## 1 Introduction  
Starting from the seminal work of Nobel laureate [PERSON] [1] and [PERSON]'s influential paper [2], managerial decisions have been classified into _structured_, _semi-structured_, and _unstructured_. Structured decisions include those that follow a clear, predefined process or set of rules, often relying on established criteria or quantitative data (e.g., inventory management and production scheduling). Unstructured managerial decisions include those that are complex, novel, and lack a clear or predefined process. These decisions often require judgment, intuition, and creativity, as they deal with uncertain or ambiguous situations. Examples include strategic planning, crisis management, market entry decisions, and innovation initiatives. Various studies have indicated that a significant portion of them fall into the semi-structured category. For instance, in his landmark book [3], management guru [PERSON] highlighted that the majority of decisions are neither entirely routine (structured) nor completely novel (unstructured). In particular, he emphasized that such a category is quite common in middle management, where decisions often involve both a structured component (e.g., financial analysis) and an unstructured part (e.g., judgment on market conditions). Semi-structured managerial decisions depend on human intuition and experience for the final judgment, while utilizing data and analytical models to generate a sequence of tentative solutions that progressively incorporate the decision makers' preferences. Hence, they involve a combination of standardized procedures (which are peculiar to structured decisions) and human assessment (which is typical of unstructured decisions). They are common in managerial and strategic contexts where decisions cannot be entirely algorithmic and require a nuanced approach. Examples include budgeting decisions (see, e.g., ([PERSON] et al., 2016)), where standard procedures can be used for creating budgets, while managerial judgment is needed to allocate funds based on strategic priorities and future projections. Another example is marketing campaign design (see, e.g., ([PERSON] et al., 2016)), where decisions about targeting demographics and allocating resources among various media require both data analysis (e.g., past campaign performance) and creative thinking. A further remarkable example is investment decisions (see, e.g., ([PERSON] et al., 2016; [PERSON] et al., 2016)), in which evaluating investment opportunities involves the quantitative analysis of financial data as well as the qualitative assessment of market conditions and future trends. The iterative nature of semi-structured decision making involves repeated cycles of gathering data, analyzing information, generating and evaluating options, and refining decisions ([PERSON] et al., 2016). In this scheme, managers continuously adjust and incorporate their preferences in the tentative decisions, based on the insights gained in the previous iterations. This repeated and cyclical process is inherently time-consuming as each iteration requires decision makers to generate tentative solutions, analyze them carefully, and possibly integrate new elements (e.g., penalty terms in the objective function and new constraints) in the decision model (see Section 2 for more details). Preferences may reflect those of the organization's managers or incorporate the needs of various other stakeholders, including workers, customers, local communities, and others. Hereafter, we refer to the group involved in the decision-making process as the \"decision makers\". It is worth noting that all these subjects do not necessarily have to physically participate in the decision board. Their preferences may be expressed in person or can take the form of product reviews, formal complaint reports, etc., collected in the company information system.