Optimization Model for Production Scheduling and Disturbance Suppression Based on SIR Propagation Dynamics

In the heart of modern manufacturing, where machines hum and conveyor belts move with rhythmic precision, a hidden tension often builds. Factories today are designed to be flexible, capable of shifting quickly to meet custom orders or sudden changes in demand. However, this flexibility comes with a fragile side. When an urgent order arrives unexpectedly, it does not simply slot into an empty space; it acts like a stone dropped into a crowded pond, sending ripples through the entire system. These ripples are disturbances. They cause resources like machines and workers to compete fiercely, leading to bottlenecks where work piles up and delays spread from one task to another. For decades, factory managers have treated these emergencies by stopping everything immediately to handle the new request, a rigid approach that often makes the chaos worse. The challenge for researchers has been to find a way to manage these interruptions without causing the whole production line to seize up, requiring a new understanding of how delays travel through a network of interconnected tasks.

A team of researchers at Dalian Polytechnic University has proposed a fresh way to look at this problem, treating the flow of factory orders not just as a list of tasks, but as a living system where states change and spread. They drew inspiration from the way diseases move through a population, using a framework known as SIR dynamics, which tracks how individuals move from being susceptible to infected and finally to recovered. In their model, every production order is an agent that exists in one of three states: silent, meaning it is waiting to start; infectious, meaning it is currently being processed and can influence others; or recovered, meaning it is finished. Just as a virus spreads through contact, a production disturbance spreads when orders that share similar processing steps are scheduled too close together, creating pressure on the same equipment. By simulating this evolution, the researchers could see how the "infection" of a delay propagates through the factory floor, allowing them to predict where the system would buckle before it actually happened.

The core of their work involves a sophisticated optimization strategy designed to find the perfect moment to insert an emergency order. Instead of reacting instantly, the system calculates the best time to introduce the new task, balancing three competing goals. First, it aims to keep the amount of unfinished work, known as work-in-process inventory, as low as possible to save money and space. Second, it seeks to minimize the time materials spend waiting for processing. Third, and most innovatively, it tries to reduce the average pressure on the process network. This pressure is a measure of how much conflict exists between orders on any given day; if two orders require the same specific machine or tool at the same time, the pressure spikes, increasing the risk of a breakdown in the schedule. The researchers used a powerful computer algorithm to explore millions of possible schedules, looking for a set of solutions where improving one goal would not make another significantly worse.

Through extensive simulations, the study revealed that the traditional method of immediate response is often counterproductive. When an urgent order is forced into production the moment it arrives, it creates a sudden spike in network pressure, causing a chain reaction of delays that slows down the entire line. The new approach, which carefully times the insertion of the order to avoid clashing with similar tasks, proved far more effective. In their tests, this optimized strategy reduced the average network pressure by 15.28 percent. While this might seem like a small number, in the context of a factory, it represents a significant smoothing of the workflow. It means fewer moments where machines sit idle waiting for a tool, fewer piles of unfinished goods clogging the floor, and a more stable environment where the system can absorb shocks without collapsing. The researchers found that by accepting a slightly longer wait time for some materials, they could prevent the severe resource conflicts that cause much larger inefficiencies.

The findings suggest that the key to managing a flexible factory lies in understanding the hidden connections between tasks. By viewing the production schedule as a dynamic system where the state of one order affects the others, managers can make decisions that preserve the health of the entire network. The study does not claim to have solved every problem in manufacturing; it relies on simulations and assumes that processing times are fixed, ignoring real-world variables like machine breakdowns or supply delays. However, it offers a robust framework for thinking about disturbance management. It demonstrates that by actively suppressing the pressure that builds up when similar orders collide, a factory can become more resilient. The result is a system that does not just react to emergencies but anticipates their impact, allowing for a smoother, more efficient flow of goods that benefits both the factory's bottom line and its ability to deliver on time.