A bi-objective identical parallel machine scheduling problem with controllable processing times: a just-in-time approach

In this research, a bi-objective scheduling problem with controllable processing times on identical parallel machines is investigated. The direction of this paper is mainly motivated by the adoption of the just-in-time (JIT) philosophy on identical parallel machines in terms of bi-objective approach, where the job processing times are controllable. The aim of this study is to simultaneously minimize (1) total cost of tardiness, earliness as well as compression and expansion costs of job processing times and (2) maximum completion time or makespan. Also, the best possible set amount of compression/expansion of processing times on each machine is acquired via the proposed “bi-objective parallel net benefit compression-net benefit expansion” (BPNBC-NBE) heuristic. Besides that, a sequence of jobs on each machine, with capability of processing all jobs, is determined. In this area, no inserted idle time is allowed after starting machine processing. For solving such bi-objective problem, two multi-objective meta-heuristic algorithms, i.e., non-dominated sorting genetic algorithm II (NSGAII) and non-dominated ranking genetic algorithm (NRGA) are applied. Also, three measurement factors are then employed to evaluate the algorithms’ performance. Experimental results reveal that NRGA has better convergence near the true Pareto-optimal front as compared to NSGAII, while NSGAII finds a better spread in the entire Pareto-optimal region.