Adapted from:
Daskin, M. S. 1995. Network and Discrete Location: Models, Algorithms, and Applications. Hoboken, NJ, USA: John Wiley & Sons, Inc.
0. Imports and Data Creation
In [2]:
# Imports
import numpy as np
import gurobipy as gbp
import datetime as dt
# 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]))
1. Primal
In [3]:
# Instantiate Model
mPrimal_Canonical_GUROBI = gbp.Model(' -- Canonical Primal Linear Programming Problem -- ')
# Set Focus to Optimality
gbp.setParam('MIPFocus', 2)
# Decision Variables
desc_var = []
for dest in cols:
desc_var.append([])
desc_var[dest].append(mPrimal_Canonical_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='y'+str(dest+1)))
# Update Model
mPrimal_Canonical_GUROBI.update()
#Objective Function
mPrimal_Canonical_GUROBI.setObjective(gbp.quicksum(Cj[dest]*desc_var[dest][0]
for dest in cols),
gbp.GRB.MINIMIZE)
# Constraints
for orig in rows:
mPrimal_Canonical_GUROBI.addConstr(gbp.quicksum(Aij[orig][dest]*desc_var[dest][0]
for dest in cols) - Bi[orig] >= 0)
# Optimize
mPrimal_Canonical_GUROBI.optimize()
# Write LP file
mPrimal_Canonical_GUROBI.write('LP.lp')
print '\n*************************************************************************'
print ' | Decision Variables'
for v in mPrimal_Canonical_GUROBI.getVars():
print ' | ', v.VarName, '=', v.x
print '*************************************************************************'
val = mPrimal_Canonical_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 Canonical Primal Linear Programming Problem --'
print '\nJames Gaboardi, 2015'
2. Dual
In [4]:
# Instantiate Model
mDual_Canonical_GUROBI = gbp.Model(' -- Canonical Dual Linear Programming Problem -- ')
# Set Focus to Optimality
gbp.setParam('MIPFocus', 2)
# Decision Variables
desc_var = []
for dest in cols:
desc_var.append([])
desc_var[dest].append(mDual_Canonical_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='u'+str(dest+1)))
# Update Model
mDual_Canonical_GUROBI.update()
#Objective Function
mDual_Canonical_GUROBI.setObjective(gbp.quicksum(Bi[orig]*desc_var[orig][0]
for orig in rows),
gbp.GRB.MAXIMIZE)
# Constraints
for dest in cols:
mDual_Canonical_GUROBI.addConstr(gbp.quicksum(Aij[orig][dest]*desc_var[dest][0]
for orig in rows) - Cj[dest] <= 0)
# Optimize
mDual_Canonical_GUROBI.optimize()
# Write LP file
mDual_Canonical_GUROBI.write('LP.lp')
print '\n*************************************************************************'
print ' | Decision Variables'
for v in mDual_Canonical_GUROBI.getVars():
print ' | ', v.VarName, '=', v.x
print '*************************************************************************'
val = mDual_Canonical_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 Canonical Dual Linear Programming Problem --'
print '\nJames Gaboardi, 2015'