Drum-Buffer-Rope and rolling horizon MILP for shifting bottleneck synchronization in sugar beet logistics

Abstract

Objectives: This study develops and validates a cyber-physical mathematical framework for synchronizing stochastic agricultural harvesting with deterministic industrial processing in regional sugar beet logistics. The framework addresses real-time coordination conflicts between distributed field supply nodes, limited transport capacity, dynamic field accessibility, and continuous factory demand. Prior work: Traditional static logistics models treat agro-industrial cargo as inert mass and primarily optimize spatial distance. Such approaches are poorly suited to environments characterized by high-frequency schedule nervousness, weather-driven field accessibility changes, shifting bottlenecks, and non-linear raw material degradation during temporary field storage. Approach: The proposed Digital Twin architecture combines dynamic Drum-Buffer-Rope (DBR) pull logic for shifting bottlenecks with rolling Model Predictive Control (MPC) and a multi-phase Mixed-Integer Linear Programming (MILP) heuristic. Spatial transport work is handled during seasonal stratification, feasible route assignment, and topological filtering; within the active rolling MILP core it is treated as a quasi-invariant structural term. This allows the optimization layer to focus on time-sensitive trade-offs between sucrose preservation, factory starvation avoidance, and logistical feasibility. Results: Empirical validation using an 11- year industrial dataset comprising more than 180,000 unique transactional cycles shows that the multi-phase heuristic achieves sub-second solver response times in the tested industrial scenarios, with the active MILP core converging within 0.45 seconds. Operational deployment is associated with compression of factory reception-yard turnaround time from 24.6 to 13.8 minutes and a 41% reduction in active fleet dispersion. Implications: The adaptive sigmoid switching mechanism dynamically shifts objective priorities between quality preservation and plant starvation avoidance during environmental shocks. For practitioners, the framework provides a real-time execution tool for synchronizing harvesting, loading, transportation, and factory reception under stochastic disturbances. For researchers, it demonstrates a scalable approach to time- based buffer management in temporal agro-industrial networks. Value: The scientific novelty lies in integrating adaptive DBR pull constraints, rolling MILP optimization, graph-based topological filtering, and physics- informed quality inputs into a unified cyber-physical synchronization framework. The proposed architecture transforms agricultural logistics from a rigid cost center into a resilience-oriented decision system without compromising grower equity or systemic transparency.