Graphical abstractDisplay Omitted HighlightsWe solve a fuzzy JSP with triangular fuzzy numbers to model uncertain durations.We take the stance that solution robustness means an overall acceptable performance.We define a new a priori robustness measure and adapt an a posteriori measure.We propose a hybrid approach to optimise the fuzzy makespan and the robustness.We test the algorithm and analyse the correlation between both robustness measures. In this paper we tackle a variant of the job shop scheduling problem with uncertain task durations modelled as fuzzy numbers. Our goal is to simultaneously minimise the schedule's fuzzy makespan and maximise its robustness. To this end, we consider two measures of solution robustness: a predictive one, prior to the schedule execution, and an empirical one, measured at execution. To optimise both the expected makespan and the predictive robustness of the fuzzy schedule we propose a multiobjective evolutionary algorithm combined with a novel dominance-based tabu search method. The resulting hybrid algorithm is then evaluated on existing benchmark instances, showing its good behaviour and the synergy between its components. The experimental results also serve to analyse the goodness of the predictive robustness measure, in terms of its correlation with simulations of the empirical measure.

In this paper we tackle a variant of the flexible job shop scheduling problem with uncertain task durations modelled as fuzzy numbers, the fuzzy flexible job shop scheduling problem or FfJSP in short. To minimise the schedule's fuzzy makespan, we consider different ranking methods for fuzzy numbers. We then propose a cooperative coevolutionary algorithm with two different populations evolving the two components of a solution: machine assignment and task relative order. Additionally, we incorporate a specific local search method for each population. The resulting hybrid algorithm is then evaluated on existing benchmark instances, comparing favourably with the state-of-the-art methods. The experimental results also serve to analyse the influence in the robustness of the resulting schedules of the chosen ranking method.

The fuzzy job shop scheduling problem with makespan minimisation is a problem with a significant presence in the scientific literature. However, a common meaningful comparison base is missing for such problem. This work intends to fill the gap in this domain by reviewing existing benchmarks as well as proposing new benchmark problems. First, we shall survey the existing test beds for the fuzzy job shop, analysing whether they are sufficiently varied and, most importantly, whether there is room for improvement on these instances - an essential requirement if the instances are to be useful for the scientific community in order to compare and develop new solving strategies. In the light of this analysis, we shall propose a new family of more challenging benchmark problems and provide lower bounds for the expected makespan of each instance as well as reference makespan values obtained with a memetic algorithm from the literature. The resulting benchmark will be made available so as to facilitate experiment reproducibility and encourage research competition