Connecting Cities: Solving Optimal-Resource-Distribution Problem Using Critical Range Radius

Navigating and planning optimal paths for resource delivery algorithms poses significant physical and technical challenges in urban areas, primarily due to the limitations of existing infrastructure. As smart cities continue to develop, the importance of these algorithms becomes increasingly evident. The saturation of current urban landscapes exacerbates the complexity of navigating essential resources. Navigating densely connected networks can be intricate and often requires substantial computational resources or additional algorithms, as it can easily transform into an NP problem. Unfortunately, there is a lack of explicit algorithms designed for navigating these networks, resulting in a dependence on heuristic approaches and previous network systems. This reliance can create computational challenges, as navigation in this context typically involves a combinatorial search space. Current advances in Morphological Mathematics (MM) help to model everyday tasks as processes in discrete spaces, which take advantage of the properties offered by the morphological operators. Morphological Shortest-Path-Planning (MSPP) is a recent solution that effectively calculates the optimal trajectory within complex graphs. By utilizing morphological operators, this approach takes into account discrete properties and maps the process as a complete implementation algorithm using integer logic. In larger cities, determining the optimal delivery route and time from a resource center is a common task. This process is influenced by factors such as average speed, travel time, and distance, which generate a complex graph representation of the town, complicating its analysis. This paper presents a strategy for computing and analyzing delivery times by determining the accessibility of reliable paths from a delivery center to potential destinations in dense urban areas. The strategy presented and the use of the MSPP approach are suitable for calculating the time spent delivering and the distance traveled in working journeys. The MSPP approach is found to be nearly 60% more efficient than the reference approach for computing the optimal path in the case study presented.