Impact of learning effect modelling in flowshop scheduling with makespan minimisation based on the Nawaz-Enscore-Ham algorithm

Inspired by real-life applications, mainly in hand-intensive manufacturing, the incorporation of learning effects into scheduling problems has garnered attention in recent years. This paper deals with the flowshop scheduling problem with a learning effect, when minimising the makespan. Four approaches to model the learning effect, well-known in the literature, are considered. Mathematical models are providing for each case. A solver allows us to find the optimal solution in small problem instances, while a Simulated Annealing algorithm is proposed to deal with large problem instances. In the latter, the initial solution is obtained using the well-known Nawaz-Enscore-Ham algorithm, and two local search operators are evaluated. Computational experiments are carried out using benchmark datasets from the literature. The Simulated Annealing algorithm shows a better result for learning approaches with fast learning effects as compared to slow learning effects. Finally, for industrial decision makers, some insights about how the learning effect model might affect the makespan minimisation flowshop scheduling problem are presented.