# A Cost-Optimized Model for Dynamic Port Hinterland
## 4 Experimental Design and Results
### Results: Representing the \(H(x,y)|_{(p_{n},\rho_{n})}\)
#### 4.2.1 Methodology of Analysis  
The implementation of the theoretical framework previously described required a comprehensive analytical approach that combined multiple data sources and processing techniques. The research analyzed mainland Spanish municipalities with over 1000 inhabitants, comprising 3487 population centers. The threshold was chosen to balance commercial representation and computational efficiency. The Canary and Balearic Islands were excluded due to their distinct maritime and logistical characteristics, requiring separate study. Figure 4: Hinterland in Spain: Simulation of non-perishable goods, Upper: Shangai origin. Lower: New York origin. Point is any city studied. Color shows the port influence: Valencia (red), Barcelona (green), Algeciras (blue). The geographical framework was established using a precise coordinate system, with each location mapped through its latitude and longitude coordinates. This spatial reference system was essential for accurate distance calculations and proper visualization of results. The research developed a multidimensional matrix-based calculation system for Total Logistics Cost (_TLC_), focusing on detailed transportation cost analysis. The system used interconnected matrices to compute maritime route freight costs, incorporating current market rates, bunker adjustments, terminal handling charges, and customs management fees for each origin and destination port. A sophisticated decision tree structure evaluated inland transportation options, comparing direct road transport with combined road-rail alternatives. The system explored multiple transport modes, transfer points, and storage locations to identify the most cost-effective routing. For instance, when analyzing transport from Valencia to inland destinations, the method assessed direct road transport, rail transport with local distribution, and their combinations, ultimately selecting the most economical option. The research integrated Warehouse Costs (_WHC_) using a specialized matrix structure that captured regional storage cost variations. The calculation dynamically assessed storage areas based on product characteristics, consumption patterns, and service rotation times, incorporating location-specific factors like real estate values and handling capabilities. This approach enabled efficient, flexible storage cost computation across different locations, accounting for seasonal and product-specific variations. The Time Management Cost (_TMC_) calculation used a specialized matrix to track goods' temporal value degradation. For perishable products like bananas, a non-linear depreciation model captured initial stability and subsequent rapid value loss. Orange shipments employed a linear depreciation approach starting from harvest. This temporal cost structure was critical in evaluating routing options, particularly when balancing speed against economic efficiency. The decision tree methodology effectively evaluated complex routing scenarios by treating each node as a decision point with multiple options for mode, route, and storage. The system calculated the cumulative cost impact of each choice, considering direct transportation and indirect temporal costs. This approach enabled identifying globally optimal solutions beyond local cost minimizations. The complexity of the model reflects the reality of the logistics chain, where any factor within it can determine the decision to change routes. Using simpler models may overlook factors that can be decisive in reality. An example of such factors is ignoring the value of time, which is key for non-perishable goods, or the value of customs inspections, which is crucial for goods with complicated inspections, such as fruits from certain countries. The validation process employed a multi-tiered approach to ensure result accuracy. Individual cost components were validated against current market rates and published tariffs. Complete logistics chains were cross-referenced with actual shipment data provided by logistics operators.