Scheduling non-identical parallel batch processing machines to minimize total weighted tardiness using particle swarm optimization

- A PSO algorithm is proposed to schedule jobs on non-identical parallel BPM.
- A heuristic is proposed to group the jobs into batches and schedule them on a machine.
- The algorithm consistently outperforms DE on almost all problem instances.
- Competitive performance on smaller problem instances when compared to IBM ILOG CPLEX.
- PSO outperformed IBM ILOG CPLEX by 90.3% on large problem instances.

This research aims at scheduling a set of Batch Processing Machines (BPMs) used to test printed circuit boards in an electronics manufacturing facility. The facility assembles and tests printed circuit boards (or jobs) of different sizes. The BPMs can process a batch of jobs as long as the total size of all the jobs in a batch does not exceed the machine's capacity. The objective is to minimize the total weighted tardiness, thereby minimize the total penalty incurred by the company for late deliveries. The problem under study is known to be NP-hard. Consequently, a Particle Swarm Optimization (PSO) algorithm has been proposed. Likewise, a heuristic is proposed to simultaneously group the jobs into batches and schedule them on a machine. The effectiveness of the PSO algorithm is examined using random instances and the results were compared to a differential evolution algorithm and a commercial solver used to solve a mixed-integer linear program. Experimental results indicate that the PSO algorithm is very competitive on smaller problem instances and reports better quality solutions in a short time on larger problem instances.