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Extreme-Scale EV Charging Infrastructure Planning for Last-Mile Delivery Using High-Performance Parallel Computing

Waquar Kaleem, Taner Cokyasar, Jeffrey Larson, Omer Verbas, Tanveer Hossain Bhuiyan, Anirudh Subramanyam

TL;DR

This work tackles extreme-scale planning of last-mile EV charging under stochastic demand and queueing congestion, formulating the stochastic charger location and allocation problem (SCLA) as a mixed-integer nonlinear program. To overcome intractability at metropolitan scales, it develops a Lagrangian dual decomposition that splits the problem by station, enabling parallel solution of station-level subproblems on HPC, coupled with a cutting-plane approach for nonlinear waiting-time constraints and a three-step rounding heuristic to obtain feasible integral solutions. The authors provide two exact reformulations (MIQP and MCC) and demonstrate, using Chicago-area data with hundreds of thousands of households, that the Lagrangian framework substantially outperforms direct exact methods in solvability and solution quality for extreme instances, while enabling actionable policy insights such as the benefits of multiagency collaboration and depot-plus-TAZ installations. The results show that combining existing depots with newly built stations in a multiagency setting can markedly reduce costs and congestion, offering a scalable, efficient framework for designing sustainable large-scale EV charging networks. Overall, the paper delivers a rigorous, scalable optimization methodology that supports strategic planning for expansive EV charging infrastructure in urban logistics contexts.

Abstract

This paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Extreme-Scale EV Charging Infrastructure Planning for Last-Mile Delivery Using High-Performance Parallel Computing

TL;DR

This work tackles extreme-scale planning of last-mile EV charging under stochastic demand and queueing congestion, formulating the stochastic charger location and allocation problem (SCLA) as a mixed-integer nonlinear program. To overcome intractability at metropolitan scales, it develops a Lagrangian dual decomposition that splits the problem by station, enabling parallel solution of station-level subproblems on HPC, coupled with a cutting-plane approach for nonlinear waiting-time constraints and a three-step rounding heuristic to obtain feasible integral solutions. The authors provide two exact reformulations (MIQP and MCC) and demonstrate, using Chicago-area data with hundreds of thousands of households, that the Lagrangian framework substantially outperforms direct exact methods in solvability and solution quality for extreme instances, while enabling actionable policy insights such as the benefits of multiagency collaboration and depot-plus-TAZ installations. The results show that combining existing depots with newly built stations in a multiagency setting can markedly reduce costs and congestion, offering a scalable, efficient framework for designing sustainable large-scale EV charging networks. Overall, the paper delivers a rigorous, scalable optimization methodology that supports strategic planning for expansive EV charging infrastructure in urban logistics contexts.

Abstract

This paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Paper Structure

This paper contains 42 sections, 1 theorem, 34 equations, 3 figures, 9 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Model Description
  4. Modeling Household Demand
  5. Modeling EV Operations
  6. Modeling Congestion and Network Closure
  7. Modeling Costs and Budget Constraints
  8. Final Optimization Model
  9. Differences with Existing Models
  10. Exact Solution Method
  11. A Valid Inequality
  12. Binary Representation of the Number of Chargers
  13. Linearizing the Objective Function
  14. Cutting-Plane Approach for Nonlinear Constraints
  15. Summary of Exact Formulations
  16. ...and 27 more sections

Key Result

Theorem 1

For any $j\in\mathcal{J}$, the inequality $\sum_{k \in \mathcal{K}} x_{ijk} \leq 1$ for all $i\in\mathcal{I}_j$ is valid for model $\mathbb G$.

Figures (3)

  • Figure 1: Illustration of the spatial distribution of households, potential charging stations, and existing charging depots across the Chicago metropolitan area.
  • Figure 2: Spatial distribution of open depot and TAZ stations
  • Figure 3: Sensitivity analysis of changes in $\mathbb{C}$ under various parameter adjustments.

Theorems & Definitions (5)

  • Remark 3.1: Neighborhood-level risk pooling
  • Remark 3.2: Probabilistic interpretation of fractional assignments
  • Theorem 1
  • proof
  • Remark 4.1: Extension to the $M/G/s_{jk}$ Case