library(simplexR)
--- Werners, Brigitte - Grundlagen des Operations Research (page 79)
$$ \begin{array}{rrcrcr} \max & 3x_1 & + & 2x_2 & \ s.t. & 2x_1 & + & 1x_2 & \leq & 22 \ & 1x_1 & + & 2x_2 & \leq & 23 \ & 4x_1 & + & 1x_2 & \leq & 40 \ & 1x_1 & + & 1x_2 & \geq & 5 \ & 1x_1 & - & 1/3x_2 & = & 6 \ & x_1,& & x_2 & \geq & 0 \end{array} $$
# See: Werners Brigitte, page 79 # optimal solution: x = (8, 6), z = 36 A <- matrix(c( 2, 1, 1, 2, 4, 1, 1, 1, 1, -1/3 ), nrow = 5, ncol = 2, byrow = TRUE, dimnames = list(c("R1", "R2", "R3", "R4", "R5"), c("x1", "x2"))) b <- c(22, 23, 40, 5, 6) c <- c(3, 2) sense <- 1 relation <- c("<=", "<=", "<=", ">=", "=")
canonical_tableau <- construct_tableau(A, b, c, sense, relation) canonical_tableau
simplex(tableau = canonical_tableau)
--- Examples from: Operations Research - Deterministische Modelle und Methoden - Stephan Dempe, Heiner Schreier, 1. Auflage September 2006, Wiesbaden
# See: Dempe/Schreier, page 34 # primal degeneracy: stalling and cycling # based on Beale (1955) A <- matrix(c( 1/4, -8, -1, 9, 1/2, -12, -1/2, 3, 0, 0, 1, 0 ), nrow = 3, ncol = 4, byrow = TRUE, dimnames = list(c("R1", "R2", "R3"), c("x1", "x2", "x3", "x4"))) b <- c(0, 0, 1) c <- c(3/4, -20, 1/2, -6) sense <- 1 relation <- c("<=", "<=", "<=")
cycling_case <- construct_tableau(A, b, c, sense, relation) cycling_case
simplex(tableau = cycling_case, max_iter = 7)
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