DEA efficient frontier for a single input/output pair

Draws the classic two-dimensional DEA picture: the decision-making units in input-by-output space, the production-possibility set shaded beneath the frontier, and the efficient frontier itself for the chosen returns-to-scale assumption. Optionally overlays the peer (reference) network as arrows from each inefficient unit to its efficient targets.

Usage

plot_io_frontier(
  x,
  input,
  output,
  rts = c("crs", "vrs", "drs", "irs", "fdh"),
  orientation = c("in", "out"),
  peers_network = FALSE,
  arrow_target = c("peer", "projection"),
  point_size = 2,
  transparency = 0.7,
  fade = TRUE,
  label_frontier = TRUE,
  labels = "none",
  max.overlaps.value = 10,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

x: A dea_data object, or data coercible by as_dea_data.
input, output: The single input and single output to plot, each given as a column name or as an integer position among the inputs/outputs.
rts: Returns to scale for the frontier and efficiency scores: "crs" (default), "vrs", "drs", "irs" or "fdh".
orientation: "in" (default) or "out"; affects the efficiency scores and the direction of projection arrows.
peers_network: Logical; if TRUE, draw arrows from inefficient units to their efficient reference set. Default FALSE. With a single DMU named in labels, only that unit's arrows are drawn; otherwise every inefficient unit's arrows are shown.
arrow_target: "peer" (default) draws an arrow to each efficient peer DMU, with opacity proportional to its envelopment weight (\(\lambda\)); "projection" draws one arrow per inefficient unit to its projected point on the frontier (respecting orientation), at uniform opacity.
point_size: Point size. Default 2.
transparency: Base point/arrow alpha, a number in [0, 1]. Default 0.7.
fade: Focus control when a single DMU is given to labels; see plot_io_scatter. Default TRUE.
label_frontier: Logical; label the efficient (frontier) units. Default TRUE.
labels: Labelling/focus mode: "none" (default), "all", "id", "max.overlaps", or a single DMU name to highlight.
max.overlaps.value: Passed to ggrepel. Default 10.
subtitle: Plot subtitle. NULL (default) shows “input and output sub-model RTS efficient frontier”; pass a string to override, or NA to suppress.
title: Plot title.
interactive: If TRUE, return a plotly object. Default FALSE.
...: Passed to the point geom.

Value

A ggplot object, or a plotly object when interactive = TRUE.

Details

The whole plot is a single, self-consistent two-variable DEA: the frontier, the colour scale, and the peer arrows are all derived from compute_efficiency() run on the chosen input/output pair at the chosen rts. A unit's colour is therefore its efficiency in this two-variable sub-model, which may differ from its efficiency in the full multidimensional model – so a point sitting on the frontier line reads as efficient, as it should.

References

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444. doi:10.1016/0377-2217(78)90138-8

Examples

d <- dea_data(
  chinese_cities,
  inputs  = c("industrial_labour_force", "working_funds", "investments"),
  outputs = c("gross_industrial_output", "profit_and_tax", "retail_sales"),
  id      = "DMU"
)
plot_io_frontier(d, input = "working_funds", output = "retail_sales",
                 rts = "vrs")

# peer network for one city, arrows weighted by lambda
plot_io_frontier(d, input = "working_funds", output = "retail_sales",
                 rts = "vrs", peers_network = TRUE, labels = "Beijing")