Improved Approximation Algorithms for the Multiple-Depot Split Delivery Vehicle Routing Problem

The multiple-depot split delivery vehicle routing problem is a challenging optimization problem with broad applications in logistics and transportation. The goal is to serve customers' demand using a limited fleet of capacitated vehicles stationed at multiple depots, allowing each customer's demand to be split and served by multiple vehicles, while minimizing the total travel cost. Parameterized by the number of depots, the previous best-known result was a slice-wise polynomial-time $6$-approximation algorithm (INFORMS J. Comput. 2023), and whether this ratio could be improved remained an open question. We resolve this question by proposing a fixed-parameter tractable (FPT) $(2α+1+\varepsilon)$-approximation algorithm for any constant $\varepsilon>0$, where $α