def test_double_sided_ineq(self):
m = ConcreteModel()
m.s = Set(initialize=[1.0,2.0,3.0,4.0,5.0])
m.vmin = Param(m.s, initialize=lambda m,i: i)
m.vmax = Param(m.s, initialize=lambda m,i: i**2)
m.v = Var(m.s)
def _con(m, i):
return inequality(m.vmin[i]**2, m.v[i], m.vmax[i]**2)
m.con = Constraint(m.s, rule=_con)
OUT = io.StringIO()
for i in m.s:
OUT.write(str(_con(m,i)))
OUT.write("\n")
display(m.con, ostream=OUT)
reference="""1.0 <= v[1.0] <= 1.0
4.0 <= v[2.0] <= 16.0
9.0 <= v[3.0] <= 81.0
16.0 <= v[4.0] <= 256.0
25.0 <= v[5.0] <= 625.0
con : Size=5
Key : Lower : Body : Upper
1.0 : 1.0 : None : 1.0
2.0 : 4.0 : None : 16.0
3.0 : 9.0 : None : 81.0
4.0 : 16.0 : None : 256.0
5.0 : 25.0 : None : 625.0
"""
self.assertEqual(OUT.getvalue(), reference)
def farmer_lp(solver="cplex"):
# concrete model
instance = ConcreteModel(name="Farmer_LP")
# set
instance.plants = ("wheat", "corn", "beet")
instance.action = ("buy", "sell")
instance.price = ("high", "low")
# decision variables
instance.area = Var(instance.plants, within=NonNegativeReals)
instance.wheat_act = Var(instance.action, within=NonNegativeReals)
instance.corn_act = Var(instance.action, within=NonNegativeReals)
instance.beet_price = Var(instance.price,
bounds=(0, 6000),
within=NonNegativeReals)
# constraint
def area_rule(model):
return sum(model.area[pdx] for pdx in model.plants) <= 500
instance.area_constraint = Constraint(rule=area_rule)
# constraint
def min_wheat_rule(model):
return (2.5 * model.area['wheat'] + model.wheat_act['buy'] -
model.wheat_act['sell'] >= 200)
instance.min_wheat_constraint = Constraint(rule=min_wheat_rule)
# constraint
def min_corn_rule(model):
return (3 * model.area['corn'] + model.corn_act['buy'] -
model.corn_act['sell'] >= 240)
instance.min_corn_constraint = Constraint(rule=min_corn_rule)
# constraint
def beet_price_rule(model):
return (model.beet_price['high'] + model.beet_price['low'] <=
20 * model.area['beet'])
instance.beat_price_constraint = Constraint(rule=beet_price_rule)
# objective
def min_cost_rule(model):
grow_cost = (150 * model.area['wheat'] + 230 * model.area['corn'] +
260 * model.area['beet'])
wheat_cost = (238 * model.wheat_act['buy'] -
170 * model.wheat_act['sell'])
corn_cost = (210 * model.corn_act['buy'] -
150 * model.corn_act['sell'])
beet_cost = -(36 * model.beet_price['high'] +
10 * model.beet_price['low'])
return grow_cost + wheat_cost + corn_cost + beet_cost
instance.min_cost_objective = Objective(rule=min_cost_rule, sense=minimize)
# solve
opt = SolverFactory(solver)
results = opt.solve(instance)
instance.solutions.load_from(results)
display(instance)
print("LP objective: {}".format(-instance.min_cost_objective()))