A General Local Search Pareto Approach with Regular Criteria for Solving the Job-Shop Scheduling Problem Multi-resource Resource Flexibility with Linear Routes

Abstract

The Job-shop Scheduling problem Multi-resource Resource flexibility with linear routes is an extension of the classical Job-shop Scheduling problem “JSMRFLR” where an operation needs several resources (machines) simultaneously to be processed and each machine is selected from a given set. Linear route indicates that an operation is exclusively performed for a job. Publications related to this problem are really scarce and they are dedicated to minimize makespan criterion, which aims to minimize the use of the machines. In the modern scenery of the Operations Management, the exclusive minimization of the makespan does not allow to analyze aspects of the customer service to ensure high levels of competitiveness such as the consideration of due-date and the importance between jobs. In this paper, we propose a general Pareto approach to solve the JSMRFLR with regular criteria, which operates by an efficient local search at using a fast estimation function for the criteria considering the conjunctive graph. During the search, the set of non-dominated solutions 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 total flow time is added and in the third the total tardiness. As a product of our approach, a reference of results is proposed by future research.