A Linear Programming Model with Fuzzy Arc for Route Optimization in the Urban Road Network

In the transport system, it is necessary to optimize routes to ensure that the distance, the amount of fuel used, and travel times are minimized. A classical problem in network optimization is the shortest path problem (SPP), which is used widely in many optimization problems. However, the uncertainty that exists regarding real network problems makes it difficult to determine the exact arc lengths. In this study, we analyzed the problem of route optimization when delivering urban road network products while using fuzzy logic to include factors which are difficult to consider in classical models (e.g., traffic). Our approach consisted of two phases. In the first phase, we calculated a fuzzy coefficient to consider the uncertainty, and in the second phase, we used fuzzy linear programming to compute the optimal route. This approach was applied to a real network problem (a portion of the distribution area of a delivery company in the city of Tuxtla Gutierrez, Chiapas, Mexico) by comparing the travel times between the proposed model and a classical model. The proposed model was shown to predict travel time better than the classical model in this study, reducing the mean absolute percentage error (MAPE) by 25.60%.