Controlling Air Pollution_type2.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_type2")

Add parameters

c:每個方法的成本
p:每個方法可以減少的量
r:每個汙染物至少要被減少的量

c=[8,10,7,6,11,9]
p=[[12,9,25,20,17,13],
  [35,42,18,31,56,49],
  [37,53,28,24,29,20]]
r=[60,150,125]

Add decision variables

x={}
for j in range(6):
    x[j]=m.addVar(lb=0,ub=1,name="x_%d"%j)

Update

m.update()

Add objective and constraints

m.setObjective(quicksum(c[j]*x[j] for j in range(6)),GRB.MINIMIZE)
for i in range(3):
    m.addConstr(quicksum(p[i][j]*x[j] for j in range(6))>=r[i],"c0")

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