The purpose of this study is to develop an application for finding the shortest path in the transportation sector. The application was developed using the dynamic programming method in MS Excel Visual Basic application. These types of problems are also called stagecoach problems. The purpose of the problem is finding the shortest path between the starting point (node) and the destination point. Values are related to the roads in the network to specify the distance between two nodes. In case of a small number of nodes (activities), a solution can be reached by evaluating all options. But the number of possible options to be scanned for real problems is quite large. In such cases, a suitable method is needed for the solution. It can produce effective solutions with the dynamic programming approach.
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Kumar et. al. (2020)
, presented a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions can be solved. Moreover, the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations can be solved. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated.
Kumar, Dey, Broumi and Smarandache (2020), studied three different approaches for solving the neutrosophic shortest path problem. Finally, the numerical examples are illustrated to understand the above discussed algorithms.
Majumder et. al. (2020), presented an uncertain multi-objective shortest path problem (UMSPP) for a weighted connected directed graph (WCDG), where every edge weight is associated with two uncertain parameters: cost and time. These parameters are represented as uncertain variables. They have formulated the expected value model and chance-constrained model of the proposed UMSPP, and the corresponding deterministic transformation of these models is also presented.
Tu et. al. (2020), investigated the constrained reliable shortest path (CRSP) problem for electric vehicles in the urban transportation network. A mixed-integer programming model is developed for the CRSP problem, where the reliable travel time is treated as the objective and the energy consumption, instead of the distance, is taken as the driving range constraint. The results showed that the path choice is greatly impacted by the travelers’ risk attitudes and properties of electric vehicles in the stochastic transportation network. They suggested to embed the model and algorithm to the mobile map app and provide the customized navigation service in more detail to satisfy travelers’ heterogeneous requests.