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The Electric Location-Routing Problem: Improved Formulations and Effects of Nonlinear Charging

Luiz Eduardo Cotta Monteiro, Rafael Martinelli

TL;DR

This paper tackles the Electric Location-Routing Problem (ELRP) by incorporating nonlinear charging and multiple charging-station types to better design EV fleets and charging infrastructure. It introduces the ELRP-NLMS, extending classic ELRP with a piecewise nonlinear charging model and four distinct mixed-integer programming formulations, including node-based, arc-based, recharge-arc, and recharge-path approaches, plus preprocessing to prune dominated recharge paths. Computational experiments on 80 instances show that the new formulations, especially the arc- and path-based ones, significantly reduce the average optimality gap from $29.1\%$ to $11.9\%$ and yield improved solutions in many cases compared to the node-based baseline. The study also reveals that accounting for nonlinear charging can meaningfully alter charging-location and routing decisions, underscoring the importance of realistic charging behavior in ELRP planning and infrastructure design. The work provides new instances, methodological contributions (improved formulations and preprocessing), and insights that can guide practitioners in EV logistics network design and future research directions such as metaheuristics and stochastic extensions.

Abstract

Electric Location-Routing models (ELRP) can contribute to the effective planning of electric vehicles (EVs) fleets and charging infrastructure within EV logistic networks because it simultaneously combines routing and location decisions to find optimal solutions to the network design. This study introduces ELRP models that incorporate nonlinear charging process, multiple charging station types and develop new improved formulations to the problem. Existing ELRP models commonly assume a linear charging process and employ a node-based formulation for tracking EV energy and time consumption. In contrast, we propose novel formulations offering alternative approaches for modeling EV energy, time consumption, and nonlinear charging. Through extensive computational experiments, our analysis demonstrates the effectiveness of the new formulations, reducing the average gap from 29.1% to 11.9%, yielding improved solutions for 28 out of 74 instances compared to the node-based formulation. Moreover, our findings provide valuable insights into the strategic implications of nonlinear charging in ELRP decision-making, offering new perspectives for planning charging infrastructure in EV logistic networks.

The Electric Location-Routing Problem: Improved Formulations and Effects of Nonlinear Charging

TL;DR

This paper tackles the Electric Location-Routing Problem (ELRP) by incorporating nonlinear charging and multiple charging-station types to better design EV fleets and charging infrastructure. It introduces the ELRP-NLMS, extending classic ELRP with a piecewise nonlinear charging model and four distinct mixed-integer programming formulations, including node-based, arc-based, recharge-arc, and recharge-path approaches, plus preprocessing to prune dominated recharge paths. Computational experiments on 80 instances show that the new formulations, especially the arc- and path-based ones, significantly reduce the average optimality gap from to and yield improved solutions in many cases compared to the node-based baseline. The study also reveals that accounting for nonlinear charging can meaningfully alter charging-location and routing decisions, underscoring the importance of realistic charging behavior in ELRP planning and infrastructure design. The work provides new instances, methodological contributions (improved formulations and preprocessing), and insights that can guide practitioners in EV logistics network design and future research directions such as metaheuristics and stochastic extensions.

Abstract

Electric Location-Routing models (ELRP) can contribute to the effective planning of electric vehicles (EVs) fleets and charging infrastructure within EV logistic networks because it simultaneously combines routing and location decisions to find optimal solutions to the network design. This study introduces ELRP models that incorporate nonlinear charging process, multiple charging station types and develop new improved formulations to the problem. Existing ELRP models commonly assume a linear charging process and employ a node-based formulation for tracking EV energy and time consumption. In contrast, we propose novel formulations offering alternative approaches for modeling EV energy, time consumption, and nonlinear charging. Through extensive computational experiments, our analysis demonstrates the effectiveness of the new formulations, reducing the average gap from 29.1% to 11.9%, yielding improved solutions for 28 out of 74 instances compared to the node-based formulation. Moreover, our findings provide valuable insights into the strategic implications of nonlinear charging in ELRP decision-making, offering new perspectives for planning charging infrastructure in EV logistic networks.

Paper Structure

This paper contains 21 sections, 15 equations, 12 figures, 17 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. The ELRP-NLMS: Problem definition and first model formulation
  4. First ELRP-NLMS model formulation
  5. Strengthened first ELRP-NLMS model
  6. Improved model formulations
  7. Second ELRP-NLMS model formulation: Time and energy arc tracking
  8. Third ELRP-NLMS model formulation: Recharge arc model
  9. Forth ELRP-NLMS model formulation: Recharge path model
  10. Preprocessing of recharge paths
  11. Computational Experiments
  12. ELRP-NLMS Instance Generation
  13. Result Analysis
  14. Effects of nonlinear charging function on ELRP decisions
  15. Conclusions
  16. ...and 6 more sections

Figures (12)

  • Figure 1: Piecewise linear approximation for different types of CS charging (adapted from Montoya et al., 2017).
  • Figure 2: General results per model type.
  • Figure 3: Optimality Gap comparison per instance group.
  • Figure 4: Linear charge function and non-linear piecewise approximation charging function. (Adapted from Montoya et al., 2017)
  • Figure 5: Detailed solution for instance 12 in ELRP-Linear and ELRP-NLMS
  • ...and 7 more figures