A Branch and Price Algorithm for the Heterogeneous Fleet Multi-Depot Multi-Trip Vehicle Routing Problem with Time Windows

Abstract

The multi-trip vehicle routing problem (MTVRP) extends the well-known VRP by allowing vehicles to perform several trips in a workday. The motivation arises from the new challenges in city logistics that push companies to use smaller and cleaner vehicles such as cargo bikes. With the integration of small vehicles into the fleet, many companies start to operate with a heterogeneous fleet and use multiple depots located in the city centers to reload the small vehicles. Inspired by these new challenges the companies face, we study the heterogeneous fleet multi-depot MTVRP with time windows under shared depot resources where small and large vehicles have different travel times in certain areas. We formulate this problem using workday variables and propose a branch and price algorithm that exhibits an enhanced performance by a new heuristic algorithm based on the reduction in the graph size. The proposed algorithm introduces a new way to compute the completion bounds using the iterative structure of the state-space augmenting algorithm and eliminates the need for solving a separate relaxation. We conduct experiments on modified small- and medium-size instances from Solomon’s benchmark set. The results of our computational experiments show that the proposed algorithm is very effective and can solve instances with up to 40 customers, three depots, and two types of vehicles.

A Two-Echelon Multi-Trip Capacitated Vehicle Routing Problem with Time Windows for Fresh E-Commerce Logistics under Front Warehouse Mode

“…Ref. [49] studied the heterogeneous fleet multi-depot MTVRPTW under shared depot resources, in which the travel times of small and large vehicles in a specific area are different. However, they have not considered the two-echelon system, nor have they focused on the front warehouse mode under the new retail context.…”

A Systematic Literature Review of Vehicle Routing Problems with Time Windows

“…Multi-objective optimization: Multi-objective optimization is an approach to optimization that considers multiple conflicting objectives simultaneously. For example, in VRPTW, one objective may be to minimize travel time, while another may be to minimize transportation costs [72], such as fuel consumption. Multi-objective optimization can help find trade-offs between conflicting objectives and identify optimal solutions.…”

A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research

“…The multi-depot vehicle routing problem (MDVRP) is an extension of the basic vehicle routing problem, which refers to the service of multiple users by multiple depots at the same time, requiring an appropriate arrangement of the vehicles and routes of each depot to ensure that the total transport cost is minimized while satisfying the needs of all users. MDVRP is one of the most challenging variants of VRP; in combination with other features, it greatly enriches the study of VRP models [76][77][78][79].…”