reserved to prevent the sudden occurrence of the production line. e completion time refers to the time spent in the system from the time of the workpiece that arrives at the site to its completion, and the total completion time is the sum of the completion time of all the workpieces. erefore, the total completion time is expected to be minimized. at is, the inprocess inventory of the factory is expected to be minimized to reduce the cost of inventory
Summary
Parallel machine in a production environment can be divided into three categories according to the nature of the machine: identical, uniform, and unrelated parallel machines. Chung et al [1] explored a two identical parallel-machine scheduling problem with molds constraints. Because the problem is NP-hard, they present a mathematical programming model to solve it and, compare the performance of the longest processing time first (LPT) algorithm with the list scheduling (LS) via computational experiments. Xu et al [3] examined a two parallel machine scheduling problem to minimize the makespan.
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