cflp: Capacitated Facility Location Problem (CFLP)

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

Capacitated Facility Location Problem (CFLP)

Description

Solves the Capacitated Facility Location Problem: minimize total weighted distance from demand points to facilities, subject to capacity constraints at each facility. Unlike standard p-median, facilities have limited capacity and demand may need to be split across multiple facilities.

Usage

cflp(
  demand,
  facilities,
  n_facilities,
  weight_col,
  capacity_col,
  facility_cost_col = NULL,
  cost_matrix = NULL,
  distance_metric = "euclidean",
  verbose = FALSE
)

Arguments

demand	An sf object representing demand points.
facilities	An sf object representing candidate facility locations.
n_facilities	Integer. Number of facilities to locate. Set to 0 if using facility_cost_col to determine optimal number.
weight_col	Character. Column name in demand containing demand weights (e.g., population, customers, volume).
capacity_col	Character. Column name in facilities containing capacity of each facility.
facility_cost_col	Optional character. Column name in facilities containing fixed cost to open each facility. If provided and n_facilities = 0, the solver determines the optimal number of facilities to minimize total cost.
cost_matrix	Optional. Pre-computed distance/cost matrix (demand x facilities).
distance_metric	Distance metric: "euclidean" (default) or "manhattan".
verbose	Logical. Print solver progress.

Details

The CFLP extends the p-median problem by adding capacity constraints. Each facility j has a maximum capacity Q_j, and the total demand assigned to it cannot exceed this capacity.

When demand exceeds available capacity at the nearest facility, the solver may split demand across multiple facilities. The .split column indicates which demand points have been split, and the allocation_matrix in metadata shows the exact fractions.

Two modes of operation:

1. Fixed number: Set n_facilities to select exactly that many facilities

2. Cost-based: Set n_facilities = 0 and provide facility_cost_col to let the solver determine the optimal number based on fixed + variable costs

Value

A list with two sf objects:

• ⁠$demand⁠: Original demand sf with .facility column (primary assignment) and .split column (TRUE if demand is split across facilities)

• ⁠$facilities⁠: Original facilities sf with .selected, .n_assigned, and .utilization columns

Metadata is stored in the "spopt" attribute, including:

• objective: Total cost (transportation + facility costs if applicable)

• mean_distance: Mean weighted distance

• n_split_demand: Number of demand points split across facilities

• allocation_matrix: Full allocation matrix (n_demand x n_facilities)

References

Daskin, M. S. (2013). Network and discrete location: Models, algorithms, and applications (2nd ed.). John Wiley & Sons. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/9781118537015")}

Sridharan, R. (1995). The capacitated plant location problem. European Journal of Operational Research, 87(2), 203-213. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/0377-2217(95)00042-O")}

Examples

library(sf)

# Demand points with population
demand <- st_as_sf(data.frame(
  x = runif(100), y = runif(100), population = rpois(100, 500)
), coords = c("x", "y"))

# Facilities with varying capacities
facilities <- st_as_sf(data.frame(
  x = runif(15), y = runif(15),
  capacity = c(rep(5000, 5), rep(10000, 5), rep(20000, 5)),
  fixed_cost = c(rep(100, 5), rep(200, 5), rep(400, 5))
), coords = c("x", "y"))

# Fixed number of facilities
result <- cflp(demand, facilities, n_facilities = 5,
               weight_col = "population", capacity_col = "capacity")

# Check utilization
result$facilities[result$facilities$.selected, c("capacity", ".utilization")]

# Cost-based (optimal number of facilities)
result <- cflp(demand, facilities, n_facilities = 0,
               weight_col = "population", capacity_col = "capacity",
               facility_cost_col = "fixed_cost")
attr(result, "spopt")$n_selected

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