Vehicle Routing Problem with Reverse Cross-Docking: An Adaptive Large Neighborhood Search Algorithm

Abstract

Cross-docking is a logistics strategy that aims at less transportation costs and fast customer deliveries. Incorporating an efficient vehicle routing could increase the benefits of the cross-docking. In this paper, the vehicle routing problem with reverse cross-docking (VRP-RCD) is studied. Reverse logistics has attracted more attention due to its ability to gain more profit and maintain the competitiveness of a company. VRP-RCD includes a four-level supply chain network: suppliers, crossdock, customers, and outlets, with the objective of minimizing vehicle operational and transportation costs. A two-phase heuristic employs an adaptive large neighborhood search (ALNS) with various destroy and repair operators is proposed to solve benchmark instances. The simulated annealing framework is embedded to discover a vast search space during the search process. Experimental results show that our proposed ALNS obtains optimal solutions for 24 out of 30 problems of the first set of benchmark instances while getting better results for all instances in the second set of benchmark instances compared to optimization software.

Vehicle Routing Problem with Forward and Reverse Cross-Docking: Formulation and Matheuristic Approach

“…Constraint (9) ensures that if a vehicle visits suppliers, then that vehicle starts the trip from the cross-dock. Constraint (10) ensures the outflow and inflow of a vehicle. Constraint (11) ensures that each supplier is visited at most once.…”

“…The first phase aims to find as many candidate routes as possible (Algorithm 1 Lines 1-38), while the second phase focuses on determining the best route combination over all routes found in the first phase (Algorithm 1 Line 39). We adopted the ALNS of [10] for the first phase (Section III-A). In order to handle the second stage, we formulate a set partitioning formulation and solve it by an optimization solver, CPLEX (Section III-B).…”

“…In order to handle the second stage, we formulate a set partitioning formulation and solve it by an optimization solver, CPLEX (Section III-B). The difference between the VRP-RCD [10] and the VRP-FRCD is that the VRP-RCD includes the individual pickup (delivery) process in the retailer (supplier) nodes, while the VRP-FRCD includes a simultaneous pickup and delivery process in both retailer and supplier nodes. Hence in the VRP-FRCD, supplier i is visited (m i = 1) if there is any returned products sent (supplied products) to (from) supplier i; 0 otherwise, and retailer i is visited (m i = 1) if there is any delivery (returned products) to (from) retailer i; 0 otherwise.…”

“…In previous work [9], we studied the VRP with reverse cross-docking (VRP-RCD) that models a four-level supply chain network consisting of suppliers, customers (more appropriate to be addressed as retailers), outlets, and a cross-dock facility. In [10] and [11], we revisited this VRP-RCD and designed an adaptive large neighborhood search (ALNS) algorithm and matheuristic to effectively solve the problem, respectively.…”

“…The proposed VRP-FRCD is formally presented as a mixed integer linear programming model. Then we design a two-phase matheuristic including an ALNS algorithm (adopted from [10]) and set partitioning (adopted from [11]) to effectively solve the problem.…”