This module provides an interface to the standard simplex algorithm.
For example, the following LP problem
maximize 4 x_1  3 x_2 + 2 x_3
subject to
2 x_1 + x_2 <= 10
x_3 + 5 x_4 <= 20
and
x_i >= 0 can be solved as follows:
import Numeric.LinearProgramming
prob = Maximize [4, 3, 2]
constr1 = Sparse [ [2#1, 1#2] :<=: 10
, [1#2, 5#3] :<=: 20
]
> simplex prob constr1 []
Optimal (28.0,[5.0,0.0,4.0]) The coefficients of the constraint matrix can also be given in dense format:
constr2 = Dense [ [2,1,0] :<=: 10
, [0,1,5] :<=: 20
] By default all variables are bounded as x_i >= 0, but this can be
changed:
> simplex prob constr2 [ 2 :=>: 1, 3 :&: (2,7)]
Optimal (22.6,[4.5,1.0,3.8])
> simplex prob constr2 [Free 2]
Unbounded The given bound for a variable completely replaces the default,
so 0 <= x_i <= b must be explicitly given as i :&: (0,b).
Multiple bounds for a variable are not allowed, instead of
[i :=>: a, i:<=: b] use i :&: (a,b).
