Python Optimization Modeling: optlang

fromoptlangimportVariable,Constraint,Objective,Model

# Define problem parameters
# Note this can be done using any of Python's data types. Here we have chosen dictionaries
supply={"Seattle":350,"San_Diego":600}
demand={"New_York":325,"Chicago":300,"Topeka":275}

distances={# Distances between locations in thousands of miles
"Seattle":{"New_York":2.5,"Chicago":1.7,"Topeka":1.8},
"San_Diego":{"New_York":2.5,"Chicago":1.8,"Topeka":1.4}
}

freight_cost=9# Cost per case per thousand miles

# Define variables
variables={}
fororigininsupply:
variables[origin]={}
fordestinationindemand:
# Construct a variable with a name, bounds and type
var=Variable(name="{}_to_{}".format(origin,destination),lb=0,type="integer")
variables[origin][destination]=var

# Define constraints
constraints=[]
fororigininsupply:
const=Constraint(
sum(variables[origin].values()),
ub=supply[origin],
name="{}_supply".format(origin)
)
constraints.append(const)
fordestinationindemand:
const=Constraint(
sum(row[destination]forrowinvariables.values()),
lb=demand[destination],
name="{}_demand".format(destination)
)
constraints.append(const)

# Define the objective
obj=Objective(
sum(freight_cost*distances[ori][dest]*variables[ori][dest]fororiinsupplyfordestindemand),
direction="min"
)
# We can print the objective and constraints
print(obj)
print("")
forconstinconstraints:
print(const)

print("")

# Put everything together in a Model
model=Model()
model.add(constraints)# Variables are added implicitly
model.objective=obj

# Optimize and print the solution
status=model.optimize()
print("Status:",status)
print("Objective value:",model.objective.value)
print("")
forvarinmodel.variables:
print(var.name,":",var.primal)