frlm: Flow Refueling Location Model (FRLM)

In spopt: Spatial Optimization for Regionalization, Facility Location, and Market Analysis

Flow Refueling Location Model (FRLM)

Description

Solves the Flow Refueling Location Model to optimally place refueling facilities along network paths. This model maximizes the volume of origin-destination flows that can be served given vehicle range constraints.

Usage

frlm(
  flows,
  candidates,
  network = NULL,
  vehicle_range,
  n_facilities,
  method = c("greedy"),
  verbose = FALSE
)

Arguments

flows	A data frame or sf object containing flow information with columns: origin: Origin identifier destination: Destination identifier volume: Flow volume (e.g., number of trips)
candidates	An sf object with candidate facility locations (points).
network	Optional. A distance matrix between candidates. If NULL (default), Euclidean distances are computed from candidate geometries. For network distances, compute externally using packages like r5r or dodgr and pass the resulting matrix here.
vehicle_range	Numeric. Maximum vehicle range (same units as network distances).
n_facilities	Integer. Number of facilities to place.
method	Character. Optimization method: "greedy" (default and currently only option).
verbose	Logical. Print progress messages.

Details

The Flow Refueling Location Model (Kuby & Lim, 2005) addresses the problem of locating refueling stations for range-limited vehicles (e.g., electric vehicles, hydrogen fuel cell vehicles) along travel paths.

A flow (origin-destination path) is "covered" if a vehicle can complete the round trip with refueling stops at the selected facilities. The model assumes:

• Vehicles start at the origin with half a tank (can travel R/2)

• At each open station, vehicles refuel to full (can travel R)

• The round trip must be completable without running out of fuel

For a flow to be covered, three conditions must be met:

1. First open station must be within R/2 from origin (half-tank start)

2. Each subsequent open station must be within R of the previous

3. Last open station must be within R/2 of destination (to allow return)

This implementation uses a greedy heuristic that iteratively selects the facility providing the greatest marginal increase in covered flow volume.

Value

A list with class "spopt_frlm" containing:

• facilities: The candidates sf object with a .selected column

• selected_indices: 1-based indices of selected facilities

• coverage: Coverage statistics

Metadata is stored in the "spopt" attribute.

Input Format

For simple cases, you can provide:

• flows: Data frame with origin, destination, volume

• candidates: sf points for potential facility locations

• network: Pre-computed distance matrix (optional)

References

Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125-145. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.seps.2004.03.001")}

Capar, I., & Kuby, M. (2012). An efficient formulation of the flow refueling location model for alternative-fuel stations. IIE Transactions, 44(8), 622-636. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/0740817X.2011.635175")}

Examples

# Simple example with distance matrix
library(sf)

# Create candidate locations
candidates <- st_as_sf(data.frame(
  id = 1:10,
  x = runif(10, 0, 100),
  y = runif(10, 0, 100)
), coords = c("x", "y"))

# Create flows (using candidate indices as origins/destinations)
flows <- data.frame(
  origin = c(1, 1, 3, 5),
  destination = c(8, 10, 7, 9),
  volume = c(100, 200, 150, 300)
)

# Solve with vehicle range of 50 units
result <- frlm(flows, candidates, vehicle_range = 50, n_facilities = 3)

# View selected facilities
result$facilities[result$facilities$.selected, ]

spopt documentation built on April 22, 2026, 9:07 a.m.