Proactive Depot Discovery: A Generative Framework for Flexible Location-Routing

The Location-Routing Problem (LRP), which combines the challenges of facility (depot) locating and vehicle route planning, is critically constrained by the reliance on predefined depot candidates, limiting the solution space and potentially leading to suboptimal outcomes. Previous research on LRP without predefined depots is scant and predominantly relies on heuristic algorithms that iteratively attempt depot placements across a planar area. Such approaches lack the ability to proactively generate depot locations that meet specific geographic requirements, revealing a notable gap in current research landscape. To bridge this gap, we propose a data-driven generative DRL framework, designed to proactively generate depots for LRP without predefined depot candidates, solely based on customer requests data which include geographic and demand information. It can operate in two distinct modes: direct generation of exact depot locations, and the creation of a multivariate Gaussian distribution for flexible depots sampling. By extracting depots' geographic pattern from customer requests data, our approach can dynamically respond to logistical needs, identifying high-quality depot locations that further reduce total routing costs compared to traditional methods. Extensive experiments demonstrate that, for a same group of customer requests, compared with those depots identified through random attempts, our framework can proactively generate depots that lead to superior solution routes with lower routing cost. The implications of our framework potentially extend into real-world applications, particularly in emergency medical rescue and disaster relief logistics, where rapid establishment and adjustment of depot locations are paramount, showcasing its potential in addressing LRP for dynamic and unpredictable environments.