Scipy Linprog - not giving expected solution

Question

I have a set of simple linear equations and am using sciprog to solve it. Objective function is to minimize x(i)*c.

where :

c is defined below(constants)

i ranges from 1 to 28

I also have equality constraints(14 equations) based on which I could I need a solution. Infact the solution is very straightforward. Expected solution is mentioned in excel. But when I use linprog to solve this, it fails. Any reason to check for ?

from scipy.optimize import linprog

A_eq = [[1211.881188118812, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 3599.9999999999995, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 2006.5573770491803, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2185.714285714286, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2147.3684210526317, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 290.04739336492895, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 382.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 181.87221396731056, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 382.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 291.4285714285714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 382.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1224.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3599.9999999999995, 0.0]
        ]

b_eq = [0, 0, 1397.8722944969109, 1215.3540665438804, 0, 1217.8280665438817,
        177.21022795303054, 1217.8280665438822, 177.21022795303054, 177.21022795303048,
        177.21022795303054, 0, 0, 0]

c = [50,27]*14

sol = linprog(c = c, A_eq = A_eq, b_eq = b_eq, bounds = (0, None))
#sol
#Out[138]: 
#     fun: 1210.4060665438813
# message: 'Optimization failed. Unable to find a feasible starting point.'
#     nit: 13
#  status: 2
# success: False
#       x: nan

Initially I thought, it could be A14:AB14 causing this and thus replaced all coeff from 0 to 1. But still same result. Any clue?

Answer 1

Use the interior point method instead (the simplex solver is known to be rather unreliable -- not to blame on the simplex method but rather on a poor implementation). Of course this model can be solved completely in the presolve: there is nothing to optimize.

sol = linprog(c = c, A_eq = A_eq, b_eq = b_eq, bounds = (0, None), method='interior-point')

This gives:

     con: array([  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,  -2.27373675e-13,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00])
     fun: 381.92688642606663
 message: 'The solution was determined in presolve as there areno non-trivial constraints.'
     nit: 0
   slack: array([], dtype=float64)
  status: 0
 success: True
       x: array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
        0.69665204,  0.        ,  0.55604434,  0.        ,  0.        ,
        0.        ,  4.19872095,  0.        ,  0.46329471,  0.        ,
        6.69606445,  0.        ,  0.46329471,  0.        ,  0.60807431,
        0.        ,  0.46329471,  0.        ,  0.        ,  0.        ,
        0.        ,  0.        ,  0.        ])