I am trying to use linprog in order to optimise the following problem (uploaded in Google Drive). The dataset itself is uploaded here
So far I have the written the following implementation in Python:
import pandas as pd
import numpy as np
df = pd.read_csv('Supplier Specs.csv')
from scipy.optimize import linprog
def fromPandas(dataframe, colName):
return dataframe[[colName]].values.reshape(1,11)[0]
## A_ub * x <= b_ub
## A_eq * x == b_eq
A_eq = [1.0]*11
u_eq = [600.0] # demand
## reading the actual numbers from the pandas dataframe and then converting them to vectors
BAR = fromPandas(df, 'Brix / Acid Ratio')
acid = fromPandas(df, 'Acid (%)')
astringency = fromPandas(df, 'Astringency (1-10 Scale)')
color = fromPandas(df, 'Color (1-10 Scale)')
price = fromPandas(df, 'Price (per 1K Gallons)')
shipping = fromPandas(df, 'Shipping (per 1K Gallons)')
upperBounds = fromPandas(df, 'Qty Available (1,000 Gallons)')
lowerBounds = [0]*len(upperBounds) # list with length 11 and value 0
lowerBounds[2] = 0.4*u_eq[0] # adding the Florida tax bound
bnds = [(0,0)]*len(upperBounds) # bounds
for i in range(0,len(upperBounds)):
bnds[i] = (lowerBounds[i], upperBounds[i])
c = price + shipping # objective function coefficients
print("------------------------------------- Debugging Output ------------------------------------- \n")
print("Objective function coefficients: ", c)
print("Bounds: ", bnds)
print("Equality coefficients: ", A_eq)
print("BAR coefficients: ", BAR)
print("Astringency coefficients: ", astringency)
print("Color coefficients: ", color)
print("Acid coefficients: ", acid)
print("\n")
A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, -11.5, -0.75, 0, -4.5]) # limits for the inequalities
b_ub = b_ub * u_eq[0] # scaling the limits with the demand
xOptimized = linprog(c, A_ub, b_ub, [A_eq], u_eq, bounds=(bnds))
print(xOptimized) # the amounts of juice which we need to buy from each supplier
The optimisation method returns that cannot find a feasible starting point. I believe that I have a principal error in working with the method but so far I couldn't understand it.
Some help ?
Thanks in advance!
EDIT: the expected value of the objective function is 371724
the expected solution vector [0,0,240,0,15.8,0,0,0,126.3,109.7,108.2]
That was indeed a premature guess from me. [A_eq] is of course two-dimensional with 1xn. That your script works in principle shows the example, when you remove all your negative constraints from
A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, -11.5, -0.75, 0, -4.5]) # limits for the inequalities
And this seems to be the crux of the problem. Since A_ub * x <= b_ub, you look for a solution for
BAR * x <= 12.5
and
-BAR * x <= -11.5, i.e.
11.5 <= BAR * x <= 12.5
That obviously fails to produce any results. You are actually looking for
A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, 11.5, 0.75, 0, 4.5]) # limits for the inequalities
This converges now, but gives a different result from your expected solution, you published now in your edit. Obviously, you have to re-evaluate your inequality parameters, which you haven't specified in your question.