Multidepot Capacitated Vehicle Routing with Improved Approximation Guarantees
arxiv(2023)
摘要
The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-known
variant of the classic Capacitated Vehicle Routing Problem (CVRP), where we
need to route capacitated vehicles located in multiple depots to serve
customers' demand such that each vehicle must return to the depot it starts,
and the total traveling distance is minimized. There are three variants of
MCVRP according to the property of the demand: unit-demand, splittable and
unsplittable. We study approximation algorithms for k-MCVRP in metric graphs,
where k is the capacity of each vehicle. The best-known approximation ratios
for the three versions are 4-Θ(1/k), 4-Θ(1/k), and 4,
respectively. We give a (4-1/1500)-approximation algorithm for unit-demand
and splittable k-MCVRP, and a (4-1/50000)-approximation algorithm for
unsplittable k-MCVRP. When k is a fixed integer, we give a
(3+ln2-max{Θ(1/√(k)),1/9000})-approximation algorithm for the
splittable and unit-demand cases, and a
(3+ln2-Θ(1/√(k)))-approximation algorithm for the unsplittable
case.
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