Flexible job-shop scheduling method based on interval grey processing time

With the complexity of industrial products, the processing time of products is affected by many factors, and it is difficult to give a concrete time estimate. Therefore, it is significant to study the flexible job shop scheduling problem (FJSP) with uncertain processing time. This paper defines the uncertain processing time as the interval grey processing time (IGPT). Also, an FJSP model with IGPT (G-FJSP) is formulated to minimize the interval grey maximum completion time, and the mathematical operation rules of IGPT are improved. Based on this, a step-size adaptive discrete particle swarm algorithm with load balancing (LS-DPSO) is put forward to solve the G-FJSP model. The experimental analysis on six classical test cases indicates that LS-DPSO outperforms four algorithms proposed in recent literature in terms of speed and solution quality. Taking IMK05 as an example, the minimum and the average values of LS-DPSO IGPT are 1.8% and 2.2% smaller than the optimal results of other four algorithms. Also, the resulting grey Gantt chart has better processing time flexibility to guide practical production.