Linear Programming with cvxpy

Question

I would like to ask you regarding on the Linear Program for optimization.

I have an objective function, and constraint functions as below,

variables(x1, x2, x3, x4, x5, x6) are quantities of the products, and the quantities of products have to be fixed numbers now.

the goal of this problem is the optimizing the quantities of products.

Objective Function (c.T * [x1, x2, x3, x4, x5, x6])

[[c11, c12, c13, c14, c15 c16],

[c21, c22, c23, c24, c25, c26],
                              X     [x1, x2, x3, x4, x5, x6]  
[c31, c32, c33, c34, c35, c36],

[c41, c42, c43, c44, c45, c45]]

The result that I would like to optimize is going to be as below

c11*x1 + c12*x2 + c13*x3 + c14*x4 + c15*x5 + c16*x6 +
c21*x1 + c22*x2 + c23*x3 + c24*x4 + c25*x5 + c26*x6 + 
c31*x1 + c32*x2 + c33*x3 + c34*x4 + c35*x5 + c36*x6 + 
c41*x1 + c42*x2 + c43*x3 + c44*x4 + c45*x5 + c46*x6 = optimized value

Constraint Function

1) constraint_1

5500000*x1+2500000*x2+825000*x3+5500000*x4+5500000*x5+5500000*x6 <= 800000000

2) constraint_2

x1 <= 10
x2 <= 10
x3 <= 10
x4 <= 10
x5 <= 10
x6 <= 10

The problem that I am suffering from is the in the "Objective Function of Cs(c1,1 ~ c4,5)".

I have solved the Linear Programming that has integers values in the Objective Functions, but not the matrix.

I have tried all other ways that I could, but now I really need helps on this.

Please kindly suggest me any kind of ideas or codes for this question.

I'm not sure I understand where exactly you see a problem. If I define `Ki` as `c1i+c2i+c3i+c4i`, then your problem becomes maximizing `K1*x1 + K2*x2 + ... + K6*x6` and you claim that you know how to solve that kind of problems. So where is the roadblock for you? — SergGr, Dec 06 '18 at 12:01
If an objective function is like 3 * x1 + 2 * x2 + 3 * x3 + 4 * x4 + 5 * x5 + 6 * x6, then the code will be as below, — Jay Kim, Dec 06 '18 at 12:32
`c = np.array([3, 2, 3, 4, 5, 6])` `A = np.array([[5500000, 2500000, 825000, 5500000, 5500000, 5500000], [1,0,0,0,0,0], [0,1,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]])` `b = np.array([800000000, 10, 10, 10, 10, 10, 10])` `c = matrix(c, tc='d')` `G = matrix(A, tc='d')` `h = matrix(b, tc='d')` `status, x = glpk.ilp(c, g, h, I=set([0,1,2,3,4,5]))` — Jay Kim, Dec 06 '18 at 12:40
The problem that I am having is I am not sure how to extend the `c` parts. In the code, it is the 1 x 6 matrix, but now I need solve with the 4 x 6 matrix(c11 to c46). — Jay Kim, Dec 06 '18 at 12:44

score 0 · Answer 1 · answered Dec 07 '18 at 03:01

Suppose you have store the original cij in a numpy array, you might like to sum up terms like c11+c21+c31+c41 first. This can be done by summing up each column, try c.sum(axis = 0)

>>> import numpy as np
>>> c = np.arange(24).reshape(4,6)
>>> c
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23]])
>>> c = c.sum(axis=0)
>>> c
array([36, 40, 44, 48, 52, 56])

Linear Programming with cvxpy

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