How to define constraints in Pyomo using sets and variables

Question

I am trying to model the transportation problem of Dantzig in Pyomo (see the GAMS code here https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_trnsport.html or the description here https://www.math.uh.edu/~rohop/fall_06/Chapter1.pdf).

I have problem defining the constraints for the supply using sets and variables. So basically what I want to do is to add the constraints: For all set_plants Sum over all set_markets x(set_plants, set_markets) <= param_capacityOfPlant (set_plants)

in GAMS it is this line

supply(i).. sum(j, x(i,j)) =l= a(i);

and in the description (https://www.math.uh.edu/~rohop/fall_06/Chapter1.pdf) it is equation 1.2

I am struggeling to implement this in Pyomo. I tried different things and I always get the error "TypeError: Cannot apply a Set operator to an indexed Var component (variable_x)"

Here you can see my code in which the lines at the very bottom are problematic (after #Constraints):

# -*- coding: utf-8 -*-
"""
Transport problem in Pyomo

Created on Mon Feb 15 09:55:06 2021


"""

import pyomo.environ as pyo

#Define the model

model = pyo.ConcreteModel()


#Define the sets
model.set_plants = pyo.Set(initialize=['Seattle', 'San_Diego'])
model.set_markets = pyo.Set(initialize=['New_York', 'Chicago', 'Topeka'])


# Parameters

valuesForCapacity = {'Seattle':350, 'San_Diego':600}
valuesForDemand = {'New_York': 325, 'Chicago': 300, 'Topeka': 275}

model.param_capacityOfPlants = pyo.Param(model.set_plants, initialize=valuesForCapacity)
model.param_demandAtMarkets = pyo.Param(model.set_markets, initialize=valuesForDemand)

model.param_capacityOfPlants.pprint()
model.param_demandAtMarkets.pprint()


#Parameter entry as table

valuesForDistance =  {('Seattle', 'New_York'): 2.5, ('Seattle', 'Chicago'): 1.7, ('Seattle', 'Topeka'): 1.8,
('San_Diego', 'New_York'): 2.5, ('San_Diego', 'Chicago'): 1.8, ('San_Diego', 'Topeka'): 1.4}
                      
model.param_distances = pyo.Param(model.set_plants, model.set_markets, initialize=valuesForDistance)

model.param_distances.pprint()


#Scalar
freightCostsPerUnitPerThousandMiles = 90


#Variables

model.variable_x = pyo.Var(model.set_plants,model.set_markets, within=pyo.NonNegativeReals)
model.variable_totalCosts = pyo.Var()

model.variable_x.pprint()


#Constraints

def supplyConstraintRule(model):
    #First try
    # return pyo.summation(variable_x)<=model.param_capacityOfPlants
    #Second try
    #return sum(variable_x for j in model.set_markets)<=model.param_capacityOfPlants
    # Third try
    return sum(variable_x(i,j) for j in model.set_markets)<=model.param_capacityOfPlants(i)


model.constraint_supply = pyo.Constraint (model.variable_x, rule=supplyConstraintRule)

Do you know how I have to implement this? I'd appreciate every comment from you.

Answer 1

Replace the Def and last line of your code with the following lines:

model.constraint_supply = pyo.ConstraintList()
    for i in model.set_plants:
        model.constraint_supply.add(sum(model.variable_x[i, j] for j in model.set_markets) <= model.param_capacityOfPlants[i])
model.constraint_supply.pprint()

The output will be as follow:

constraint_supply : Size=2, Index=constraint_supply_index, Active=True
    Key : Lower : Body                                                                                          : Upper : Active
      1 :  -Inf :       variable_x[Seattle,New_York] + variable_x[Seattle,Chicago] + variable_x[Seattle,Topeka] : 350.0 :   True
      2 :  -Inf : variable_x[San_Diego,New_York] + variable_x[San_Diego,Chicago] + variable_x[San_Diego,Topeka] : 600.0 :   True

Instead of using Def I used for loop for constraint definitions. If the constraints are not correct you can play with the for loop mentioned here. Generally there is no difference in the output of these two approaches in defining the constraints.

Edit: the following changes in your code solve the problem of using Def:

def supplyConstraintRule(model,i):
    # First try
    # return pyo.summation(variable_x)<=model.param_capacityOfPlants
    # Second try
    # return sum(variable_x for j in model.set_markets)<=model.param_capacityOfPlants
    # Third try
    return sum(model.variable_x[i, j] for j in model.set_markets) <= model.param_capacityOfPlants[i]

model.constraint_supply = pyo.Constraint(model.set_plants, rule=supplyConstraintRule)