Minimal-cost route planning via Fibonacci-heap-typed data structure

Efficient route planning in transportation networks, particularly under stochastic conditions like severe weather (i.e. snow or hail), poses a significant computational challenge. This article addresses this challenge by modeling the route planning problem as a Markov decision process (MDP) problem, establishing reachability criteria, and identifying the minimum-weight arborescence in the directed graph. To achieve this, the reachability determination algorithm is designed to assess the courier company's reachability to all junctions based on the queue-typed data structure and breadth-first search idea. Subsequently, the minimal-cost route planning algorithm is developed to find a feasible transport route with the minimal cost of clearing obstacles by resorting to the Edmonds' algorithm and some feasible data structures. In particular, the article introduces a Fibonacci-heap-typed data structure to the minimal-cost route planning algorithm, resulting in a remarkable reduction of the time complexity from $O\left(mn\right)$ to $O(m+n\log n)$, where $m$ and $n$ represent the cardinalities of the arc set and nodeset, respectively. Ultimately, the proposed method is applied to optimize route planning in a transportation network, providing a cost-efficient solution for logistics and transportation planning.