Controlling Air Pollution_type1.md

Controlling Air Pollution example

POLab
2017/10/08
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● 本範例為講義第三章p25.26題目

Import gurobipy

from gurobipy import*

Model

m=Model("controlling air pollution")

Add decision variable

x1=m.addVar(lb=0,ub=1,name="x1")
x2=m.addVar(lb=0,ub=1,name="x2")
x3=m.addVar(lb=0,ub=1,name="x3")
x4=m.addVar(lb=0,ub=1,name="x4")
x5=m.addVar(lb=0,ub=1,name="x5")
x6=m.addVar(lb=0,ub=1,name="x6")

Update

m.update()

Add objective and constraints

m.setObjective(8*x1+10*x2+7*x3+6*x4+11*x5+9*x6,GRB.MINIMIZE)

m.addConstr(12*x1+9*x2+25*x3+20*x4+17*x5+13*x6>=60,"c0")
m.addConstr(35*x1+42*x2+18*x3+31*x4+56*x5+49*x6>=150,"c1")
m.addConstr(37*x1+53*x2+28*x3+24*x4+29*x5+20*x6>=125,"c2")

<gurobi.Constr *Awaiting Model Update*>

Result

m.optimize()
print("Obj:",m.objVal)
for v in m.getVars():
    print("%s:%.3f"%(v.varName,v.x))

Optimize a model with 3 rows, 6 columns and 18 nonzeros
Coefficient statistics:
  Matrix range     [9e+00, 6e+01]
  Objective range  [6e+00, 1e+01]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+01, 2e+02]
Presolve time: 0.00s
Presolved: 3 rows, 6 columns, 18 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    0.0000000e+00   6.171875e+00   0.000000e+00      0s
       4    3.2154631e+01   0.000000e+00   0.000000e+00      0s

Solved in 4 iterations and 0.01 seconds
Optimal objective  3.215463133e+01
('Obj:', 32.154631330359486)
x1:1.000
x2:0.623
x3:0.343
x4:1.000
x5:0.048
x6:1.000