Particle swarm optimization for integrated scheduling problem with batch additive manufacturing and batch direct-shipping delivery

This study addresses a novel proRblem for the integrated scheduling of additive manufacturing and delivery processes with the objective of minimizing the total weighted completion time of the ordered parts. In the manufacturing process, batch production on non-identical parallel additive manufacturing machines is considered. A single batch of production, which is referred to as a build, consists of parts requiring the same material. Sequence-dependent setup times occur between two adjacent builds. Once the production run is completed, the parts in the builds are regrouped into delivery batches within the same customer. In the delivery process, parts are delivered by homogeneous vehicles to the corresponding customers through direct-shipping method. To optimally solve the small problem, a mixed-integer linear programming model is formulated. For solving largescale problems, three rule-based heuristics that are embedded in particle swarm optimization (PSO) are proposed. A tight lower bound is developed to evaluate the performance of the proposed algorithms. The computational experiment shows that the proposed PSO with delivery waiting time minimization rule is effective to solve small-scale problems, while in large-scale problems, capacity usage maximization rule performs the best and both outperform another existing metaheuristic. Several sensitivity analyses are also performed to provide additional managerial insights.