linearProductionGame: Cooperative linear production games

In coopProductGame: Cooperative Aspects of Linear Production Programming Problems

Description

Given a linear production problem, the linearProductionGame function solves the problem by making use of lpSolveAPI where each agent provides his own resources.

Usage

linearProductionGame(c, A, B, plot = FALSE, show.data = FALSE)

Arguments

c	vector containing the benefits of the products.
A	production matrix.
B	matrix containing the amount of resources of the several players where each row is one player.
plot	logical value indicating if the function displays graphical solution (TRUE) or not (FALSE). Note that this option only makes sense when we have a two-dimension problem.
show.data	logical value indicating if the function displays the console output (TRUE) or not (FALSE). By default the value is TRUE.

Value

linearProductionGame returns a list with the solutions of the associated problem of each coalition and the objective value for coalition N.

Author(s)

D. Prieto

Examples

# Vector of benefits
c <- c(68,52)
# Production matrix
A <- matrix(c(4,5,6,2),ncol=2, byrow = TRUE)
# Matrix of resources. Each column is the vector of resources of each player
B <- matrix(c(4, 6, 60, 33, 39, 0),ncol = 3, byrow = TRUE)
# Solution of the associated linear production game
linearProductionGame(c, A, B, show.data = TRUE)

 # ------------------------------------------------------------------------
 # Optimal solution of the problem for each coalition: 
 # ------------------------------------------------------------------------
 # 
 # S={1}      1.00  0.00
 # S={2}      1.50  0.00
 # S={3}      0.00  0.00
 # S={1,2}    2.50  0.00
 # S={1,3}    1.68 11.45
 # S={2,3}    2.86 10.91
 # S={1,2,3} 10.00  6.00
 # 
 # ------------------------------------------------------------------------
 #   Cooperative production game: 
 # ------------------------------------------------------------------------
 #                S={0} S={1} S={2} S={3} S={1,2} S={1,3} S={2,3} S={1,2,3}
 # Associated game    0    68   102     0     170     710     762       992
 # ------------------------------------------------------------------------

  

Example output

 ------------------------------------------------------------------------
 Optimal solution of the problem for each coalition: 
 ------------------------------------------------------------------------
                     
S={1}      1.00  0.00
S={2}      1.50  0.00
S={3}      0.00  0.00
S={1,2}    2.50  0.00
S={1,3}    1.68 11.45
S={2,3}    2.86 10.91
S={1,2,3} 10.00  6.00

 ------------------------------------------------------------------------
 Cooperative production game: 
 ------------------------------------------------------------------------
                S={0} S={1} S={2} S={3} S={1,2} S={1,3} S={2,3} S={1,2,3}
Associated game     0    68   102     0     170     710     762       992
 ------------------------------------------------------------------------

coopProductGame documentation built on May 1, 2019, 10:32 p.m.