Collaborative multi-depot logistics network design with time window assignment

Abstract

In logistics operation, delivery times are often uncertain for customers, and accommodating this uncertainty poses operation challenges as well as extra cost for logistics service providers. The delivery time uncertainty is particularly an issue if there are multiple service providers in a logistics network. To address this issue, we formulate and solve a collaborative multi-depot vehicle routing problem with time window assignment (CMDVRPTWA) to effectively reduce the impact of changing time windows on operating costs. This paper establishes a bi-objective programming model that optimize the total operating cost and the total number of delivery vehicles. A hybrid heuristic algorithm consisting of K-means clustering, Clarke–Wright (CW) saving algorithm and an Extended Non-dominated Sorting Genetic Algorithm-II (E-NSGA-II) is presented to efficiently solve CMDVRPTWA. The clustering and CW saving algorithm are employed to increase the likelihood of finding the optimal vehicle routes by identifying a feasible initial solution. The E-NSGA-II procedure combines partial-mapped crossover (PMC), relocation, 2-opt* exchange and swap mutation operations to find the optimal solution with pre-defined iteration and termination rules. Profit allocation schemes are then analyzed using the Game Quadratic Programming (GQP) method, and the optimal sequences of joining coalitions are obtained based on the principle that coalition participants’ benefits should be non-decreasing when a new participant joins the coalition. We conduct three empirical studies on a small-scale example, on several benchmark datasets and on a large-scale logistics network in Chongqing city, China. Further comparative analysis indicates that E-NSGA-II outperforms most other algorithms in solving CMDVRPTWA. This novel approach identifies profit allocation strategies that ensure the stability and reliability of the collaborative coalitions in the context of flexible customer service time windows, and can be utilized to improve the efficiency of urban logistics and intelligent transportation networks.