Minimising makespan and total tardiness in no-wait open-shop scheduling problems using metaheuristic algorithms: a narrative review

This study begins with a comprehensive narrative review of shop layout and task scheduling, establishing its novelty by being the first to apply an open-shop nonlinear methodology to four metaheuristic algorithms. The research addresses the no-wait open-shop scheduling problem (NWOSP) through a mixed integer nonlinear problem (MINLP) framework, focusing on minimising completion time (Makespan) and total tardiness while considering machine availability, job sequencing, and machine-to-machine transfer durations influenced by job types. An innovative transportation method with unlimited capacity eliminates delays. Comparative analysis reveals that particle swarm optimisation (PSO) and simulated annealing (SA) consistently outperform other algorithms, while Harris Hawks optimiser (HHO) and genetic algorithm (GA) show competitive performance in specific cases. The study integrates bi-objectives using reference point programming with Euclidean distances (RPPED) into a single nonlinear objective, contributing to operations research (OR) with streamlined optimisation processes, enhancing practical applications for complex scheduling problems.