Particle swarm optimization and opposite-based particle swarm optimization for two-agent multi-facility customer order scheduling with ready times

Recently, multi-agent scheduling and customer order scheduling have separately received much attention in scheduling research. However, the two-agent concept has not been introduced into order scheduling in the multi-facility setting. To fill this research gap, we consider in this paper two-agent multi-facility order scheduling with ready times. The objective is to minimize the total completion time of the orders of one agent, with the restriction that the total completion time of the orders of the other agent cannot exceed a given limit. We first develop a branch-and-bound algorithm incorporating several dominance rules and a lower bound to solve this intractable problem. We then propose a particle swarm optimization algorithm (PSO), an opposite-based particle swarm optimization (OPSO) algorithm, and a particle swarm optimization algorithm with a linearly decreasing inertia weight (WPSO) to obtain near-optimal solutions. Applying two levels of number of particles and number of neighbourhood improvements for the PSO and OPSO algorithms, we execute them at a fixed inertia weight, and execute WPSO at a varying decreasing inertia weight. We perform a one-way analysis of variance of the performance of the five PSO algorithms in tackling the problem with small and big orders. We demonstrate through extensive computational studies that the proposed PSO algorithms are very efficient in quickly finding solutions that are very close to the optimal solutions.