Single station MILP scheduling in discrete and continuous time

Abstract

This article focuses on production planning in the metallurgical sector. This study undertakes a detailed comparative study of mixed-integer linear programming models using different time representations: continuous and discrete. The analysis shows that the continuous model consistently outperforms its discrete counterpart in all evaluated scenarios. The key difference between the continuous and discrete models is the continuous model’s ability to deliver better makespan results, achieving an improvement of up to 15% compared to the discrete model. This advantage holds even in complex environments with a high number of tasks and machines, where the continuous model consistently outperforms the discrete model by over 6% in the scenario with the highest number of tasks and machines. This preference extends beyond makespan considerations. The continuous model also maintains an edge in terms of runtime efficiency, achieving better times with a 99% improvement over the discrete model in all scenarios except one. These findings provide concrete evidence for the use of continuous models, which promise more effective production planning in analogous manufacturing domains.