Designing a Fuzzy Mathematical Model for a Two-Echelon Allocation-Routing Problem by Applying Route Conditions: A New Interactive Fuzzy Approach

Abstract

In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching real-world conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multi-objective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches.