Solving Resource Recharging Station Location-routing Problem through a Resource-space-time Network Representation

TL;DR

This paper introduces a novel resource-space-time network model and an Lagrangian relaxation-based algorithm to optimize the location and routing of recharging stations in resource-constrained vehicle routing problems.

Contribution

It presents a generic ILP formulation and a decomposition framework that simplifies complex constraints and efficiently solves large-scale resource recharging station location-routing problems.

Findings

Effective in large-scale networks

Lagrangian relaxation improves solution quality

Model simplifies complex resource constraints

Abstract

The resource recharging station location routing problem is a generalization of the location routing problem with sophisticated and critical resource consumption and recharging constraints. Based on a representation of discretized acyclic resource-space-time networks, we propose a generic formulation to optimize dynamic infrastructure location and routes decisions. The proposed integer linear programming formulation could greatly simplify the modeling representation of time window, resource change, and sub-tour constraints through a well-structured multi-dimensional network. An approximation solution framework based on the Lagrangian relaxation is developed to decompose the problem to a knapsack sub-problem for selecting recharging stations and a vehicle routing sub-problem in a space-time network. Both sub-problems can be solved through dynamic programming algorithms to obtain optimal solution. A number of experiments are used to demonstrate the Lagrangian multiplier adjustment-based location routing decision making, as well as the effectiveness of the developed algorithm in large-scale networks.