Scheduling in a Simple Assembly Robotics Cell to Minimize Earliness and Tardiness

Background: Robotics Assembly Cells (RAC) have been designed to meet the flexibility requirements demanded by today's globalized market. The objective is to manufacture a vast variety of products at a low cost, which requires equipment with a high level of flexibility, such as robots. The need to schedule a great variety of jobs in an RAC is a very relevant issue, as efficiency and productivity depend on the sequence in which jobs are scheduled. Studies around this matter have developed models with analytical and heuristic approaches, as well as simulation methods and genetic algorithms, seeking to improve performance measures based mainly on time, utilization, and costs. Method: The purpose of this article is to formulate an exact mathematical model using mixed-integer linear programming (MILP) to optimize small scheduling problems. The objective is to minimize the measure of performance related to the tardiness and earliness of jobs. This optimization aims to mitigate the effects of delays in product deliveries, queue times, and work-in-process inventory in subsequent processes. Doing so facilitates adherence to agreed-upon delivery deadlines and prevents bottlenecks in the assembly cell. Results: The proposed mathematical model generates optimal solutions to the job scheduling problem in the assembly cell, which serves as a case study. This addresses the need to minimize tardiness to meet delivery deadlines or minimize earliness while avoiding an increase in work-in-process inventories. The model ensures that optimal scheduling decisions are made to optimize both delivery performance and inventory levels. Conclusions: Due to the NP-hard complexity of the scheduling problem under study, the proposed mathematical model demonstrates computational efficiency in solving scheduling problems with fewer than 20 jobs. The model is designed to handle such smaller-scale problems within a reasonable computational time frame, considering the inherent complexity of the scheduling problem.