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#!/usr/bin/env python
# @(#) $Jeannot: test5.py,v 1.2 2004/03/20 17:06:54 js Exp $
# Market splitting problems from:
# G. Cornuejols, M. Dawande, A class of hard small 0-1 programs, 1998.
# With m>=4, these problems are often *very* difficult.
# Import PuLP modeler functions
from pulp import *
# Import random number generation functions
from random import *
# A new LP problem
prob = LpProblem("test5", LpMinimize)
# Parameters
# Number of constraints
m = 3
# Size of the integers involved
D = 100
# Number of variables
n = 10*(m-1)
# A vector of n binary variables
x = LpVariable.matrix("x", list(range(n)), 0, 1, LpInteger)
# Slacks
s = LpVariable.matrix("s", list(range(m)), 0)
w = LpVariable.matrix("w", list(range(m)), 0)
# Objective
prob += lpSum(s) + lpSum(w)
# Constraints
d = [[randint(0,D) for i in range(n)] for j in range(m)]
for j in range(m):
prob += lpDot(d[j], x) + s[j] - w[j] == lpSum(d[j])/2
# Resolution
prob.solve()
# Print the status of the solved LP
print("Status:", LpStatus[prob.status])
# Print the value of the variables at the optimum
for v in prob.variables():
print(v.name, "=", v.varValue)
# Print the value of the objective
print("objective=", value(prob.objective))
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