# EPO Extension of Dispatching Rules to Minimize Effects of Time Uncertainty in Production Scheduling
## 1 Introduction  
[PERSON] et al. [1] define the concept of digital twins as \"dynamic virtual representations of physical objects or systems that rely on real-time and historical data to enable understanding, learning, and reasoning.\" In the realm of modern manufacturing and production processes, the integration of digital twin technology is revolutionizing the way planning and scheduling are approached. Digital twin technology enables real-time monitoring, scenario analysis, and optimization of production processes by creating a virtual replica of physical resources, processes, or systems. DT plays an essential role in receiving real-time data for scheduling simulation and prediction, ultimately allowing adjustments to scheduling plans based on virtual feedback [2], enabling dynamic rescheduling in production systems, and improving overall efficiency and responsiveness to unexpected events [3]. Many research studies highlight the importance of integrating digital twin technology with planning and scheduling systems to effectively manage uncertain factors in production activities [4]. Competitive global markets make it essential to produce goods in a timely and cost-effective manner. However, this requires collaboration between supply chain participants to develop effective supply management strategies, planning, and scheduling of equipmentand personnel. To maximize machine utilization, manufacturers must implement efficient operational schedules [5]. Recent literature reviews dedicated to production planning, scheduling, sequencing [6], as well as scheduling in Industry 4.0 [7] show that the problem of scheduling is still a pressing issue. This is also evidenced by a recent increase in the number of publications on this topic. In this evolving industrial landscape, digital twins (DT) have emerged as a key enabler of real-time data acquisition and system transparency. However, the mere availability of real-time data does not inherently guarantee robust or effective planning. The inherent heterogeneity and dynamic nature of data generated within digital twin environments significantly exacerbate the complexity of scheduling tasks, which surpasses the capabilities of traditional algorithmic approaches to maintain robustness and responsiveness under uncertainty. Consequently, there is a growing demand for advanced algorithmic frameworks such as simineuristics, robust optimization, stochastic programming, and machine learning capable of dynamically interpreting real-time inputs and generating schedules that remain stable and efficient under a wide range of operational conditions [8]. Scheduling can be briefly defined as the process of allocation of scarce resources over time [9; 10]. In the context of job scheduling, it deals with the allocation of resources to jobs over given time periods in order to optimize one or more objective functions. This decision-making process plays a very important role in the manufacturing and service industries [10]. The consequences of poor scheduling in manufacturing practice could be unnecessary tension on the shop floor, poor productivity, and problems with meeting due dates required by customers. According to APICS (American Production and Inventory Control Society), \"detailed scheduling of jobs relies on assignment of resources starting and/or completion dates to operations or groups of operations to show when these must be done if the manufacturing order is to be completed on time\" [11]. There are two most well-known approaches to production scheduling: forward and backward (see Figure 1). In forward scheduling, resources are assigned to jobs as early as possible, i.e., when both job and resource are available. This can be easily performed manually by a planner, and it typically ensures continuous machine utilization as long as there are jobs to be scheduled.