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.

In the sequel, we consider the fuzzy job-shop problem, which is a variation of the job-shop problem where duration of tasks may be uncertain and where due-date constraints are allowed to be flexible. Uncertain durations are modeled using triangular fuzzy numbers, and due-date constraints are fuzzy sets with decreasing membership functions expressing a flexible threshold ldquoless than.rdquo Also, the objective function is built using fuzzy decision-making theory. We propose the use of a genetic algorithm (GA) to find solutions to this problem. Our aim is to provide a semantics for this type of problems and use this semantics in a methodology to analyze, evaluate, and, therefore, compare solutions. Finally, we present the results obtained using the GA and evaluate them using the proposed methodology.