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

The Location-Routing Problem (LRP) is a critical optimization challenge in the urban logistics industry, combining two interdependent decisions: selecting depot locations where vehicles commence and conclude their tasks, and planning vehicle routes for serving customers. This integration is crucial as the depot locations can directly affect the vehicle route planning, thereby impacting overall costs [1]. The LRP can be formally defined as [2]: Given a set of customers with specific location and quantity of demands, and a set of potential depot candidates each with a fleet of vehicles featuring fixed capacity, aiming to properly select a subset of depots and plan routes for vehicles departing from these chosen depots to meet customers' demands, while minimizing both depot-related and route-related costs, without violating specific constraints. In this traditional problem configuration, solving LRP have relied on a predefined set of depot candidates [3, 4, 5, 6] instead of directly generating desired optimal depot locations, thereby limiting the solution space and potentially leading to suboptimal outcomes. This constraint is particularly pronounced in scenarios where the optimal depot locations are not included in the candidates set, or when the problem configuration demands a high degree of flexibility in depot placement, requiring quickly establish and adjust depot locations. The real-world application that underscores the necessity of generating depots without predefined candidates is medical rescue and disaster relief logistics: In the aftermath of a natural disaster, such as an earthquake or flood, the existing infrastructure may be severely damaged, rendering previously established depots unusable. In such scenarios, the ability to dynamically generate new depot locations based on current needs and constraints is crucial for efficient and effective relief operations.