Leveraging Electric School Buses for Disaster Recovery: Optimizing Routing and Energy Scheduling via Branch-and-Price

Abstract

Natural disasters threaten the resilience of power systems, causing widespread power outages that disrupt critical loads (e.g., hospitals) and endanger public safety. Compared to the conventional restoration methods that often have long response times, leveraging government-controlled electric school buses (ESBs) with large battery capacity and deployment readiness offers a promising solution for faster power restoration to critical loads during disasters while traditional maintenance is underway. Therefore, we study the problem of routing and scheduling a heterogeneous fleet of ESBs to satisfy the energy demand of critical isolated loads around disasters addressing the following practical aspects: combined transportation and energy scheduling of ESBs, multiple back-and-forth trips of ESBs between isolated loads and charging stations, and spatial-wise coupling among multiple ESB routes. We propose an efficient mixed-integer programming model for routing and scheduling ESBs, accounting for the practical aspects, to minimize the total restoration cost over a planning horizon. We develop an efficient exact branch-and-price (B&P) algorithm and a customized heuristic B&P algorithm integrating dynamic programming and labeling algorithms. Numerical results based on a real case study of San Antonio disaster shelters and critical facilities demonstrate that our proposed exact B&P and heuristic B&P algorithms are computationally 121 and 335 times faster, respectively, than Gurobi. Using network sparsity to incorporate the limitation in shelter-ESB type compatibility in the model demonstrates that the total restoration cost increases, on average, by 207% as the network becomes fully sparse compared to fully connected. The capacity utilization metric reflects that the proposed practical ESB routing and scheduling enables an ESB to meet the energy demand 4.5 times its effective usable capacity.

Figures (8)

• Figure 1: Visualization of the problem and model for routing and scheduling of ESBs.
• Figure 2: The flowchart of the LA-integrated DP.
• Figure 3: Geographical locations of mega-shelters, CSs, and the depot in the case study.
• Figure 4: Effect of network sparsity level on the (a) total cost, and (b) required fleet composition.
• Figure 5: Effect of shelters' energy demand on total cost and required fleet composition.

Theorems & Definitions (10)

• Remark 1
• Proposition 1
• Proposition 2
• Proposition 3
• Proposition \ref{prop:symmetry_breaking}
• proof
• Proposition \ref{prop:NP-hardness}
• proof
• Proposition \ref{prop_dominance}
• proof