# The Impact of Downtime on the Stability of the Production Schedule
## 1 Introduction  
Production scheduling is a key element of the production process that directly influences operational efficiency, cost reduction or the timely delivery of products to the customer [1, 2, 3, 4]. It also makes it possible to ensure the optimal allocation of resources, minimize downtime or adapt production to a dynamically changing economic environment, which is particularly important in the context of Industry 4.0 [5, 6, 7]. On the other hand, although production schedules are crucial, their complexity can lead to challenges in their practical implementation, especially in environments with high demand variability and uncertainty. Scheduling stability therefore requires a balance of various factors to ensure that the scheduling process itself remains effective despite changes in task duration, resource availability and external conditions [8, 9]. Changes in production schedules are often necessary to maintain the efficiency and adaptability (flexibility) of production processes [10]. They depend on a number of factors that can significantly affect the productivity and efficiency of production. Understanding these factors is key to optimizing production processes, minimizing disruption and ensuring production stability. Some of the key factors influencing changes in production schedules are outlined below. Changes in demand--fluctuations in customer demand, as well as changes in order volumes and lead times, require rescheduling to accommodate new variables [11, 12, 13]. Changes in resource availability--unforeseen breakdowns or maintenance and delayed deliveries of materials and raw materials require action to be taken on production schedule changes [14; 15]. The availability of skilled staff is also crucial to ensure the stability of production processes [12]. Production strategies and scheduling methods--lean manufacturing and just-in-time production play a key role in adjusting schedules to meet operational efficiency and customer requirements [1]. Above and beyond this, production schedule adjustments based on real-time data can significantly improve stability and productivity [4]. In the context of Industry 4.0, real-time process data acquisition, as well as the use of advanced optimization methods based on artificial intelligence, genetic algorithms or neural networks, are essential to increasing flexibility to changing conditions so that the rescheduling process (changes to production schedules) takes place as efficiently and optimally as possible given the criteria adopted [14]. While these factors highlight the complexity of production scheduling, it is also important to consider that an excessive focus on scheduling flexibility and the ability to respond quickly to change can lead to increased operating costs and process inefficiencies [15]. The use of production rescheduling methods and strategies appears to be essential to maintaining the correct flow of products out of the process as well as the assumed flexibility of production. These methods resolve disruptions and optimize production schedules to achieve operational goals. Various strategies for dealing with the need for production schedule changes are available in the literature. In the paper [16], the authors present a web-based rescheduling agent that uses exploratory reinforcement learning. This method enables the autonomous optimization of schedules, taking into account nervousness (the concept of nervousness refers to the instability caused by changes in the production schedule), which is a new approach in the field. Ref. [17] proposed a relaxation heuristic method that allows for rescheduling for hybrid production lines, focusing on minimizing the costs associated with delays. Many authors are developing genetic algorithms to assist in the rescheduling of production. Ref. [18] proposed a genetic algorithm that allows for effective fault management by applying rules, such as right-shifting or complete rescheduling, based on the type of fault events.