Abstract: In the sequel, we consider a multiobjective open shop scheduling problem with uncertain durations modelled as fuzzy numbers. Given crisp due dates, the objective is to minimise both the makespan and the maximum tardiness. We formulate the multiobjective problem as a fuzzy goal programming model based on lexicographical minimisation of expected values. The resulting problem is solved using a particle swarm optimisation approach searching in the space of possibly active schedules. To asses the performance of this algorithm, we present results of an extensive experimental study on several problem instances, including: a parametric analysis, the experimental evaluation of different priority structures compared to single-objective approaches in terms of objective values as well target achievement, an experimental analysis of the relationship between lexicographical and Pareto solutions and an empirical study based on a-posteriori semantics showing the advantages of taking into account the uncertainty along the scheduling process.

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