def main():
t = 'k out of n'
n = 12
seed(100)
bound = [randint(5, 15) for _ in range(n)]
tableutils.printmat([['Max sum of'] + bound])
for k in range(1, n + 1):
s = pywraplp.Solver(t, pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
x = [s.NumVar(0, bound[i], '') for i in range(n)]
y = [s.NumVar(0, bound[i], '') for i in range(n)]
Costx = sum(x[i] for i in range(n))
Costy = sum(y[i] for i in range(n))
s.Maximize(Costx + Costy)
k_out_of_n(s, k, x, '==')
ldg = sosn(s, k, y)
rc = s.Solve()
if rc != 0:
print 'Error', rc
sy = SolVal(y)
sx = SolVal(x)
yy = [[' ', 'x'][e > 0] for e in sy]
xx = [[' ', 'x'][e > 0] for e in sx]
tableutils.printmat(
tableutils.wrapmat(
[xx, yy],
['{0}/{1}'.format(k, n), 'Adjacent {0}/{1}'.format(k, n)],
None), 0, False)
return rc
def main():
bounds = []
s = pywraplp.Solver('',pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
a = [[2],[-2]]
b = [3,-12]
x = s.NumVar(2,5,'x')
z,l = maximax(s,a,[x],b)
rc = s.Solve()
print 'x = ',SolVal(x)
print 'z = ',SolVal(z)
print '\delta = ', SolVal(l)
def solve_model(D):
s = newSolver('Project management')
n = len(D)
max = sum(D[i][1] for i in range(n))
t = [s.NumVar(0,max,'t[%i]' % i) for i in range(n)]
Total = s.NumVar(0,max,'Total')
for i in range(n):
s.Add(t[i]+D[i][1] <= Total)
for j in D[i][2]:
s.Add(t[j]+D[j][1] <= t[i])
s.Minimize(Total)
rc = s.Solve()
return rc, SolVal(Total),SolVal(t)
def solve_model_clp(D):
t = 'Project management'
s = pywraplp.Solver(t,pywraplp.Solver.CLP_LINEAR_PROGRAMMING)
n = len(D)
max = sum(D[i][1] for i in range(n))
t = [s.NumVar(0,max,'t[%i]' % i) for i in range(n)]
Total = s.NumVar(0,max,'Total')
for i in range(n):
s.Add(t[i]+D[i][1] <= Total)
for j in D[i][2]:
s.Add(t[j]+D[j][1] <= t[i])
s.Minimize(Total)
rc = s.Solve()
return rc, SolVal(Total),SolVal(t)
def minimize_piecewise_linear(Points,B,convex=True):
t = 'Piecewise'
s = pywraplp.Solver(t,pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
n = len(Points)
x = s.NumVar(Points[0][0],Points[n-1][0],'x')
l = [s.NumVar(0,1,'l[%i]' % (i,)) for i in range(n)]
s.Add(1 == sum(l[i] for i in range(n)))
d = sosn(s, 2, l)
s.Add(x == sum(l[i]*Points[i][0] for i in range(n)))
s.Add(x >= B)
Cost = s.Sum(l[i]*Points[i][1] for i in range(n))
s.Minimize(Cost)
rc = s.Solve()
return rc,SolVal(l),SolVal(d[1])
def solve_model(D, F):
t = 'Facility location problem'
s = pywraplp.Solver(t, pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
m, n = len(D) - 1, len(D[0]) - 1
x = [[s.NumVar(0, D[i][-1], '') for j in range(n)] for i in range(m)]
y = [s.IntVar(0, 1, '') for i in range(m)]
for i in range(m):
s.Add(D[i][-1] * y[i] >= sum(x[i][j] for j in range(n)))
for j in range(n):
s.Add(D[-1][j] == sum(x[i][j] for i in range(m)))
Fcost = s.Sum(y[i] * F[i] for i in range(m))
Dcost = s.Sum(x[i][j] * D[i][j] for i in range(m) for j in range(n))
s.Minimize(Dcost + Fcost)
rc = s.Solve()
return rc, ObjVal(s), SolVal(x), SolVal(y)
def solve_model(S, I, R, P):
s = newSolver('Staff Scheduling', True)
nbS, nbI, nbSets, nbPairs, nbC = len(S), len(I), len(R), len(
P), S[-1][1] + 1
print nbS, nbI, nbSets, nbPairs, nbC
nbT = 1 + max(e[2] for e in S)
x = [[s.IntVar(0, 1, '') for _ in range(nbS)] for _ in range(nbI)]
z = [[[s.IntVar(0,1,'') for _ in range(len(P[p][1]))] for p in range(nbPairs)] \
for _ in range(nbI)]
for j in range(nbS):
k_out_of_n(s, 1, [x[i][j] for i in range(nbI)], '<=')
for i in range(nbI):
s.Add(sum(x[i][j] for j in range(nbS)) >= I[i][1][0])
s.Add(sum(x[i][j] for j in range(nbS)) <= I[i][1][1])
for t in range(nbT):
k_out_of_n(s, 1, [x[i][j] for j in range(nbS) if S[j][2] == t],
'<=')
WC = sum(x[i][j] * I[i][2][c] for i in range(nbI) \
for j in range(nbS) for c in range(nbC) if S[j][1] == c)
WR = sum(I[i][3][r] * sum(x[i][j] for j in R[r][1]) \
for r in range(nbSets) for i in range(nbI))
for i in range(nbI):
for p in range(nbPairs):
if I[i][4][p] != 0:
for k in range(len(P[p][1])):
reify(s, [1, 1],
[x[i][P[p][1][k][0]], x[i][P[p][1][k][1]]], 2,
z[i][p][k], '>=')
WP = sum(z[i][p][k]*I[i][4][p] for i in range(nbI) \
for p in range(nbPairs) for k in range(len(P[p][1])) if I[i][4][p] != 0)
s.Maximize(WC + WR + WP)
rc, xs = s.Solve(), []
for i in range(nbI):
xs.append([
i,
[[
j,
(I[i][2][S[j][1]],
sum(I[i][3][r] for r in range(nbSets) if j in R[r][1]),
sum(
SolVal(z[i][p][k]) * I[i][4][p] / 2
for p in range(nbPairs) for k in range(len(P[p][1]))
if j in P[p][1][k]))
] for j in range(nbS) if SolVal(x[i][j]) > 0]
])
return rc, SolVal(x), xs, ObjVal(s)
def solve_model(Part,Target,Cost,Inventory,D,SC,SL):
s = newSolver('Multi-period soap blending problem')
Oils, Periods, Acids = range(len(Part)), range(len(Cost[0])), range(len(Part[0]))
Buy = [[s.NumVar(0,D,'') for _ in Periods] for _ in Oils]
Blnd = [[s.NumVar(0,D,'') for _ in Periods] for _ in Oils]
Hold = [[s.NumVar(0,D,'') for _ in Periods] for _ in Oils]
Prod = [s.NumVar(0,D,'') for _ in Periods]
CostP= [s.NumVar(0,D*1000,'') for _ in Periods]
CostS= [s.NumVar(0,D*1000,'') for _ in Periods]
Acid = [[s.NumVar(0,D*D,'') for _ in Periods] for _ in Acids]
for i in Oils:
s.Add(Hold[i][0] == Inventory[i][0])
for j in Periods:
s.Add(Prod[j] == sum(Blnd[i][j] for i in Oils))
s.Add(Prod[j] >= D)
if j < Periods[-1]:
for i in Oils:
s.Add(Hold[i][j] + Buy[i][j] - Blnd[i][j] == Hold[i][j+1])
s.Add(sum(Hold[i][j] for i in Oils) >= SL[0])
s.Add(sum(Hold[i][j] for i in Oils) <= SL[1])
for k in Acids:
s.Add(Acid[k][j] == sum(Blnd[i][j]*Part[i][k] for i in Oils))
s.Add(Acid[k][j] >= Target[0][k] * Prod[j])
s.Add(Acid[k][j] <= Target[1][k] * Prod[j])
s.Add(CostP[j] == sum(Buy[i][j] * Cost[i][j] for i in Oils))
s.Add(CostS[j] == sum(Hold[i][j] * SC for i in Oils))
Cost_product = s.Sum(CostP[j] for j in Periods)
Cost_storage = s.Sum(CostS[j] for j in Periods)
s.Minimize(Cost_product+Cost_storage)
rc = s.Solve()
B,L,H,A,P = SolVal(Buy),SolVal(Blnd),SolVal(Hold),SolVal(Acid),SolVal(Prod)
CP,CS = SolVal(CostP),SolVal(CostS)
return rc,ObjVal(s),B,L,H,P,A,CP,CS
def solve_model(D):
t = 'Power distribution problem'
s = pywraplp.Solver(t, pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
m, n = len(D) - 1, len(D[0]) - 1
B = sum([D[-1][j] for j in range(n)])
G = [[s.NumVar(0,B if D[i][j] else 0,'') for j in range(n)] \
for i in range(m)]
for i in range(m):
s.Add(D[i][-1] >= sum(G[i][j] for j in range(n)))
for j in range(n):
s.Add(D[-1][j] == sum(G[i][j] for i in range(m)))
Cost = s.Sum(G[i][j] * D[i][j] for i in range(m) for j in range(n))
s.Minimize(Cost)
rc = s.Solve()
return rc, ObjVal(s), SolVal(G)
def solve_model_eliminate(D, Subtours=[]):
t = 'TSP'
s = pywraplp.Solver(t, pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
n = len(D)
x = [[s.IntVar(0, 1, '') for j in range(n)] for i in range(n)]
for i in range(n):
s.Add(1 == sum(x[i][j] for j in range(n)))
s.Add(1 == sum(x[j][i] for j in range(n)))
s.Add(0 == x[i][i])
for sub in Subtours:
K = [x[sub[i]][sub[j]]+x[sub[j]][sub[i]]\
for i in range(len(sub)-1) for j in range(i+1,len(sub))]
s.Add(len(sub) - 1 >= sum(K))
s.Minimize(s.Sum(x[i][j] * D[i][j] for i in range(n) for j in range(n)))
rc = s.Solve()
tours = extract_tours(SolVal(x), n)
return rc, ObjVal(s), tours
def solve_model(M, nf, Q=None, P=None, no_part=False):
t = 'Staffing'
s = pywraplp.Solver(t, pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
nbt, n, B = len(M) - 1, len(M[0]) - 1, sum(M[t][-1]
for t in range(len(M) - 1))
x = [s.IntVar(0, B, 'x[%i]' % i) for i in range(n)]
for t in range(nbt):
s.Add(sum([M[t][i] * x[i] for i in range(n)]) >= M[t][-1])
if Q:
for i in range(n):
s.Add(x[i] >= Q[i])
if P:
s.Add(sum(x[i] for i in range(nf)) >= P)
if no_part:
for t in range(nbt):
s.Add(B*sum([M[t][i] * x[i] for i in range(nf)]) \
>= sum([M[t][i] * x[i] for i in range(nf,n)]))
s.Minimize(sum(x[i] * M[-1][i] for i in range(n)))
rc = s.Solve()
return rc, ObjVal(s), SolVal(x)
def solve_gas(C, D):
s = newSolver('Gas blending problem')
nR, nF = len(C), len(D)
Roc, Rmax, Rcost = 0, 1, 2
Foc, Fmin, Fmax, Fprice = 0, 1, 2, 3
G = [[s.NumVar(0.0, 10000, 'G[%i][%i]' % (i, j)) for j in range(nF)]
for i in range(nR)]
R = [s.NumVar(0, C[i][Rmax], 'R[%i]' % i) for i in range(nR)]
F = [s.NumVar(D[j][Fmin], D[j][Fmax], 'F[%i]' % j) for j in range(nF)]
for i in range(nR):
s.Add(R[i] == sum(G[i][j] for j in range(nF)))
for j in range(nF):
s.Add(F[j] == sum(G[i][j] for i in range(nR)))
for j in range(nF):
s.Add(F[j] *
D[j][Foc] == s.Sum([G[i][j] * C[i][Roc] for i in range(nR)]))
Cost = s.Sum(R[i] * C[i][Rcost] for i in range(nR))
Price = s.Sum(F[j] * D[j][Fprice] for j in range(nF))
s.Maximize(Price - Cost)
rc = s.Solve()
return rc, ObjVal(s), SolVal(G)
def solve_model(C, D=None, Z=False):
t = 'Multi-commodity mincost flow problem'
s = pywraplp.Solver(t, pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
K, n = len(C), len(C[0]) - 1,
B = [sum(C[k][-1][j] for j in range(n)) for k in range(K)]
x = [[[s.IntVar(0,B[k] if C[k][i][j] else 0,'') \
if Z else s.NumVar(0,B[k] if C[k][i][j] else 0,'') \
for j in range(n)] for i in range(n)] for k in range(K)]
for k in range(K):
for i in range(n):
s.Add(C[k][i][-1] - C[k][-1][i] == sum(x[k][i][j]
for j in range(n)) -
sum(x[k][j][i] for j in range(n)))
if D:
for i in range(n):
for j in range(n):
s.Add(sum(x[k][i][j] for k in range(K)) <= \
D if type(D) in [int,float] else D[i][j])
Cost = s.Sum(x[k][i][j]*C[k][i][j] \
for i in range(n) for j in range(n) for k in range(K))
s.Minimize(Cost)
rc = s.Solve()
return rc, ObjVal(s), SolVal(x)
for j in Teams[e]:
s.Add(sum(x[i][j][w] for w in range(nbWeeks)) == nbInter)
for w in range(nbWeeks):
for i in range(nbTeams):
s.Add(
sum(x[i][j][w] for j in range(nbTeams) if i < j) +
sum(x[j][i][w] for j in range(nbTeams) if j < i) <= nbPerWeek)
Value = [
w * x[i][j][w] for Div in Teams for i in Div for j in Div
for w in range(nbWeeks) if i < j
]
s.Maximize(s.Sum(Value))
rc, Cal = s.Solve(), []
if rc == 0:
Cal = [[(i, j) for i in range(nbTeams - 1)
for j in range(i + 1, nbTeams) if SolVal(x[i][j][w]) > 0]
for w in range(nbWeeks)]
return rc, ObjVal(s), Cal
import time
def add_intra(s, Teams, nbWeeks, nbIntra, x):
for Div in Teams:
for i in Div:
for j in Div:
if i < j:
s.Add(sum(x[i][j][w] for w in range(nbWeeks)) == nbIntra)