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The resource recharging station location routing problem is a generalizationof the location routing problem with sophisticated and critical resourceconsumption and recharging constraints. Based on a representation ofdiscretized acyclic resource-space-time networks, we propose a genericformulation to optimize dynamic infrastructure location and routes decisions.The proposed integer linear programming formulation could greatly simplify themodeling representation of time window, resource change, and sub-tourconstraints through a well-structured multi-dimensional network. Anapproximation solution framework based on the Lagrangian relaxation isdeveloped to decompose the problem to a knapsack sub-problem for selectingrecharging stations and a vehicle routing sub-problem in a space-time network.Both sub-problems can be solved through dynamic programming algorithms toobtain optimal solution. A number of experiments are used to demonstrate theLagrangian multiplier adjustment-based location routing decision making, aswell as the effectiveness of the developed algorithm in large-scale networks.

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