## 1 Introduction  
Entropy serves as a foundational concept in various scientific domains, encompassing fields such as physics, chemistry, computer science, or information theory [1]. In physics, entropy functions as a metric for the degree of disorder or randomness within a system. The second law of thermodynamics posits that the entropy of an isolated system tends to increase over time, ultimately reaching a state of maximal disorder. In chemistry, entropy finds relevance in its association with the distribution of energy among the microscopic states of particles within a system. During a chemical reaction, alterations in entropy can signify a system's inclination towards either a more disorganized or a more ordered state. In essence, entropy can be seen as intricately linked to the dispersion of energy within a given system [2]. Moving to computer science, particularly information theory, entropy extends beyond its thermodynamic origins, serving as a measure of uncertainty or unpredictability related to a source of information [3]. For instance, measuring the uncertainty of a neural network output is relevant in AI applications such as deep learning-based image classification. In this context, the entropy of the output can serve as a reliable metric for gauging the level of uncertainty in the system [4]. When considering a sequence of symbols in a message, an increase in entropy corresponds to a higher level of unexpectedness for the subsequent symbol. Beyond apparent disorder, entropy reveals the inherent uncertainty in a message represented by a sequence of data, essentially acting as a measure of outcome likelihoods for a random event. [PERSON]'s seminal 1948 article [5] introduced information entropy, a metric designed to quantify the average information content within a message. A core tenet of [PERSON]'s theory posits a direct correlation between uncertainty and information: the greater the uncertainty surrounding an event's outcome, such as the next symbol in a message, the more information it conveys when it occurs [6]. In short, Shannon entropy assigns a value based on the probability of each message outcome. Less probable outcomes contribute more significantly to the overall entropy, as their unexpected nature translates to more informational content [7]. In industrial management, a significant challenge arises from the inherent complexity that emerges when multiple companies collaborate to form a supply chain (SC). At least one prior, recent investigation [8] posits that SCs can be regarded as complex adaptive systems (CASs), often evolving autonomously and independent of a deliberate creation process. Like other types of CASs, it proves beneficial to assess and manage the level of complexity that an SC accrues during its evolution [9], as demonstrated by previous related studies. Among many others, ref. [10] analyzed the underpinning structure of SCs, refs. [11,12] identified drivers that may boost the complexity level in SCs, and refs. [13,14] examined how complexity can influence business performance in SCs, while ref. [15] studied a dedicated tool conceived to measure complexity in SCs. Finally, ref. [16] presents an entropy-based algorithm tailored to measure complexity in SCs. These last two approaches both have a similar gap, which this study aims to bridge. Each company within the collaboration scenario depicted by the SC pursues distinct objectives, spanning areas such as raw material supply, engineering services, transportation, warehousing, manufacturing, and distribution. Despite having individual goals, they all have a shared overarching objective: collectively meeting the requirements of a specific customer type [17]. Beyond their unique operational strategies tailored to meet local objectives, companies operating within an SC must adhere to a meta-strategy that governs the entire system. This meta-strategy outlines global objectives, encompassing the collective goals of all members involved in activities [18].