## 1 Introduction  
Globalization and the increasing virtualization of business relationships have greatly expanded the complexity of logistics challenges since the 1980s. With the interconnection between product flows, logistics has recently begun to consider the entire supply chain of a company instead of considering only the company [1]. Global logistics flows have increased dramatically in recent years due to the globalized world economy, which has introduced challenges inherent in establishing international business [2]. This international competition is most evident in meeting the level of service in terms of the delivery date, delivery reliability, and nature of the delivery, which increases pressure on supply flexibility [3]. Furthermore, demand volatility in almost all industry sectors appears to be higher than in the past due to shorter product and technology lifecycles, sales promotions, rearranged quantities, and unplanned outages [4]. At the same time, many producers are confronted with untransparent and volatile behavior in demand, which causes large deviations in sales forecasts [5]. In this way, forecast errors have grown constantly in recent years, despite the use of information systems for this purpose [6]. The conventional response to this challenge when dealing with uncertainty is to increase the safety stock of products to ensure the expected level of service [7]. The trends shown have led to an increase in the complexity of relationships and processes [8]. In this context, being able to face the changing needs of customers, the volatility of demand, and the launches of new products are becoming increasingly important factors to gain a competitive advantage [9]. This shifts the prioritization of supply chain objectives to customer service, delivery performance, and flexibility, rather than relying solely on costs [10]. Based on this fact, many companies organize themselves in cooperation networks to achieve synergies [11]. Through this intensification of cooperative work, the objective of improving the reaction capacity of the supply chain as a whole and providing a cost-efficient supply to the market is pursued [12]. Robust and reliable plans are key for optimizing costs and securing the long-term success of the parties involved along the supply chain. In this context, the German Logistics Association specifies that supply chain reliability has the highest importance in terms of logistics costs, reaction capability, flexibility, and resource utilization [13]. The supply chain goal of robustness as the capability of a system to deal with disturbances, deviations, and changes without modification of the system structure [14] is continuously increasing in its relevance as a strategic goal to remain competitive. In this context, the planning methods currently in use are often not appropriate for present-day processing options and real-time information availability, leading to unexpected deviations that cannot be corrected in the short term [15]. In this way, conventional planning methods based on average values are highly extended in practice [16]. This is how constant values are determined with high frequency in planning systems [17]. An update of the planning parameters is carried out over long intervals of time, usually annually [18]. As a result, production planning is carried out based on outdated input data that are far from reality, which causes the quality of planning to be insufficient in many cases. Another aspect that limits the quality of planning is the realization of partial planning. In this way, uncoordinated partial plans usually present contradictory results, offering inconsistent solutions [19]. Disturbances in supply chain planning need to be considered and analyzed to obtain new methodologies [20]. Therefore, planning systems today have planning deficiencies that must be compensated through additional costs [18].