## Materials and Methods
### Demand Assessment
#### 2.4.2 Value and Price Models  
We established the demand component of the model based on biomass valuing and pricing. For value, we adopted the definitions according to the value \"whatever I want in a product\", since it can be converted in terms of subjective satisfaction concerning products [18]. Different stakeholders look for different characteristics in a product, which makes the value of that product dependent on the point of view of different groups of interest. A forest stand, for example, may not have the same value for the forest industry, tourists or mushroom pickers. The question then becomes: what is each stakeholder looking for and how can that information be converted into value? We addressed these questions with the Analytic Hierarchy Process (AHP) [44] and Multi-Attribute Utility Theory (MAUT) [45] multi-criteria analysis methods. AHP is one of the most widely used methods around the world and it has been applied to decision making in many fields [46], including forestry (e.g., [47; 48]). AHP is based on the pairwise comparison of criteria in a decision scheme as well as on the alternatives under each criterion using a certainty scale of priorities [49]. MAUT is similar to AHP in many ways [50], but instead of pairwise criteria comparisons, it uses utility functions ranging from 0 to 10 for the level of satisfaction for each criterion [51]. There are several examples of applications of MAUT in forestry, for example [52; 53]. AHP was used in our framework to obtain weights for criteria in a decision tree and MAUT to link weights with the weight utility model for each criterion, or data category, of spatial datasets associated to each criterion. The relationship between criteria and spatial information was synthetized using a utility function where attributes were given weights according to priorities (Table 3). The value model considered published information [54; 55; 56; 57] for the establishment of criteria and weights assigned to criteria/sub-criteria (Figure 5). Sub-criteria road transport CO\({}_{2}\) emissions and road transport distance were considered within policy criteria, mechanizable (slope class) and road transport fuel consumption within economy, and protection areas, land use, and distance to rivers within environment. Weights, defined for the present year (t\({}_{0}\)) and for simulation year 20 (t\({}_{20}\)) (Figure 6), were constant  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Description** \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Scenario 1 \\ (Control) \\ \end{tabular}  } & \begin{tabular}{c} Corresponds to Biomass I (B1), where demand comes from an already existing pellets production plant located outside (Chaves) but consuming biomass from the study area; all the available pine biomass in the region can be used by this plant only; this is the control scenario and it will be used as reference for other scenarios \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 2 \\ \end{tabular}  } & Scenario 1 + Biomass II (B2), a bioenergy plant located in Braganca; no supply restrictions \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 3 \\ \end{tabular}  } & Scenario 2 + Biomass III (B3), a bioenergy plant located in Vimioso; no supply restrictions \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 4 \\ \end{tabular}  } & Scenario 1 + Biomass III (B3), no supply restrictions \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 5 \\ \end{tabular}  } & Scenario 1 + Biomass II (B2) and Sawmill (S1); supply in B1 and B2 restricted to biomass extracted by thinning \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 6 \\ \end{tabular}  } & Scenario 5; biomass supply to B1 and B2 from thinning and falling when average dbh \textless{} 25 cm at stand age 30 years \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 7 \\ \end{tabular}  } & Scenario 5 + Biomass III (B3); supply in B1, B2 and B3 from thinning and falling when average dbh \textless{} 25 cm at stand age 30 years \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Scenario 8 \\ \end{tabular}