The last-mile vehicle routing problem with delivery options

Abstract

The ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

Adaptive Large Neighborhood Search for Vehicle Routing Problems with Transshipment Facilities Arising in City Logistics

“…To be precise, we compare the results of our ALNS on the instances to those reported by Ozbaygin et al (2017), Dumez et al (2021a), andTilk et al (2020). To compare our results to those reported by Ozbaygin et al (2017), we set the maximum number of vehicles to the number reported by Ozbaygin et al (2017), as done in Dumez et al (2021a), andTilk et al (2020). In summary, as shown in Tables 5 and 6, we can observe that the best-known values, as reported in the literature, are found for all 120 instances.…”

“…Extending their work on the VRPDO, Dumez et al (2021b) introduce an adapted Balas-Simonetti neighborhood to their LNS to further improve the solution quality. Moreover, Tilk et al (2020), also address the VRPDO and present a branch-price-and-cut algorithm that solves instances with up to 50 customers and 100 options to optimality.…”

“…In order to solve both the VRPRDL and VRPHRDL, Ozbaygin et al (2017) developed a branch-and-price algorithm. Later, Dumez et al (2021a), Dumez et al (2021b), as well as Tilk et al (2020) also study both problems to validate their algorithms for the VRPDO, leading to new best solutions and large time improvements on the instances of Ozbaygin et al (2017) and Reyes et al (2017).…”

“…In order to validate our algorithm's performance on problem instances with time windows, we utilize the 120 instances from the VRPRDL and VRPHRDL of Reyes et al (2017) and Ozbaygin et al (2017) and compare our algorithm with recent studies. To be precise, we compare the results of our ALNS on the instances to those reported by Ozbaygin et al (2017), Dumez et al (2021a), andTilk et al (2020). To compare our results to those reported by Ozbaygin et al (2017), we set the maximum number of vehicles to the number reported by Ozbaygin et al (2017), as done in Dumez et al (2021a), andTilk et al (2020).…”

A Hybrid Genetic Algorithm for the Vehicle Routing Problem with Roaming Delivery Locations

“…The first exact method is a branch-and-price (B&P) algorithm proposed by (Ozbaygin et al 2017), which can solve optimally instances of up to 60 customers and 237 locations within a few minutes. An improved exact method called branchand-price-and-cut is introduced in (Tilk, Olkis, and Irnich 2021). It can find optimal solutions for most of existing instances except seven 120-customer instances.…”