binary variable multiplying by another variable in python

Answered

Saina Akbari Kouchaksaraei

• February 27, 2023 02:03
• Edited

Hello everyone

I am quite new to Gurobi. I have a basic mathematical model for replenishment that I want to code in Python using Gurobi. However, in some part of the model and constraints I have to multiply binary variable to another positive variable which return error as : GurobiError: Invalid argument to QuadExpr addition

this error just happen in objective function.

I searched and found an answer from Gurobi that we can add

m.params.NonConvex = 2
m.setParam('NonConvex', 2)

to solve the problem but still it does not work an returns the same error.

my code is as below:

import math
import gurobipy as gp
from gurobipy import GRB

# Set data______________________________________________________________________________________________________________________

suppliers = [1]
warehouses = [1]
retailers = [1]
time_periods = list(range(1, 11))

# Parameter data________________________________________________________________________________________________________________

capacity = {'i': 600, 'j': 600}
capacity2= {'r':600}
cost = {(1, 1): 2}
cost2 = {(1, 1): 2}
setupcost1={(1,1):300}
setupcost2={(1,1):300}

# Create model
m = gp.Model('Profit_SC')


# setup cost for delivering from warehouse to retailer

for j in warehouses:
    for r in retailers:
        m.addVar(lb=setupcost2.get((j,r), 0), ub=setupcost2.get((j,r), 0), vtype=gp.GRB.CONTINUOUS, name="setupcost2_{}_{}".format(j,r))


#demand in retailer r at time t

def demand(r,t):
    for r in retailers:
            return (50*0.7*(8 * (100*0.01 / (math.e ** (0.1 * t)))))
for t in range(1, 11):
    print("t =", t, "r=",r, "Demand =", demand(r,t))


# Add variables
#quantity of products delivers from supplier to warehouse
x = {}
for i in suppliers:
    for j in warehouses:
        for t in time_periods:
            x [i,j,t] = m.addVar(vtype="C", name="x" )

#quantity of products delivers from warehouseto retailer     
y = {}
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            y [j,r,t] = m.addVar(vtype="C", name="y" )  

        
# binary variable equals to 1 ifdelivery between warehouse and retailer happens otherwise zero        
gama2={}
for r in retailers:
    for t in time_periods:
        gama2[r,t] = m.addVar(vtype=gp.GRB.BINARY, name="gama2")


#inventory level at retailer        
inv={}
for r in retailers:
    for t in time_periods:
        inv[r,t]=m.addVar(vtype="C", name="inventory" ) 
        
# Add constraints_______________________________________________________________________________________________________________
#constraints for capacity            
m.addConstrs((gp.quicksum(x[i, j, t] for j in warehouses  for i in suppliers for t in time_periods) <= capacity['i']
              for i in suppliers for t in time_periods), name='supply')
m.addConstrs((gp.quicksum(y[j, r, t] for j in warehouses) <= capacity['j']*gama2[r,t]
             for r in retailers for t in time_periods), name='supply2')


#constraints for binary variable
m.addConstr((gp.quicksum(gama2[r,t]  for r in retailers for t in time_periods)<=1), name='binary variable 2')

#constraints for inventory
for r in retailers:
    for t in time_periods:
        if t>1:
          m.addConstrs((inv[r, t] == inv[r,t-1]+(y[j,r,t]*gama2[r,t])-demand(r,t) for j in warehouses ), name='inventory')

m.addConstrs((inv[r,t]+ gp.quicksum(y[j,r,t]*gama2[r,t] for j in warehouses)<= demand(r, t) for r in retailers for t in time_periods) , name='inventory balance')


# Set objective function________________________________________________________________________________________________________

m.setObjective(gp.quicksum((y[j, r, t] * cost2[j, r]*gama2[r,t] for j in warehouses for r in retailers for t in time_periods )) +
               gp.quicksum((x[i, j, t] * cost[i, j] for i in suppliers for j in warehouses for t in time_periods )) +
               (setupcost2[j,r]*gama2[r,t] for j in warehouses for r in retailers for t in time_periods),
              sense=gp.GRB.Minimize)

m.update()

# Solve the model
m.optimize()


# Print the results_____________________________________________________________________________________________________________

print('x values:',x)
for i in suppliers:
    for j in warehouses:
        for t in time_periods:
            print(f"x({i}, {j}, {t}) = {x[i, j, t].X}")

print('y values:',y)
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            print(f"y({j}, {r}, {t}) = {y[j, r, t].X}")
            

print('inventory:',inv)
for r in retailers:
    for t in time_periods:
        print(f"inv({r}, {t}) = {inv[r, t].X}")
            

Also, I have found from your answers to this issue in previous questions that I can use big M technique. I tried to define that as below, however the model returns AttributeError: type object 'GRB' has no attribute 'Minimize'

the model is as below. I would highly appreciate it if you could help me with this issue

import math
import gurobipy as gp
from gurobipy import GRB

# Set data______________________________________________________________________________________________________________________
suppliers = [1]
warehouses = [1]
retailers = [1]
time_periods = list(range(1, 11))
M=[7000]

# Parameter data________________________________________________________________________________________________________________
capacity = {'i': 600, 'j': 600}
capacity2= {'r':600}
cost = {(1, 1): 2}
cost2 = {(1, 1): 2}
setupcost1={(1,1):300}
setupcost2={(1,1):300}

# Create model
m = gp.Model('Profit_SC')


# setup cost
for i in suppliers:
    for j in warehouses:
            m.addVar(lb=setupcost1.get((i,j), 0), ub=setupcost1.get((i,j), 0), vtype=gp.GRB.CONTINUOUS, name="setupcost1_{}_{}".format(i,j))


for j in warehouses:
    for r in retailers:
        m.addVar(lb=setupcost2.get((j,r), 0), ub=setupcost2.get((j,r), 0), vtype=gp.GRB.CONTINUOUS, name="setupcost2_{}_{}".format(j,r))


#demand_________________________________________________________________________________________________________________________

def demand(r,t):
    for r in retailers:
            return (50*0.7*(8 * (100*0.01 / (math.e ** (0.1 * t)))))
for t in range(1, 11):
    print("t =", t, "r=",r, "Demand =", demand(r,t))




# Add variables_________________________________________________________________________________________________________________

#quantity of products delivers from supplier to warehouse
x = {}
for i in suppliers:
    for j in warehouses:
        for t in time_periods:
            x [i,j,t] = m.addVar(vtype= GRB.CONTINUOUS, lb =0, name="x" )

#quantity of products delivers from warehouseto retailer  
y = {}
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            y [j,r,t] = m.addVar(vtype= GRB.CONTINUOUS, lb =0, name="y" )  
        

# binary variable equals to 1 ifdelivery between warehouse and retailer happens otherwise zero
gama2={}
for r in retailers:
    for t in time_periods:
        gama2[r,t] = m.addVar(vtype=gp.GRB.BINARY, name="gama2")

#inventory level at retailer       
inv={}
for r in retailers:
    for t in time_periods:
        inv[r,t]=m.addVar(vtype= GRB.CONTINUOUS, lb =0, name="inventory" ) 


#new variable to linearize the equations
z={}
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            z[j,r,t]=m.addVar(vtype="C", name="new variable for linearization" )
        
# Add constraints_______________________________________________________________________________________________________________

#constraints for capacity            
m.addConstrs((gp.quicksum(x[i, j, t] for j in warehouses  for i in suppliers for t in time_periods) <= capacity['i'] for i in suppliers), name='supply')
m.addConstrs((gp.quicksum(y[j, r, t] for j in warehouses) <= capacity['j']*gama2[r,t]
             for r in retailers for t in time_periods), name='supply2')


#constraints for binary variable
m.addConstr((gp.quicksum(gama2[r,t]  for r in retailers for t in time_periods)<=1), name='binary variable 2')


#linearization process by z

for j in warehouses:
    for r in retailers:
        for t in time_periods:
            m.addConstr((z[j,r,t]==gama2[r,t]*7000), name='linear 1')
        
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            m.addConstr((z[j,r,t]>=0), name='linear 2')

for j in warehouses:
    for r in retailers:
        for t in time_periods:
            m.addConstr((z[j,r,t]<=gp.quicksum(y[j,r,t] for j in warehouses)), name='linear 3')
        
for j in warehouses:
    for r in retailers:
        for t in time_periods:
            m.addConstr((z[j,r,t]>=y[j,r,t]-(1-gama2[r,t])*7000), name='linear 4')


#constraint for inventory
for r in retailers:
    for t in time_periods:
        if t>1:
          m.addConstrs((inv[r, t] == inv[r,t-1]+(z[j,r,t])-demand(r,t) for j in warehouses ), name='inventory')

for r in retailers:
    for t in time_periods:
        m.addConstr((inv[r,t]+ gp.quicksum(z[j,r,t] for j in warehouses)<= demand(r, t)),name='inventory balance')



# Set objective function________________________________________________________________________________________________________


m.setObjective(gp.quicksum((z[j,r,t] for j in warehouses for r in retailers for t in time_periods ))*2 +
               gp.quicksum((x[i, j, t] for i in suppliers for j in warehouses for t in time_periods ))*2 + 
               (gp.quicksum(gama2[r,t] for r in retailers for t in time_periods))*300,
              sense=gp.GRB.Minimize)


m.update()

# Solve the model
m.optimize()

 

 

Related to

• Python
• Error
• Formulation

0

• 

  Riley Clement

  Gurobi Staff

  • February 27, 2023 11:39

  Hi Saina,

  The capitalization matters here, i.e. use gp.GRB.MINIMIZE.

  Based off the second code block, it looks like you solved your original problem?

  - Riley

  0
• 

  Saina Akbari Kouchaksaraei

  • February 27, 2023 11:53

  

  

  

  Many thanks for your reply
  I tried the capital letters but still doesn’t work
  I’m not sure if I did the linearisation correctly, I only tried to use the relations based on big M like this link

  https://or.stackexchange.com/questions/39/how-to-linearize-the-product-of-a-binary-and-a-non-negative-continuous-variable

  I was wondering if there is any way that I can run the model without converting the model into linear one (based on first model)
  Sincere thanks

  0
• 

  Riley Clement

  Gurobi Staff

  • February 27, 2023 12:12

  Hi Saina,

  When using gp.GRB.MINIMIZE the second code block you posted above runs without problems.

  The model is infeasible - but the code is fine.

  If you wish to understand why the model is infeasible you can compute an IIS.
  
  You also have the option of not linearizing the model and asking Gurobi to solve a non-convex model.  You may need to set the NonConvex parameter to 2 to allow this - the solver output will tell you.

   

  - Riley

  0
• 

  Saina Akbari Kouchaksaraei

  • February 27, 2023 22:50
  • Edited

  

  

  

  Dear Riley

  I am so thankful for your help. It was my mistake that only checked capital letters on my first block. But yes the second one works.

  I only have one another question for the first block. As I need to develop my model later, it is easier to work with the first one. I tried to set Nonconvex parameter to 2 but it still returns error (
  TypeError: unsupported operand type(s) for *: 'generator' and 'int'). my modified code is as below. I would be grateful if you could help me to correct this issue as well.

  Sincere thanks

   

  import math
  import gurobipy as gp
  from gurobipy import GRB
  
  
  # Set data______________________________________________________________________________________________________________________
  
  suppliers = [1]
  warehouses = [1]
  retailers = [1]
  time_periods = list(range(1, 11))
  
  # Parameter data________________________________________________________________________________________________________________
  
  capacity = {'i': 600, 'j': 600}
  capacity2= {'r':600}
  cost = {(1, 1): 2}
  cost2 = {(1, 1): 2}
  setupcost1={(1,1):300}
  setupcost2={(1,1):300}
  
  # Create model
  m = gp.Model('Profit_SC')
  
  m.params.NonConvex = 2
  m.setParam('NonConvex', 2)
  
  # setup cost for delivering from warehouse to retailer
  
  for j in warehouses:
      for r in retailers:
          m.addVar(lb=setupcost2.get((j,r), 0), ub=setupcost2.get((j,r), 0), vtype=gp.GRB.CONTINUOUS, name="setupcost2_{}_{}".format(j,r))
  
  
  #demand in retailer r at time t
  
  def demand(r,t):
      for r in retailers:
              return (50*0.7*(8 * (100*0.01 / (math.e ** (0.1 * t)))))
  for t in range(1, 11):
      print("t =", t, "r=",r, "Demand =", demand(r,t))
  
  
  
  
  # Add variables
  
  #quantity of products delivers from supplier to warehouse
  x = {}
  for i in suppliers:
      for j in warehouses:
          for t in time_periods:
              x [i,j,t] = m.addVar(vtype="C", name="x" )
  
  #quantity of products delivers from warehouseto retailer     
  y = {}
  for j in warehouses:
      for r in retailers:
          for t in time_periods:
              y [j,r,t] = m.addVar(vtype="C", name="y" )  
  
          
  # binary variable equals to 1 ifdelivery between warehouse and retailer happens otherwise zero        
  gama2={}
  for r in retailers:
      for t in time_periods:
          gama2[r,t] = m.addVar(vtype=gp.GRB.BINARY, name="gama2")
  
  
  #inventory level at retailer        
  inv={}
  for r in retailers:
      for t in time_periods:
          inv[r,t]=m.addVar(vtype="C", name="inventory" ) 
          
  # Add constraints_______________________________________________________________________________________________________________
  
  
  #constraints for capacity            
  m.addConstrs((gp.quicksum(x[i, j, t] for j in warehouses  for i in suppliers for t in time_periods) <= capacity['i']
                for i in suppliers for t in time_periods), name='supply')
  m.addConstrs((gp.quicksum(y[j, r, t] for j in warehouses) <= capacity['j']*gama2[r,t]
               for r in retailers for t in time_periods), name='supply2')
  
  
  #constraints for binary variable
  m.addConstr((gp.quicksum(gama2[r,t]  for r in retailers for t in time_periods)<=1), name='binary variable 2')
  
  
  #constraints for inventory
  for r in retailers:
      for t in time_periods:
          if t>1:
            m.addConstrs((inv[r, t] == inv[r,t-1]+(y[j,r,t]*gama2[r,t])-demand(r,t) for j in warehouses ), name='inventory')
  
  m.addConstrs((inv[r,t]+ gp.quicksum(y[j,r,t]*gama2[r,t] for j in warehouses)<= demand(r, t) for r in retailers for t in time_periods) , name='inventory balance')
  
  
  
  
  # Set objective function________________________________________________________________________________________________________
  
  
  m.setObjective(gp.quicksum(((y[j, r, t]*gama2[r,t] for j in warehouses for r in retailers for t in time_periods )*2 )) +
                 gp.quicksum(((x[i, j, t] for i in suppliers for j in warehouses for t in time_periods ) * 2 )) +
                 ((gama2[r,t] for r in retailers for t in time_periods)*300  ),
                sense=gp.GRB.MINIMIZE)
  
  m.update()
  
  # Solve the model
  m.optimize()
  
  
  # Print the results_____________________________________________________________________________________________________________
  
  print('x values:',x)
  for i in suppliers:
      for j in warehouses:
          for t in time_periods:
              print(f"x({i}, {j}, {t}) = {x[i, j, t].X}")
  
  print('y values:',y)
  for j in warehouses:
      for r in retailers:
          for t in time_periods:
              print(f"y({j}, {r}, {t}) = {y[j, r, t].X}")
              
  
  print('inventory:',inv)
  for r in retailers:
      for t in time_periods:
          print(f"inv({r}, {t}) = {inv[r, t].X}")
           

  0
• 

  Riley Clement

  Gurobi Staff

  • February 28, 2023 01:57

  Hi Saina,

  Let's have a look at the objective that is causing you the problem

  m.setObjective(gp.quicksum(((y[j, r, t]*gama2[r,t] for j in warehouses for r in retailers for t in time_periods )*2 )) +
                 gp.quicksum(((x[i, j, t] for i in suppliers for j in warehouses for t in time_periods ) * 2 )) +
                 ((gama2[r,t] for r in retailers for t in time_periods)*300  ),
                sense=gp.GRB.MINIMIZE)

  and compare it to the other objective which works fine:

  m.setObjective(gp.quicksum((z[j,r,t] for j in warehouses for r in retailers for t in time_periods ))*2 +
                 gp.quicksum((x[i, j, t] for i in suppliers for j in warehouses for t in time_periods ))*2 + 
                 (gp.quicksum(gama2[r,t] for r in retailers for t in time_periods))*300,
                sense=gp.GRB.Minimize)

  One works, but one doesn't.  Can you spot the difference (noting that your error message specifically highlights the * operator)?

  - Riley

   

  0
• 

  Saina Akbari Kouchaksaraei

  • February 28, 2023 03:17
  • Edited

  

  

  

  I got it, it works now

  Thanks

  0

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