## 3 Material and Methods
### HMP-Coffee Model
#### 3.2.2 Hierarchical-Multicriteria Phase  
To convert the conceptual model into a profitability estimation model, we used the qualitative multi-criteria decision analysis tool called DEX (Decision Expert) [36]. DEX breaks a complex decision problem into smaller, and less complicated, sub-problems and organizes them hierarchically into a Decision Tree. Consequently, DEX provides high interpretability to the model. The construction of the hierarchical multi-criteria phase based on DEX comprises the attributes, scales, weights definition, and rules generation [36]. **The scale definition** represents different impact levels for each basic attribute of the HMP-Coffee model. For scaling definition, we assigned ordinal values to each basic attribute of the model based on the experts' knowledge. The assignment of qualitative values reflects how much the attribute affects the level of profitability. For instance, \"Investment in harvest time\" is represented using three-scale values (**High**, **Average**, and **Low**) and \"Profitability\" (**Favorable**, **Average**, and **Unfavorable**). The red qualitative values have a negative connotation, and the green ones have a positive connotation on profitability. In this regard, an \"Investment in harvest time\" **High** contributes to **Unfavorable** profitability, and an \"Investment in harvest time\" **Low** contributes to **Favorable** profitability. It is important to note that the attribute scale values are independent of the local context. For instance, HMP-Coffee defines three-scale values for the \"Transportation\" basic attribute (**High**, **Average**, and **Low**) anywhere in the world. In contrast, the meaning of the scale values or ranges can be different between countries, and even regions, of the same country. For example, 10 dollars can be **High** for \"Transportation,\" in Colombia while they can be **Average** in Brazil. Table 4 presents the qualitative scales defined by the panel of experts to HPM-Coffee (grey cells) and the meaning by qualitative value (i.e., ranges) determined by a group of local coffee growers (white cells). In this case, the coffee growers work for the Cafiambiente Association. Particularly, for defining the levels of profitability (i.e., vo, variable objective),  
the experts considered Pr, given by Equation (1) [37], and [PERSON]'s hierarchy of needs [38]. They agreed to classify the profitability as follows. Unfavorable (Pr \(\leq\) 1), smallholders cannot meet their physiological needs. Average (1 \(<\) Pr \(\leq\) 1.4), the smallholder gets enough profit for meeting physiological needs. Favorable (Pr \(>\) 1.4), the small-coffee production generates incomes that allow meeting safety needs. The table columns contain the Id and the basic attribute names, the qualitative scale names (e.g., Low time, Average time and High time) and the unit of measure of the quantitative ranges (e.g., hours, Costa Rica Colon (CRC), USD, Bushel per Hectare (Bsh/ha)). \[Pr=\frac{Income}{Investment}=\frac{Income\ from\ coffee\ sales}{Production\ costs} \tag{1}\]  
**The weights definition** determines the attributes' relevance regarding profitability. The weights were defined based on real values obtained from the \"La Sultana\" farm, including cost of supplies, crop management activities, harvesting, administrative expenses, coffee processing, transformation process, and profit. It is noteworthy that \"La Sultana\"