Compute the maximal coverage location-allocation for discrete problems

allocation_discrete() allocates facilities in a discrete location problem. It uses the accumulated cost algorithm to identify optimal facility locations based on the share of demand to be covered, given a user-defined set of candidate locations and a maximum number of allocable facilities.

If a objectiveshare parameter is specified, the algorithm identifies the best set of size of up to n_fac facilities to achieve the targeted coverage share. The problem is solved using a statistical heuristic approach that generates samples of the candidate locations (on top of the existing locations) and selects the facilities in the one that minimizes the objective function.

See allocation() for continuous location-allocation problems.

Usage

allocation_discrete(
  demand,
  bb_area,
  candidate,
  facilities = NULL,
  n_fac = Inf,
  n_samples = 1000,
  traveltime = NULL,
  mode = "walk",
  dowscaling_model_type = "lm",
  res_output = 100,
  weights = NULL,
  objectiveminutes = 15,
  objectiveshare = NULL,
  approach = "norm",
  exp_demand = 1,
  exp_weights = 1,
  par = FALSE
)

Arguments

demand

A RasterLayer object with the demand layer (e.g. population density).

bb_area

A sf boundary box object with the area of interest.

candidate

A sf object with the candidate locations for the new facilities.

facilities

A sf object with the existing facilities.

n_fac

(optional) A positive integerish number indicating the maximum number of facilities that can be allocated (default: Inf).

n_samples

(optional) A positive integerish number indicating the number of samples to generate in the heuristic approach for identifying the best set of facilities to be allocated (default: 1000).

traveltime

A list with the output of the traveltime() function. If not provided, the function will run the traveltime() function based on the provided parameters.

mode

(optional) A character string indicating the mode of transport. Options are "fastest" and "walk" (default = "walk").

For "fastest": The friction layer accounts for multiple modes of transport, including walking, cycling, driving, and public transport, and are based on the Malaria Atlas Project (2019) Global Travel Speed Friction Surface.
For "walk": The friction layer accounts only for walking speeds and is based on the Malaria Atlas Project (2015) Global Walking Only Friction Surface.

dowscaling_model_type

(optional) A character string indicating the type of model used for the spatial downscaling of the friction layer. Options are "lm" (linear model) and "rf" (random forest) (default: "lm").

res_output

(optional) A positive integerish number indicating the spatial resolution of the friction raster (and of the analysis), in meters. If the resolution is less than 1000, a spatial downscaling approach is used (default: 100).

weights

(optional) A raster with the weights for the demand (default: NULL).

objectiveminutes

(optional) A number indicating the target travel time in minutes used to compute the statistics (default: 15).

objectiveshare

(optional) A number indicating the proportion of the demand to be covered by adding at most the number of facilities defined by the n_fac parameter from the pool of candidate facilities (default: NULL).

approach

(optional) The approach to be used for the allocation. Options are "norm" and "absweights". If "norm", the allocation is based on the normalized demand raster multiplied by the normalized weights raster. If "absweights", the allocation is based on the normalized demand raster multiplied by the raw weights raster (default: "norm").

exp_demand

(optional) The exponent for the demand raster. Default is

A higher value will give less relative weight to areas with higher demand - with respect to the weights layer. This is useful in cases where the users want to increase the allocation in areas with higher values in the weights layer (default: 1).

exp_weights

(optional) The exponent for the weights raster. Default is

A higher value will give less relative weight to areas with higher weights - with respect to the demand layer. This is useful in cases where the users want to increase the allocation in areas with higher values in the demand layer (default: 1).

par

(optional) A logical flag indicating whether to run the function in parallel or not (default: FALSE).

Value

An invisible list with the following elements:

coverage: A numeric value indicating the share of demand covered within the objective travel time after allocating the new facilities.
unmet_demand: A numeric value indicating the share of demand that remains unmet after allocating the new facilities.
objective_minutes: The value of the objectiveminutes parameter used.
objective_share: The value of the objectiveshare parameter used.
facilities: A sf object with the newly allocated facilities.
travel_time: A raster RasterLayer object representing the travel time map with the newly allocated facilities.

Examples

if (FALSE) { # \dontrun{
  library(dplyr)
  library(sf)

  allocation_data <-
    naples_population |>
    allocation_discrete(
      traveltime = traveltime,
      bb_area = naples_shape,
      facilities = naples_fountains,
      candidate = naples_shape |> st_sample(20),
      n_fac = 2,
      weights = naples_hot_days,
      objectiveminutes = 15,
      objectiveshare = 0.9
    )

  allocation_data |> glimpse()

  allocation_data |> allocation_plot(naples_shape)
} # }

Usage

Arguments

Value

See also

Examples