A Fast and Efficient Fluid Relaxation Algorithm for Large-Scale Re-entrant Flexible Job Shop Scheduling

ADVANCES IN PRODUCTION MANAGEMENT SYSTEMS: ARTIFICIAL INTELLIGENCE FOR SUSTAINABLE AND RESILIENT PRODUCTION SYSTEMS, PT V(2021)

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Abstract
In this paper, we study a large-scale re-entrant flexible job shop scheduling problem (FJSP) with the objective of makespan minimization. In the proposed problem, machine quantities, job types, and processes of jobs are known in advance. At least one machine is available for each process. The large production demand for each type of jobs leads to a large-scale manufacture feature in this problem. To address the problem, we first establish a fluid model for the large-scale re-entrant FJSP. Then, we design a priority update rule to improve the assignment of jobs and machines. We finally propose a fast and efficient fluid relaxation algorithm (FRA) to solve the large-scale re-entrant FJSP through the relaxation fluid optimal solution. Numerical results show that the FRA is asymptotically optimal with the increase of the problem scale. The scale of problems has little effect on the FRA’s solving speed. Therefore, we conclude the FRA is suitable for solving the large-scale re-entrant FJSP.
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Key words
Flexible job shop scheduling,Fluid model,Fluid relaxation,Re-entrant flows,Large scale optimization
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