| Summary: | 碩士 === 國立臺灣大學 === 工業工程學研究所 === 104 === The hybrid flow shop scheduling (HFS) problem has drawn much attention in the past decades. Common examples of the HFS problem can be found in many industries, which usually accompanies with a lot of queue time constraints, the violations of which can lead to scraps. In practice, the mixed-integer linear programming (MILP) based real-time production control is applied, and the admission decisions are made based on the system status. However, the NP-hard nature of the production scheduling problem implies that the complexity of the problem substantially increases as the number of lots in the system increases, and the computational time would be too long to act as a good real-time approach. In this research, the Mixed Integer Programming with LAgrangian Relaxation (MIPLAR) method is proposed. In this method, a time-indexed MILP model with a separable structure for the production scheduling problem with queue time constraints is formulated. Lagrangian relaxation techniques are used to decompose the problem into job-level subproblems, which are solved by dynamic programming with significant improvement in computation time. The subgradient method is used to solve the Lagrangian dual problem. Computational results show that the optimal solution or a near-optimal solution can be obtained by using the Lagrangian relaxation techniques within a reasonable time frame. In addition, a simulation study shows that the MIPLAR method achieves the improvement in scrap count up to 83.72% and increases throughput up to 4.52% in a 4.6-month simulated case study.
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