Sustainable open vehicle routing with release-time and time-window: a two-echelon distribution system

In an increasingly competitive economic environment, outsourcing for logistics has emerged as a cost-efficient strategy during freight transportation. The open vehicle routing problem is a type of classical vehicle routing problem, in which businesses outsource logistics to a third-party company and the vehicles do not return to the depot at the end of their journey. This paper develops a mixed integer linear programming model for two-echelon open vehicle routing problem that integrates city distribution constraints such as time-window and release-time. The release-time refers to the time at which products become ready at satellites for downstream distribution, and it is influenced by limited available resources and work load of each satellite. The proposed model determines the optimal configuration of the routes while minimizing the handling costs, penalty costs, and transportation costs. We use a comprehensive emission model that accounts for load, distance, speed and vehicle characteristics to estimate fuel consumption. Finally, we utilize a numerical example to illustrate the proposed model and explore the effects of release-time on total cost