Application of Predictive Control Model on Flow Line Production System in Sugar Factory at Milling Station Using Max-Plus Algebra

Abstract

Efficient timing and synchronization are crucial elements in flow-line production systems, as delays in a single processing stage can propagate to subsequent operations. This study applies a Model Predictive Control (MPC) strategy to a sugar factory milling station modeled as a Max-Plus Linear (MPL) system. The main objective is to develop a mathematical representation of the milling production flow and determine feasible input-event time sequences under operational constraints. The 12-station milling production system is represented using constrained Max-Plus algebraic state equations. The MPC formulation is then constructed by incorporating input-spacing constraints, output deadlines, prediction horizons, and control horizons to minimize the makespan while suppressing Work-in-Process (WIP). The model was tested using realistic configurations for processing and transition time parameters. Computational results demonstrate that the MPC-MPL controller successfully generates input-time sequences that satisfy output deadline limits and operational constraints. Compared to the FIFO Baseline method, MPC reduces the makespan by up to ∼ 7.6% and decreases WIP accumulation in buffers/tanks by over 70%. These findings prove the applicability and robustness of the MPC-MPL framework as a structured solution for optimizing production scheduling in sugar milling operations.