Pyomo is an example of a recent generation of modeling languages that are fully integrated with an underlying scripting language.
The purpose of this tutorial is to introduce the basics of constructing Pyomo models. In this first example we consider the production of two products, 'A' and 'B', subject to constraints. The objective is to maximize profit
\begin{align} \max_{x,y} \mbox{profit} = 40 x + 30 y \end{align}subject to \begin{align} x & \leq 40 \\ x + 2y & \leq 80 \\ x + y & \leq 100 \end{align}
where $x$ refers the production of 'A', and $y$ to the production of 'B'.
At the highest level, Pyomo employs two objects -- a model and a solver -- to generate a resulting solution.
from pyomo.environ import *
model = ConcreteModel()
solver = SolverFactory('glpk')
from pyomo.environ import *
# create a model
model = ConcreteModel()
# index for x
idx = ['Product A', 'Product B']
# create decision variables
model.x = Var(idx, domain=NonNegativeIntegers)
# create objective
model.maxprofit = Objective(expr = 40*model.x['Product A'] + 30*model.x['Product B'], sense=maximize)
# create constraints
model.constraints = ConstraintList()
model.constraints.add(model.x['Product A'] <= 40)
model.constraints.add(model.x['Product A'] + model.x['Product B'] <= 80.5)
model.constraints.add(model.x['Product A'] + model.x['Product B'] <= 100)
solver = SolverFactory('glpk')
results = solver.solve(model)
for i in idx:
print(i, model.x[i]())
Product A 0.0 Product B 80.0
data = {'penny':1, 'nickel':5, 'dime':10, 'quarter':25, 'half-dollar':50}
data
{'dime': 10, 'half-dollar': 50, 'nickel': 5, 'penny': 1, 'quarter': 25}
data.keys()
dict_keys(['penny', 'nickel', 'dime', 'quarter'])
data.values()
dict_values([1, 5, 10, 25])
model = ConcreteModel()
model.x = Var(data.keys(), domain=NonNegativeIntegers)
model.ncoins = Objective(expr = sum(model.x[c] for c in data.keys()), sense=minimize)
model.cons = Constraint(expr = 83 == sum(data[c]*model.x[c] for c in data.keys()))
solver = SolverFactory('glpk')
solver.solve(model)
model.pprint()
1 Set Declarations
x_index : Dim=0, Dimen=1, Size=5, Domain=None, Ordered=False, Bounds=None
['dime', 'half-dollar', 'nickel', 'penny', 'quarter']
1 Var Declarations
x : Size=5, Index=x_index
Key : Lower : Value : Upper : Fixed : Stale : Domain
dime : 0 : 0.0 : None : False : False : NonNegativeIntegers
half-dollar : 0 : 1.0 : None : False : False : NonNegativeIntegers
nickel : 0 : 1.0 : None : False : False : NonNegativeIntegers
penny : 0 : 3.0 : None : False : False : NonNegativeIntegers
quarter : 0 : 1.0 : None : False : False : NonNegativeIntegers
1 Objective Declarations
ncoins : Size=1, Index=None, Active=True
Key : Active : Sense : Expression
None : True : minimize : x[penny] + x[nickel] + x[dime] + x[quarter] + x[half-dollar]
1 Constraint Declarations
cons : Size=1, Index=None, Active=True
Key : Lower : Body : Upper : Active
None : 83.0 : x[penny] + 5*x[nickel] + 10*x[dime] + 25*x[quarter] + 50*x[half-dollar] : 83.0 : True
4 Declarations: x_index x ncoins cons