Adaptive Large Neighborhood Search Metaheuristic for the Capacitated Vehicle Routing Problem with Parcel Lockers

Abstract

With the expansion of online shopping, urban logistics must handle the increasing customer demand, making the last-mile delivery process more challenging. Furthermore, this expansion significantly contributes to companies’ distribution costs. To overcome some of the last-mile delivery costs, parcel lockers-as a delivery option-can be an alternative solution. Parcel lockers extend delivery options beyond home delivery, offering cost-saving benefits. However, incorporating multiple delivery options introduces additional complexity to the delivery management system. Existing studies on the Capacitated Vehicle Routing Problem (CVRP) have primarily focused on home delivery. This study provides a mathematical model and a solution algorithm for the Capacitated Vehicle Routing Problem with Delivery Options (CVRPDO), which includes locker delivery as one of the delivery options. The problem involves creating a set of routes for vehicles that visit each customer at their delivery location or deliver their parcels to one of the lockers. These routes should respect the capacity of each vehicle and the capacities at shared delivery locations while minimizing the total routing costs and the number of utilized vehicles. This problem is solved with An Adaptive Large Neighborhood Search (ALNS). The solution suggests some specific destroy and repair operators and integrates them with various selection schemes. The proposed method results are compared with the exact solution of the MIP model of the problem for validation. Also, it was found that the ALNS algorithm outperformed the solver solution, especially with large-size instances. The results of objective function values were improved when solving the problem with an ALNS with a 120 s runtime compared with the MIP model (with a runtime of 3 h) by 25%, 30%, 7%, 5%, and 6% for 1000, 800, 600, 400, and 200 customers, respectively.

Tri-Objective Vehicle Routing Problem to Optimize the Distribution Process of Sustainable Local E-Commerce Platforms

“…Ropke and Pisinger [19] propose an adaptive selection of the LS operator to use at each iteration according to the solutions generated by each LS operator in the previous iterations. Although adaptive algorithms are widely adopted in single-objective problems, even when dealing with the latest topics like electric vehicles [20] and parcel lockers [21], they are still rarely implemented to address multiple goals [22].…”

“…Therefore, some of the solutions in the archive could be removed if they are dominated by s ′ . If one of the Pareto solutions dominates s ′ , this latter does not concur to define the Pareto front but it could be selected as the reference solution s* for the next iteration of the MOSA with a probability computed in Equation (21). In particular, the probability to select s ′ as the new s* is computed as the product, for each objective o ∈ O, of the exponential of the difference between the objective function calculated for s ′ (f o s ′ ) and the objective function calculated for s* (f o s* ) divided by the current temperature temp.…”

A Compact Model for the Clustered Orienteering Problem

“…We refer the interested reader to [3][4][5][6] for exhaustive reviews of the scientific literature on these problems. Optimization approaches for last-mile logistics, in general, have become more and more popular in recent years due to the dramatic increase in e-commerce [7], which automatically generates a great need for effective operational solutions [8][9][10][11][12].…”