How to constrain the subject to rounded integer using Python Pulp

Question

I'm using pulp for a linear optimization problem. I want the subject to be rounded to 100. How should I do it.

I saw the answer to this one, But I don't know how to defined a integer variable I in this case. Use mod function in a constraint using Python Pulp

Thank you!!!

What do you mean by 'rounded to 100'? Could you provide an example? — abc
– abc, Commented Jun 13, 2019 at 15:48
Like I want results be 100 multiplier, if it returns 90 I wanted to be 100 — hhd
– hhd, Commented Jun 13, 2019 at 15:58
Can you share the code snippet and share where it causes the error ? — Pirate X
– Pirate X, Commented Jun 13, 2019 at 16:58

abc · Accepted Answer · 2019-06-13 17:07:50Z

2

Consider a simple ILP which consist of an objective function and constraints on the variables:

min x1 + x2
s.t.
x1 + x2 >= 50
x1 >= 0 
x2 >= 0

To enforce your condition you can add 2 variables y and z and 2 constraints:

y >= x1 + x2
y == 100 * j for some j >= 1

and change your objective function in min y.

In code:

Original formulation

x1 = pulp.LpVariable('x1',lowBound=0,cat=pulp.LpContinuous)
x2 = pulp.LpVariable('x2',lowBound=0,cat=pulp.LpContinuous)

prob1 = pulp.LpProblem('example1',pulp.LpMinimize)
# obj
prob1+= 5*x1 + 10*x2
# constraints
prob1+= x1 + x2 >= 50

prob1.solve() 
print(pulp.value(prob1.objective)) #250

Converted one

y = pulp.LpVariable('y',lowBound=0, cat=pulp.LpContinuous)
z = pulp.LpVariable('z',lowBound=1, cat=pulp.LpInteger)

prob2 = pulp.LpProblem('example2',pulp.LpMinimize)
# obj
prob2+= y
# constraints
prob2+= y >= 5*x1 + 10*x2
prob2+= y == 100 * z
prob2+= x1 + x2 >= 50

prob2.solve()
print(pulp.value(prob2.objective)) #300

answered Jun 13, 2019 at 17:07

abc

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2 Comments

hhd Over a year ago

Thanks a lot. Can you also take a look at this one:stackoverflow.com/questions/57949190/…

Sri Pallavi Over a year ago

What would be the approach for applying a condition that each LP variable should be a multiple of 100? I am trying to solve a supply chain problem where the quantity of each part (i.e. LP variable) should be multiple of 100. Kindly help

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