A particle swarm optimization algorithm for minimizing makespan of nonidentical parallel batch processing machines

This research is motivated by our interactions with an electronics manufacturer who assembles and tests printed circuit boards (PCBs) used in consumer products. Environmental stress screening (ESS) chambers are commonly used to test PCBs to detect early failures before they are used in the field. The chambers are capable of testing multiple PCBs simultaneously (i.e., batch processing machines). The minimum testing time of each PCB and their size are known. The objective is to group these PCBs into batches and schedule the batches formed on ESS chambers such that the makespan is minimized. The ESS chambers can process a batch of jobs as long as its capacity is not violated. Each ESS chamber is unique with respect to its capacity. The problem is NP-hard. Consequently, a particle swarm optimization (PSO) algorithm is proposed. The effectiveness of the PSO algorithm is evaluated by comparing its results to a random-key genetic algorithm and a commercial solver used to solve a mixed-integer linear program. A thorough experimental study conducted indicates that the PSO algorithm reports better quality solution in a short time on larger problem instances.