Optimizing EV Charger Placement in Northwest Arkansas

🚗 Optimizing EV Charger Placement in Northwest Arkansas

Final OR Project — Urban Charging Accessibility Model

Team: Drake Wolfenden, Fernando Nunez

Project Summary & Skills Used

Our project developed a p-median–style optimization model to determine where Northwest Arkansas should install new DC fast-charging stations. The model minimizes total population-weighted travel distance across 33 ZIP codes in Benton and Washington Counties.

Industrial Engineering concepts applied:

  • Facility-location modeling
  • Integer programming
  • Geographic data synthesis
  • Scenario and sensitivity analysis

Skills used:

  • AMPL modeling and debugging
  • Geographic data collection and cleaning
  • Constructing a full ZIP-to-ZIP distance matrix
  • Interpreting optimization output and communicating results

Project Development Process

The project involved creating a mathematical model, preparing several data tables, and translating the full system into AMPL. Major challenges included formatting the distance matrix correctly, ensuring ZIP identifiers aligned across all data files, and configuring the assignment and open-station constraints so AMPL produced feasible solutions. Scenario testing for multiple values of p also required additional validation and interpretation.

Throughout the build, we used maps, intermediate data checks, and solver outputs to verify that the assignments and chosen sites matched geographic intuition and model logic.

Key Features or Highlights

1. Mathematical Optimization Model

We created a facility-location optimization model that selects which ZIP codes should host new EV fast-charging stations and assigns each demand ZIP to exactly one of the open stations. The goal of the model is to minimize the total population-weighted travel distance across Northwest Arkansas.

Decision Variables

  • y_j indicates whether a new station is built in ZIP code j. If the value is 1, a station is installed there; if it is 0, it is not selected.
  • x_ij represents the portion of demand from ZIP code i that is assigned to the station located in ZIP code j. Although this is modeled as a fractional variable, it effectively behaves like a 0–1 assignment in the optimal solution.

Parameters

  • w_i is the population of ZIP code i and serves as the demand weight in the model.
  • d_ij is the distance between ZIP code i and ZIP code j, calculated using centroid-to-centroid distances.
  • p is the number of new charging stations the model is allowed to open. We tested scenarios with p equal to 3, 5, and 7.

Objective

The objective of the model is to minimize the total population-weighted travel distance. This means the model attempts to place stations in ZIP codes that reduce the amount of travel required for the largest number of residents.

Constraints

  1. Each ZIP must be fully assigned.
    Every demand ZIP must be assigned entirely to exactly one charging station. This ensures 100 percent of regional demand is covered.

  2. Demand can only be assigned to ZIPs that have a station.
    A ZIP code is only allowed to send demand to another ZIP if a station is built there. If no station exists at a location, no demand can be assigned to it.

  3. Exactly p stations must be opened.
    The model enforces that the solution includes exactly p new charging stations. This reflects the planning budget or investment level being evaluated.

2. Data Collection & Parameter Construction

Data originated from:

SimpleMaps (2024). United States ZIP Code Database.
https://simplemaps.com/data/us-zips

Steps: - Filtered ZIP codes to Benton & Washington Counties
- Extracted populations → demand weights w_i
- Used ZIP centroid coordinates to compute d_ij via the Haversine formula
- Constructed a complete 33×33 distance matrix
- Entered all parameters into AMPL tables
- Treated p as a scenario variable to study multiple planning cases

Results & Scenario Analysis

We tested three investment levels:
- p = 3 (minimal)
- p = 5 (baseline)
- p = 7 (expanded network)

Each run identified optimal station ZIPs, assignment patterns, and total weighted travel distances.

Baseline Scenario (p = 5)

Total population: 541,371
Average distance: 4.56 miles per person

Selected ZIPs:
- 72701
- 72704
- 72712
- 72758
- 72764

These ZIPs align with Fayetteville, Springdale, Rogers, and Bentonville—areas with the largest populations and strongest geographic centrality.

Scenario p = 3

Average distance: 6.87 miles

Chosen ZIPs (72704, 72712, 72764) must absorb very large population loads, and rural ZIPs travel significantly farther. This confirms that three stations provide insufficient coverage.

Scenario p = 7

Average distance: 3.23 miles

Additional stations appear in more peripheral ZIPs (e.g., 72756, 72761), reducing distances for previously underserved areas.

Diminishing Returns

p Avg Distance
3 6.87 miles
5 4.56 miles
7 3.23 miles

The largest improvement occurs when increasing from 3 → 5 stations. Further expansion improves rural accessibility but yields smaller overall distance reductions.

Reflection

This project strengthened my understanding of how optimization models support real planning problems. Working through the full process—from model formulation to data construction, implementation, and scenario interpretation—helped me build confidence in designing OR models that use real datasets and geographic information. I also improved at debugging AMPL, validating assumptions, and interpreting solver output in a decision-focused way. Overall, this experience made facility-location modeling and AMPL feel much more intuitive and reinforced how OR tools can guide infrastructure planning in a meaningful way.