## 2 Data Source Integrity and Parametric Space Definition
### Variable Selection: Engineering Rationale  
The selection of input features was guided by both physical causality and empirical sensitivity evidence reported in the literature. Each variable was retained based on its measurable and quantifiable contribution to at least one of the model's two target outputs: total unit cost (USD/m\({}^{3}\)) and total CO\({}_{2}\)-equivalent emissions (kg/m\({}^{3}\)). The final set of five independent variables was determined following iterative statistical screening, correlation analysis, and engineering validation.  
The first variable, Transport Distance (X\({}_{1}\)), refers to the one-way haulage length between the steel slag production site and the target construction zone. It directly affects the diesel fuel consumed in freight operations, and therefore influences both economic and environmental outputs. The impact of this variable on CO\({}_{2}\) emissions is modeled using a linear mass-distance function, as shown in Equation (1):  
\[\text{Emission}_{\text{transport}}=\text{D}\,\rho\,\text{EF}_{\text{ diesel}} \tag{1}\]  
here, D denotes the transport distance (km), \(\rho\) is the material density (ton/m\({}^{3}\)), and EF\({}_{\text{diesel}}\) is the diesel emission factor (kg CO\({}_{2}\)/ton\(\cdot\)km), assumed to be 0.13 in accordance with CSN EN 16258 [21].  
The second variable, Processing Energy Intensity (X\({}_{2}\)), represents the electricity demand (kWh/ton) required for mechanical treatment processes, including crushing, screening, and drying. It scales linearly with both the operating cost and the electricity-related emissions, which are computed with Equation (2):  
\[\text{Emission}_{\text{processing}}=\text{E}\,\text{EF}_{\text{grid}} \tag{2}\]where E is the site-specific energy demand and EFgrid is the regional emission factor of electricity production (kg CO2/kWh), varying by energy mix.  
A third critical variable is the initial Moisture Content (X3) of the steel slag at the point of extraction. Moisture increases the latent thermal load required for drying and significantly affects both cost and emission through elevated energy usage. The drying energy can be thermodynamically approximated by Equation (3):  
\[\text{E}_{\text{D}}=\text{c}_{\text{p}}\text{ m }\Delta\text{T} \tag{3}\]  
where cP is the specific heat of water (kJ/kg\(\cdot\)K), m is the mass of moisture (kg), and \(\Delta\text{T}\) is the temperature differential needed to achieve sufficient drying. The inclusion of moisture thus introduces a nonlinear effect on both objective functions, reinforcing its necessity in the model.  
The Gradation Adjustment Level (X4) is treated as an ordinal categorical variable, denoting the intensity of mechanical sieving or particle size correction. It is coded as 0 for no adjustment, 1 for basic screening, and 2 for crushing plus screening. While this feature may appear qualitative, its effect is operationalized through discrete shifts in both energy intensity and maintenance costs, especially relevant in coarse/fine transitions or specification compliance [22].  
Finally, the Grid CO2 Emission Factor (X5) accounts for regional differences in the carbon intensity of electricity used in processing. Its inclusion is essential to generalize the model across geographies and regulatory regimes. Since this factor is used directly in Equation (2), it modifies the slope of emission increase with energy intensity, thus playing a critical role in optimization scenarios targeting emission reductions.