Problem of Locating and Allocating Charging Equipment for Battery Electric Buses under Stochastic Charging Demand

TL;DR

This paper develops an optimization framework for efficiently locating and allocating charging stations for battery electric buses, considering stochastic demand and queueing dynamics, with scalable algorithms and a case study demonstrating cost benefits.

Contribution

It introduces a novel MINLP model for PLACE-BEB, incorporating queueing and stochastic demand, and proposes scalable solution algorithms like SA and GA for large-scale problems.

Findings

GA outperforms other algorithms for large-scale problems

Joint deployment of charging stations reduces overall costs

Waiting time significantly impacts station placement decisions

Abstract

Bus electrification plays a crucial role in advancing urban transportation sustainability. Battery Electric Buses (BEBs), however, often need recharging, making the Problem of Locating and Allocating Charging Equipment for BEBs (PLACE-BEB) essential for efficient operations. This study proposes an optimization framework to solve the PLACE-BEB by determining the optimal placement of charger types at potential locations under the stochastic charging demand. Leveraging the existing stochastic location literature, we develop a Mixed-Integer Non-Linear Program (MINLP) to model the problem. To solve this problem, we develop an exact solution method that minimizes the costs related to building charging stations, charger allocation, travel to stations, and average queueing and charging times. Queueing dynamics are modeled using an M/M/s queue, with the number of servers at each location treated as a decision variable. To improve scalability, we implement a Simulated Annealing (SA) and a Genetic Algorithm (GA) allowing for efficient solutions to large-scale problems. The computational performance of the methods was thoroughly evaluated, revealing that SA was effective for small-scale problems, while GA outperformed others for large-scale instances. A case study comparing garage-only, other-only, and mixed scenarios, along with joint deployment, highlighted the cost benefits of a collaborative and a comprehensive approach. Sensitivity analyses showed that the waiting time is a key factor to consider in the decision-making.