Compute DEA multiplier (weight) solutions

Solves the input-oriented, constant-returns-to-scale (CCR) multiplier DEA model for every decision-making unit and returns the optimal efficiency scores together with the input and output weights. A non-Archimedean lower bound epsilon keeps all weights strictly positive.

Usage

compute_multiplier_weights(x, epsilon = 1e-06)

Arguments

x

A dea_data object, or a data frame coerced by as_dea_data.

epsilon

Non-Archimedean lower bound on every multiplier weight; must be a single non-negative number. Defaults to 1e-6.

Value

A list with components

eff

named numeric vector of efficiency scores.

input_weights

matrix of input multipliers (one row per DMU, one column per input).

output_weights

matrix of output multipliers (one row per DMU, one column per output).

All rows are labelled with the DMU labels carried by x.

Details

For unit \(o\) the model maximises the weighted output \(u^\top y_o\) subject to the normalisation \(v^\top x_o = 1\) and \(u^\top y_j - v^\top x_j \le 0\) for every unit \(j\), with \(u, v \ge \epsilon\). The optimal value is the unit's efficiency score.

DEA multiplier solutions are generally not unique: efficient units and degenerate vertices admit alternative optimal weight vectors. This function returns one optimal solution (the vertex the solver settles on), not a canonical one. Treat the returned weights accordingly when they feed downstream calculations such as cross-efficiency.

See also

compute_efficiency for scores via dea; dea_data for the data contract.

Examples

df <- data.frame(i_x = c(2, 3, 4), o_y = c(1, 2, 2))
w <- compute_multiplier_weights(df)
w$eff
#>    1    2    3 
#> 0.75 1.00 0.75 
w$input_weights
#>           x
#> 1 0.5000000
#> 2 0.3333333
#> 3 0.2500000