# Beyond Kanban: POLCA-Constrained Scheduling for Job Shops
## 1 Introduction  
The concept of the Intelligent Factory describes a highly digitalized and interconnected business model where industrial processes generate a Digital Twin, serving as a real-time simulation and optimization environment. This transformation necessitates a technological shift, including the adoption of Intelligent Decision Support Systems (IDSSs), which process large volumes of data to enhance decision-making through mathematical algorithms. Additionally, Advanced Production Scheduling (APS) and Finite Capacity Scheduling (FCS) software are becoming increasingly integrated with Enterprise Resource Planning (ERP) systems to provide real-time insights into workcenter utilization and job status, enabling more responsive production planning.  
Despite these advancements, the implementation of an Intelligent Factory often prioritizes heavy capital investments in advanced machinery and cyber-physical systems, alongside significant efforts to integrate them with existing operations. Consequently, managers strive for maximum utilization to achieve the fastest return on investment. However, Make-to-Order (MTO) production systems face increasing market pressure for agility and rapid response times, conflicting with the operational focus on high utilization.  
From a queuing theory perspective, [PERSON]'s equation demonstrates that excessive utilization leads to disproportionately longer lead times and reduced responsiveness to demand fluctuations. This effect is particularly critical in high-mix, low-volume (HMLV) job shops, where complex job routings and high workcenter utilization levels can make FCS-based scheduling less effective, as it prioritizes efficiency at the cost of flexibility for urgent orders.  
To address these challenges, Production Control Systems (PCSs) in lean manufacturing environments employ feedback-driven mechanisms to regulate shop floor flow, reducing inventory levels and lead times--though often at the expense of top utilization rates. This study investigates the integration of finite capacity scheduling with POLCA (Paired-cell Overlapping Loops of Cards with Authorization) to bridge the gap between scheduling efficiency and responsiveness, thereby achieving a more balanced and adaptive production system. By integrating POLCA-based workload control into a mathematical framework, the objective is to demonstrate how incorporating production control constraints into formal models enhances decision-making and secures significant operational benefits, even in environments where established control methods are already in place.  
The article is structured into two main experimental phases. The first phase evaluates POLCA's impact within a controlled and simplified job shop environment, where the system's performance is analyzed in comparison to a constraint programming model through simulation. The second phase extends this comparison to a real-world industrial case within the aerospace manufacturing sector, assessing how the integration of POLCA within a constraint-based optimization model affects multiple objective functions. Through this dual experimental approach, the study provides a comprehensive assessment of POLCA's strengths and limitations, particularly in its capacity to handle multi-objective scheduling challenges.  
By bridging the gap between theoretical scheduling models and practical production control systems, this research underscores the continued relevance of mathematical modeling in modern job shop environments, demonstrating its ability to enhance the effectiveness of existing workload control methods and unlock new performance gains in high-mix, low-volume production settings.