Simulated annealing approach to minimise total weighted tardiness of non-identical parallel batch processing machines

A variety of industries use batch processing machines (BPMs) that can process multiple jobs simultaneously per machine. This research considers the scheduling of multiple jobs onto non-identical parallel BPMs while minimising the total weighted tardiness. The problem under study is NP-hard and solving it to optimality using a commercial solver requires long run times when the size of the problem increases. A simulated annealing (SA) approach is proposed to find good solutions for large problem instances within short run times. The results obtained are compared to two metaheuristics, particle swarm optimisation (PSO) and differential evolution (DE), proposed in the literature and a commercial solver (CPLEX). An experimental study is conducted to evaluate the different solution approaches on a set of problem instances. Based on results, the authors conclude that SA is highly effective in solving large problem instances within reasonable run times when compared to CPLEX, PSO and DE.