A Particle Swarm Optimization to Minimize Makespan for a Four-Stage Multiprocessor Open Shop with Dynamic Job Release Time

This paper considers the scheduling problem observed in chip sorting operation of LED manufacturing, where each lot (job) with release time have four operations to be processed on a set of processing stages without pre-determined necessary route. Each stage has one and more identical sorting machines. The sorting machines scheduling problem can be treated as a four-stage multiprocessor open shop problem with dynamic job release, and the objective is minimizing the makespan in the paper. This problem is formulated into a mixed integer programming (MIP) model and empirically shows its computational intractability. Due to the computational intractability, a particle swarm optimization (PSO) algorithm is proposed. A series of computational experiments are conducted to evaluate the performance of the proposed PSO in comparison with exact solution on various small-size problem instances. The results show that the PSO algorithm could finds most optimal or better solutions in one second.