An Efficient Algorithm for Minimizing Regular Criteria in the Job-Shop Scheduling Multi-resource Resource Flexibility with Linear Routes

Abstract

The level of publications of extensions derived from the Job-shop scheduling problem is really low. The Flexible Job-shop scheduling problem is the most studied and the minimization of the makespan is the dominant approach in the literature. The level of the customer service cannot be measured efficiently minimizing makespan, since it does not consider relevant aspects like the due date of jobs and the importance between customers. In this paper, we propose an efficient and fast local search general algorithm to minimize regular criteria in the Job-shop Scheduling Multi-resource Resource Flexibility with Linear Routes Problem “JSMRFLR”. JSMRFLR models situations in which an operation to be processed needs simultaneously several resources or machines, where each resource is selected from a given set of candidate resources. Our approach makes use of the disjunctive graph model to represent schedules or solutions and guide the search for an optimal solution by a fast estimation function. The transformation in the conjunctive graph is evaluated at swapping a critical arc (\( x,y \)) that affects the criterion and the reassignment of \( x \) and \( y \) separately. The efficiency of our approach is evidenced in instances of literature for the case of makespan criterion and a reference of results is proposed by the case of the total flow time, the maximum and total tardiness.