# A Cost-Optimized Model for Dynamic Port Hinterland
## 4 Experimental Design and Results
### Results: Representing the \(H(x,y)|_{(p_{n},\rho_{n})}\)
#### 4.2.5 Quantitative Analysis  
The quantitative assessment of port influence across major Spanish cities reveals complex patterns of competition and market penetration. Table 10 presents a detailed breakdown of port influence percentages across key urban centers, along with the dominant factors driving these distributions. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Product—Origin** & **Weight (Tn)** & **\%** \\ \hline Orange—Durban & 15,544.95 & 0.89 \\ Banana—Manzanillo & 14,001.24 & 0.004 \\ Non-Perishable—Shanghai & 2,586,956.7 & 0.005 \\ Non-Perishable—New York & 263,887.78 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Weights and % influence for each product and origin (only for 4 selected). Source: Own elaboration from AEAT data. Madrid, Spain's central logistics hub, shows a particularly nuanced distribution of port influence, with Valencia commanding 45.2% of the market share, followed by Algeciras at 32.5% and Barcelona at 22.3%. This distribution reflects the capital's strategic position and its excellent multimodal connectivity. Valencia's stronger position can be attributed to its robust rail connections and optimized inland logistics networks, while Algeciras maintains significant influence through competitive pricing and efficient handling of time-sensitive cargo. Zaragoza presents an interesting case of nearly balanced influence between Valencia (42.1%) and Barcelona (42.6%), with Algeciras maintaining a smaller but significant presence (15.3%). This equilibrium stems from the city's geographic position and its role as a major logistics hub. The minimal difference between Valencia and Barcelona's influence demonstrates how infrastructure investments and service quality can effectively counterbalance geographic advantages. The analysis of Valladolid reveals a more evenly distributed competition, with influence shares of 28.7%, 38.9%, and 32.4% for Algeciras, Valencia, and Barcelona, respectively. This distribution reflects the city's position in the northern logistics corridor and its strong multimodal connections. The relatively balanced influence suggests that factors beyond pure distance, such as service frequency and logistics chain integration, play crucial roles in port selection. Sevilla demonstrates the strongest single-port dominance in the study, with Algeciras commanding 78.4% of the influence, while Valencia maintains 18.5%, and Barcelona shows minimal presence at 3.1%. This strong skew reflects both geographic proximity and well-established logistics patterns in southern Spain. However, Valencia's significant secondary presence indicates that competitive service offerings can penetrate even strongly dominated markets. In the northern region, Bilbao's distribution (Algeciras 25.6%, Valencia 35.2%, Barcelona 39.2%) shows how rail connectivity and specialized service offerings can overcome geographic disadvantages. Barcelona's slight lead in this market demonstrates the importance of efficient inland transportation networks and integrated logistics services. The influence percentages detailed in Table 9 are visually represented in Figure 5, where the color intensities correspond to the calculated market shares. The strong dominance of Algeciras in Sevilla (78.4%) is clearly visible in the deep blue coloring of the region,