Infeasible model

Answered

mina torabi

July 27, 2023 22:16 Edited

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Hi,

I have a model based on a paper that I want to implement in Gurobi, but the constraint 13e makes the model infeasible. Any suggestions on what the error might be?

Thanks

Here is the code:

 

from gurobipy import *
p = [16682, 19802, 25610, 28357, 18389, 30305, 18242, 16129, 15957]
landa_max = [(0.95*i)/(52*5*8) for i in p]
landa_min = 0.125
#we have 9 demand points. the candidate locations for the facility are: 1, 2, 3
t = [[0,0.66,0.3],
    [0.66,0,0,36],
    [0.3,0.36,0],
    [0.58,0.3,0.59],
    [0.64,0.52,0.65],
    [0.23,0.61,0.24],
    [0.48,0.54,0.18],
    [0.66,0.72,0.36],
    [0.53,0.59,0.23]]
f = [23, 23.89, 16]
c = [10, 10, 10]
alpha = 0.25
beta =1
tau_max = 1.5
L = 10000
eps = 0.1
mu = [50,55,60,65,70,75,80,85]
m = 3 #facilities
n = 9 #customers

model = Model (name = "model")

x = model.addMVar((m,), name = 'x', vtype = GRB.BINARY)
y = model.addMVar((n, m), name = 'y', lb =0, vtype = GRB.CONTINUOUS)
z = model.addMVar((n, m), name = 'z', vtype = GRB.BINARY)
mu = model.addMVar((m, ), name = 'mu',lb =0, vtype = GRB.CONTINUOUS)
aux1 = model.addMVar((n, ), name = 'aux1', vtype = GRB.CONTINUOUS)
aux2 = model.addMVar((n, ), name = 'aux2', vtype = GRB.CONTINUOUS)
aux3 = model.addMVar((m, ), name = 'aux3', vtype = GRB.CONTINUOUS)
aux4 = model.addMVar((n,m), name = 'aux4', vtype = GRB.CONTINUOUS)

model_Obj = quicksum(f[j]*x[j] for j in range(m)) +quicksum(c[j]*mu[j] for j in range(m))

model.setObjective(model_Obj, GRB.MINIMIZE)

model.addConstrs(z[i, j] <= x[j] for i in range(n) for j in range(m)) #13.a
model.addConstrs(y[i, j] <= z[i, j] for i in range(n) for j in range(m)) #13.b
model.addConstrs(quicksum(z[i, j] for j in range(m)) >= 1 for i in range(n)) #13.c
model.addConstrs(quicksum(landa_max[i]*y[i, j] for i in range(n)) >= landa_min*x[j] for j in range(m)) #13.d

model.addConstrs(quicksum(x[j]*y[i,j] for j in range(m)) == aux1[i] for i in range(n))

for i in range(n):
    model.addGenConstrLog(aux1[i], aux2[i])
        
############
model.addConstrs((mu[j]-quicksum(landa_max[r]*y[r,j] for r in range(n))) == aux3[j] for j in range(m))

model.addConstrs(aux2[i]*aux3[j] == aux4[i,j] for i in range(n) for j in range(m))

############
model.addConstrs((alpha*t[i][j]*aux3[j]+beta*alpha +aux4[i, j])*y[i, j] == 0.0 
                 for i in range(n) for j in range(m)) #13e

model.addConstrs(alpha*t[i][j]*(aux3[j])+ beta*alpha+aux2[i]*(aux3[j]) >= 0 
                 for i in range(n) for j in range(m)) #13f

model.addConstrs(t[i][j]*(mu[j]-quicksum(landa_max[i]*y[k,j] for k in range(n))+(1-x[j])*eps)+beta*x[j]<=
                 (tau_max + (1-z[i,j])*L)*quicksum(landa_max[i]*y[k,j] for k in range(n))
                for i in range(n) for j in range(m)) #13g

model.addConstrs((quicksum(landa_max[i]*y[i, j] for i in range(n))) <= mu[j] for j in range(m)) #13h

model.params.NonConvex = 2
model.optimize()

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• 

  Marika Karbstein

  • Gurobi Staff

  July 28, 2023 08:14

  Hi Mina,

  The default lower bound for variables is 0. You may want to define a negative lower bound for some of your aux-variables.

  Please note that the logarithmic constraint is approximated via piecewise linear functions. Tight bounds on the variables help to decrease the error in this approximation.

  I hope this helps to solve the problem,
  Marika

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  mina torabi

  July 28, 2023 22:24

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  Hi Marika,

  Thank you very much for your response. That helps a lot.

  Mina

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