Solving multi-objective green flexible job-shop scheduling problem considering operation sequence flexibility

The traditional flexible job-shop scheduling problem ([Formula: see text]) typically operates under the assumption that the product operations must follow a strict sequence, meaning that an operation can only begin once its preceding operation is finished. Nevertheless, in real-world production environments, it is frequently observed that some operations can be performed without sequence restrictions, thereby providing greater flexibility in the scheduling process. In this study, two solution approaches are proposed to tackle three performance measures (completion time, total cost and total energy consumption) in the green [Formula: see text]. The first solution is a multi-level lexicographical analysis. Three levels were proposed in this approach to handle the three performance measures, where a novel mathematical model was introduced at each level. The priorities of the three performance measures are known and fixed. The second solution approach is a weighted multi-objective fuzzy mathematical model, in which the weights for the performance measures are varied. The results illustrate the ability of the second-solution approach to dominate the results of the first-solution approach in terms of simultaneously reducing the three performance measures. The two proposed approaches help the decision-maker to deal with the operation sequence constraints in green [Formula: see text] to acquire optimal scheduling considering the priorities of performance measures.