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Gurobi_Dual_Standard.py
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Gurobi_Dual_Standard.py
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'''
GNU LESSER GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
'''
# Building a Standard Dual Linear Programming Problem
# in Python/Gurobi[gurobipy]
'''
Adapted from:
Daskin, M. S.
1995
Network and Discrete Location: Models, Algorithms, and Applications
Hoboken, NJ, USA: John Wiley & Sons, Inc.
'''
# Imports
import numpy as np
import gurobipy as gbp
import datetime as dt
def GbpDualStd():
# Constants
Aij = np.random.randint(5, 50, 25)
Aij = Aij.reshape(5,5)
AijSum = np.sum(Aij)
Cj = np.random.randint(10, 20, 5)
CjSum = np.sum(Cj)
Bi = np.random.randint(10, 20, 5)
BiSum = np.sum(Bi)
# Matrix Shape
rows = range(len(Aij))
cols = range(len(Aij[0]))
# Instantiate Model
mDual_Standard_GUROBI = gbp.Model(' -- Standard Dual Linear Programming Problem -- ')
# Set Focus to Optimality
gbp.setParam('MIPFocus', 2)
# Decision Variables
desc_var = []
for orig in rows:
desc_var.append([])
desc_var[orig].append(mDual_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='u'+str(orig+1)))
# Slack Variables
slack_var = []
for dest in cols:
slack_var.append([])
slack_var[dest].append(mDual_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='t'+str(dest+1)))
# Update Model
mDual_Standard_GUROBI.update()
#Objective Function
mDual_Standard_GUROBI.setObjective(gbp.quicksum(Bi[orig]*desc_var[orig][0]
for orig in rows),
gbp.GRB.MAXIMIZE)
# Constraints
for dest in cols:
mDual_Standard_GUROBI.addConstr(gbp.quicksum(Aij[orig][dest]*desc_var[orig][0]
for orig in rows) +
slack_var[dest][0] -
Cj[dest] == 0)
# Optimize
try:
mDual_Standard_GUROBI.optimize()
except Exception as e:
print ' ################################################################'
print ' < ISSUE : ', e, ' >'
print ' ################################################################'
# Write LP file
mDual_Standard_GUROBI.write('LP.lp')
print '\n*************************************************************************'
print ' | Decision Variables'
for v in mDual_Standard_GUROBI.getVars():
print ' | ', v.VarName, '=', v.x
print '*************************************************************************'
val = mDual_Standard_GUROBI.objVal
print ' | Objective Value ------------------ ', val
print ' | Aij Sum -------------------------- ', AijSum
print ' | Cj Sum --------------------------- ', CjSum
print ' | Bi Sum --------------------------- ', BiSum
print ' | Matrix Dimensions ---------------- ', Aij.shape
print ' | Date/Time ------------------------ ', dt.datetime.now()
print '*************************************************************************'
print '-- Gurobi Standard Dual Linear Programming Problem --'
try:
GbpDualCStd()
print '\nJames Gaboardi, 2015'
except Exception as e:
print ' ################################################################'
print ' < ISSUE : ', e, ' >'
print ' ################################################################'