A Fast Pareto Approach to Minimize Regular Criteria in the Job-shop Scheduling Problem with Maintenance Activities, Sequence Dependent and Set-up Times

Abstract

In the Job-shop scheduling problem minimizing the makespan has been the dominant approach in the literature. The level of the customer service cannot be measured efficiently for this criterion, since it does not consider relevant aspects like the due date of jobs to determine the tardiness. In this paper, we propose an innovate general approach for minimizing regular criteria in the Job-shop Scheduling which adds the conditions of maintenance activities and sequence dependent set-up times considering the Pareto optimization. Our approach makes use of the disjunctive graph model to represent schedules and support the search for an optimal solution using a classical estimation function at reversing a critical arc. The search is performed by two phases: improvement and diversification. In the improvement phase, initially, a random criterion is selected to create improving moves iteratively. When it is not possible to create a move using the selected criterion, it is penalized and a new criterion is selected. The diversification phase considers feasibility conditions to escape from a local optimal. In each move the set of solutions of the front is updated. The efficiency of our approach is illustrated on instances of literature at performing three sets of criteria. The first set considers makespan and maximum tardiness. In the second \( \sum C_{i} \) is considered and in the third the total tardiness. As a contribution of our approach, a benchmark of results is proposed by future research.