if statement of objective in linear programming

Question

I am trying to code a Linear Programming model with Pyomo. I have a question about the if statement. Let objective is minimum the time of all jobs done.

          Job1  Job2  Setup  
machine1  25    30    30  
machine2  40    50    50  
machine3  35    59    60

Each machine needs to be set up at least once, if machine 1 and machine 2 both are being used, we need extra 20 mins.

I have read some posts about the big-M method that can solve this problem. But I don't know how to do it when it related to the objective. Thanks!

We can't see the problem if you don't provide any code!

Alexey S. Larionov
– Alexey S. Larionov

2020-12-16 07:36:56 +00:00
Commented Dec 16, 2020 at 7:36 — Alexey S. Larionov
– Alexey S. Larionov, Commented Dec 16, 2020 at 7:36

Erwin Kalvelagen · Accepted Answer · 2020-12-16 10:16:14Z

1

Let m(i)∈{0,1} indicating if machine i is used. Then the additional setup time can look like:

  both12Time ≥ 20*(m(1) + m(2) - 1)
  both12Time ≥ 0

We assume here total time is minimized.

answered Dec 16, 2020 at 10:16

Erwin Kalvelagen

16.9k3 gold badges17 silver badges42 bronze badges

Sign up to request clarification or add additional context in comments.

Collectives™ on Stack Overflow

if statement of objective in linear programming

1 Answer 1

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

Comments

Your Answer

Sign up or log in

Post as a guest

Related