Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem

Abstract

Providing consistent service by satisfying customer demands with the same driver (driver consistency) at approximately the same time (arrival-time consistency) allows companies in last-mile distribution to stand out among competitors. The consistent vehicle-routing problem (ConVRP) is a multiday problem addressing such consistency requirements along with traditional constraints on vehicle capacity and route duration. The literature offers several heuristics but no exact method for this problem. The state-ofthe-art exact technique to solve VRPs-column generation (CG) applied to route-based formulations in which columns are generated via dynamic programming-cannot be successfully extended to the ConVRP because the linear relaxation of route-based formulations is weak. We propose the first exact method for the ConVRP, which can solve medium-sized instances with five days and 30 customers. The method solves, via CG, a formulation in which each variable represents the set of routes assigned to a vehicle over the planning horizon. As an upper bounding procedure, we develop a large neighborhood search (LNS) featuring a repair procedure specifically designed to improve the arrival-time consistency of solutions. Used as stand-alone heuristic, the LNS is able to significantly improve the solution quality on benchmark instances from the literature compared with state-of-the-art heuristics.

A case study of consistent vehicle routing problem with time windows

“…In the literature, most approaches to solve ConVRP problems focus on heuristic methods because exact methods of mixed-integer linear programming (MILP) allow only to solve very small instances. For example, Groër et al (2009) solved instances up to 12 customers over three days, and Goeke et al (2019) solved instances with 30 customers over five days. The exact methods are computationally intractable for the instances of the company under study since we need to solve instances with about 2000 customers over a planning horizon of at least 25 days.…”

“…In Goeke et al. (2019) an exact method for ConVRP based on the column generation technique was proposed. This method was used for solving medium‐sized instances with five days and 30 customers.…”

“…(2009) solved instances up to 12 customers over three days, and Goeke et al. (2019) solved instances with 30 customers over five days. The exact methods are computationally intractable for the instances of the company under study since we need to solve instances with about 2000 customers over a planning horizon of at least 25 days.…”

Design of Flexible Vehicle Scheduling Systems for Sustainable Paratransit Services

“…Customers had time windows in AM/PM, and it was possible to change the vehicle departure times. Recently, Goeke, Roberti, and Schneider [30] investigated the first exact methods based on column generation for ConVRP with both driver and arrival time constraints. This method can solve the medium-sized instance with five days and 30 customers.…”

Vehicle Routing Optimization for Surplus Food in Nonprofit Organizations

“…The problem of late collection of donated food staff from the donor and loading of tracks from the food banks severely affects food distribution since any delay accelerate the extent of wastage. Therefore, the presence of close monitoring and delivery of products significantly eliminate the probable long-term wastage in the service industry [5].…”