Logistics is the action of physically delivering businesses’ goods or services to the required place at the desired time and has great importance concerning businesses’ profitability. Transportation costs these days are constantly increasing, and timely delivery is one of the main issues customers focus on. For this reason, the importance of logistics activities increases daily (Kosif & Ekmekçi, 2012, p. 41). However, logistics companies spend more than half their budget on transportation activities, and obtaining the most efficient distribution path is necessary for acquiring higher profits (Zulfiqar et al., 2018, p. 371). Accordingly, one of the most important problems in logistics activities involves determining the shortest route in terms of distance that will save time and costs, and a network analysis method can be used to solve this problem. A network is an effective format used for representing complex systems. Network analysis methods are activities that ensure optimal coordination and placement of resources. Rapid progress has occurred in both the methodology and application of network analysis methods, one of these being the shortest path problem (SPP). This problem has been used to minimize a linear function representing the distance between a predetermined pair of nodes in a given network (Climaco & Martins, 1982, p. 399). Many algorithms have been developed to solve the SPP, with the Dijkstra, Prim, Bellman-Ford, Floyd-Warshall, and Johnson algorithms seen to have been widely used in the literature (Dermawan, 2019, p. 55).

This study considers a route determination problem that minimizes the total distance and time between the cities of Düzce and Artvin in Turkey for a logistics company with regard to the SPP. The aim of the study is to provide a higher level of profitability and customer service by optimizing the distribution activities of a logistics company. For this purpose, the study uses the node combination method, one of the SPP methods. Although Dijkstra’s algorithm has been used frequently, it may not be easily understood, especially when applying the labeling method. The process of solving the SPP with the node combination algorithm is relatively simple, straightforward, and efficient compared to the Dijkstra algorithm. For this reason, this study has chosen to use the node combination algorithm. The basic idea behind the node combination (NC) algorithm proposed by Lu and Camitz (2011) is based on combining nodes instead of keeping the labeling sets, as occurs in the Dijkstra algorithm and differs from the Dijkstra algorithm in this respect. The node combination finds the nearest neighbor to the starting node and combines this node with the starting node, calculating the SPP iteratively. It then updates the edge weights connected to the nearest node. The path expression used in the SPP can occur different variables such as distance, time, or cost for different problems (Gencer & Karamanoğlu, 2020, p. 50). The current study examines the path characteristics in terms of distance and time, with the results then being compared to Google Maps. The study’s findings show the total minimum distance to be 1,152 km and the total minimum time to be 16 hours and 33 minutes. The route the study obtained by considering the total minimum distance offers an alternative route with regard to shorter distance and time compared to the two routes offered by Google Maps. Moreover, the route obtained by considering the total minimum time is compatible with the route possessing the shortest distance and time that occur among the alternatives offered by Google Maps. This study has shown the node combination algorithm to have been successfully implemented for a real-life problem. In addition, the results the study obtained are expected to contribute to decision makers in terms of offering alternatives that are different from the routes provided by Google Maps. Different results may occur between those from the applied algorithm and those from various online map services such as Google Maps because the node combination algorithm implements the direct distance between two cities, whereas Google Maps might use the alternative route between two cities.

One of the limitations of this study is that the SPP was solved only by considering distance and time. The concept of optimal route depends on the needs or the nature of the problem. The optimal route may be the shortest distance, the lowest cost, or the shortest time (Bulut & Erol, 2018, p. 189). Moreover, various factors such as road conditions, traffic variations, and vehicle characteristics may change the shortest time route or the lowest cost route, despite not changing the shortest distance. For this reason, future studies can address the optimal route determination problem with these variables using various other SPP algorithms and programming languages. In cases where routes change due to some sudden reasons or due to a change in traffic density while traveling between nodes, the real-time dynamic route control system proposed by Bulut and Erol (2018) may be used. Optimization algorithms may differ in performance with regard to particular problems. Hybrid approaches that take advantage of this difference may provide higher performance in many cases. With the increases in processors’ computational capacity, hybrid methods have started being preferred more often (Uslu et al., 2020, p. 102). In addition, many problems in real world applications cannot be solved accurately in polynomial time by any known algorithm. As the number of nodes in the route increases, so does the complexity of the computational solution and the computation time (Bulut & Erol, 2018, pp. 189–190). In this case, metaheuristic algorithms may be used as stated by Uslu et al. (2020).