Mixed integer lineal programming model to schedule flexible job-shop systems in make to order environments

Abstract

Introduction: Job Shop (JS) production systems are characterized by different route process of the Jobs to be processed. A generalization of this type of systems is the Flexible Job Shop (FJS), in which there is more than one machine per station to perform some of the operations. Objective: The objective of this project was to propose a mixed integer linear programming model to program FJS systems in order to minimize the number of tardy jobs. Methodology: The model was developed using an approach based on sequence-position variables. This approach uses binary variables to decide whether a given operation is assigned to a position in the processing sequence of the assigned machine. To validate the performance of the model data from a small company with an FJS type production system, that develops its operations in an environment to order (MTO), was used. For this reason, the most important performance indicators for the company are those associated with the service level. Results: The results show a reasonable performance in terms of the objective pursued. The optimal production schedule was found in less than 3600 seconds in instances of less than 14 production orders. In larger instances, it obtained feasible solutions within the defined time limit. Conclusions: The model allows defining production schedules in systems in which the fulfillment of due dates is of vital importance. The results have allowed the company to improve its performance and reduce the costs associated with non-compliance of customer’s due dates. Future research can be developed to find more efficient solution methods in terms of computational times to obtain solutions of larger instances.

Keywords

• Production schedule
• Flexible job shop
• Mixed integer lineal programming
• tardy jobs