## 3 Materials and Methods  
According to [54], complexity can stem from three distinct sources: materials, finances, and information flows. This study acknowledges that when both material and financial uncertainties arise, it can lead to unanticipated requirements for additional information exchange. Hence, by monitoring the information flow in relevant channels, mainly uncommon requests for further information, all three sources of complexity can be effectively managed. Therefore, the primary research assumption is that to evaluate complexity, the SCM must manage relevant flows of information to fulfill the manufacturing orders received by the focal company. A previous study [55] has established a list of twenty different types of information (\(j=1,\ldots,20\)) that may or may not be necessary to complete a manufacturing order. Whether or not information \(j\) is required to fulfill an order is a binary output for a random event (\(i=1\) if the information is required; 0 otherwise). Future studies should consider intermediate levels in which information may be partially required (in this case, the outcome would be discrete, not binary). Moreover, the study has identified five relevant paths (\(k=1,\ldots,5\)) that the 20 pieces of information can follow. For each SC, the study must compute one hundred probabilities of information \(j\) being required in path \(k\) to fulfill a manufacturing order. Equation (7) uses these probabilities to calculate Shannon entropy. \[H(P)=-\sum_{k=1}^{5}\sum_{j=1}^{20}\sum_{i=1}^{2}p_{ijk}\cdot log(p_{ijk}) \tag{7}\]  
where:  
2 is the number of possible outcomes for a piece of information (required or not); 20 is the number of types of information of interest;  
5 is the number of agents considered in the SC;  
\(p_{ijk}\) are the probabilities of the information \(jk\) (20 pieces and 5 agents) that is required (\(i=1\)) or not (\(i=2\)). Setting all probabilities to 0.5 results in the maximum possible entropy. Dividing the first result (Equation (7)) by the second provides the percentage entropy, which is more useful in managing the inherent complexity of the SC. Furthermore, given that \([p_{ijk}+p_{2 jk}]=1\), that is, the sum of the probability of the information \(jk\) that is required and the probability of the information that is not required must equal 1, it follows that both probabilities cannot exceed or drop below 0.5 at the same time. For example, if \(p_{ijk}=0.25\), then it is necessary that \(p_{2 jk}=0.75\). Since the study must focus only on one value, we chose the lowest one, regardless of whether the character is active or inactive. Switching will not affect the uncertainty. The study followed a particular methodology, divided into the following steps:  
* Four focal companies were selected: two from the agrifood industry and two from the metalworking industry. In each industry, one company prioritizes competition according to cost/quality and the other according to dependability/flexibility;
* At the headquarters of companies, two managers were interviewed together, one responsible for manufacturing and the other for logistics activities. The interviews lasted around two hours. The respondents answered two rounds of questions in consensus. In the first round, they prioritized the four competition objectives. In the second round, they estimated the probabilities. To make the estimate, respondents previously consulted the fifty most important manufacturing orders from the most recent days and counted how many times information \(j\) was requested in path \(k\). Further information on orders from all respondents is confidential;
* After the first meeting, managers had enough time to search the orders' documentation to identify the number of times each piece of information was required. Managers had the chance to contact practitioners to clarify doubts. The number was rounded to facilitate communication.