# Beyond Kanban: POLCA-Constrained Scheduling for Job Shops
## 3 POLCA and the Enhanced Contraint Programming: A Basic Case
### Computational Experiments
#### 3.4.3 Computational Results  
In this section, we present and analyze the computational outcomes obtained from the integrated scheduling and simulation experiments. The results discussed herein are derived from an extensive experimental campaign that examines the performance of our proposed framework under a variety of system configurations. Our analysis focuses on key performance metrics related to lead times, tardiness, and throughput, and it provides insights into the trade-offs between a proactive scheduling approach and a reactive, simulation-driven control strategy. The experimental campaign was conducted on instances containing 200 orders, with job routings generated by randomly selecting a number of operations between 1 and the number of available workcenters \(M\). The tests were performed on configurations with \(M\in 6,9,12\) workcenters, and for each configuration, 10 distinct instances were generated using different random seeds. For every instance, the CP model was executed under varying settings for the number of POLCA cards, denoted by \(C\in 1,2,3\), and under two alternative card retrieval mechanism, also named optimization modes, referred to as \"early\" and \"late\". Each CP solution was then evaluated by means of a discrete-event simulation executed in two alternative simulation modes: \"opt\" and \"sim\". All simulation runs were executed over a fixed time horizon of 100,000 time units, while the CP model employed a multi-objective lexicographic function that minimizes the maximum lead time, the total tardiness, and the total lead time, subject to a time limit of 1500 s. Notably, all simulations and CP runs were executed using an identical number of POLCA cards per workcenter. During the simulations, deadlocks were carefully monitored. Deadlocks occur when a circular waiting situation arises among jobs and POLCA cards, leading to scenarios in which certain orders never complete because they remain permanently blocked within the system. For example, a workcenter may be unable to proceed without acquiring a specific POLCA card, yet all such cards may already be held by downstream workcenters that, in turn, are waiting for cards. Although such deadlocks are rare in practical applications, their occurrence was systematically tracked by identifying orders that lack a recorded finish time in the order data sheet. The average number of deadlocked orders was subsequently aggregated according to the card retrieval mode, number of workcenters, POLCA card settings, and simulation mode. It is important to note that, in addition to the standard POLCA cards, starvation cards are sometimes employed in production control systems to mitigate the risk of deadlocks. Starvation cards serve as a mechanism to break potential circular waiting by preemptively releasing resources, thereby enabling blocked jobs to proceed and preventing indefinite waiting. However, in the experimental tests reported herein, no starvation cards were utilized. This deliberate omission means that no additional measures were taken to prevent deadlocks, ensuring that any deadlock occurrence was a direct consequence of the inherent system dynamics under the specified configurations. As a result, instances with deadlocked orders were identified and excluded from subsequent analyses, thereby ensuring that the key performance indicators (KPIs) reflect only the intended operational dynamics without any artificial deadlock resolution interventions. Table 2 succinctly summarizes the incidence of deadlocks observed across different experimental configurations. The data indicate that when only a single POLCA card (\(C=1\)) is available, the reactive simulation mode \"sim\" consistently exhibits deadlocks in configurations with 6 and 9 workcenters, with a 100% occurrence rate. In the case of 12 workcenters, the incidence drops to 50% under the same resource limitation. Conversely, when employing two or three POLCA cards (\(C\in 2,3\)), no deadlocks were observed in either simulation mode.