Jobshop with alternative "path"

[Alexander Leiser]

I'm trying to model a jobshop problem where a job could have an alternative production path. I think the easiest explanation I can give is by using the  Example flexible jobshop problem  instead of my current one to keep it simple.

The first job in the example is:

jobs = [ # task = (processing_time, machine_id)

• [ # Job 0
  [(3, 0), (1, 1), (5, 2)], # task 0 with 3 alternatives
  [(2, 0), (4, 1), (6, 2)], # task 1 with 3 alternatives
  [(2, 0), (3, 1), (1, 2)], # task 2 with 3 alternatives
  ]...

So job 0 can run on 3 different machines in each task. What I`m trying to model right now is that for example if I use machine 2 in task 1 I don`t need to do anything in task 0 and task 2 because the machine can do all 3 tasks at once. Basically using one machine in a later task could make another task obselete. 

If I give task 0 an option with 0 processing time the optimizer would obviously always choose that one in case that machine is available at that point, so not really an option.

How can I make an earlier task depent on a later choice, any suggestions?

[Laurent Perron]

The notion of path is unclear to me. My initial reaction is to use the same literal for all tasks in a path.

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

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[Alexander Leiser]

I'm basically talking about the path a product would take. So for example in this case:

machine 1 (time 1) -> 2 (time 6) -> 2 (time 1)

one alternative would be

machine 0 (time 3) -> 1 (time 4) -> 2 (time 1)

But like this there is no way ( I found) of modelling a job path which makes one task obsolete. For example using machine 2 in task 1 makes using a machine in task 0 unnecessary or alternatively using machine 2 in task 1 requires machine 1 in task 0 but using another machine leaves all the options in task 0. I hope this clears the questions up a bit

[Laurent Perron]

Isn't this just a set of implications between the performed literals of the tasks ?

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

To view this discussion on the web visit https://groups.google.com/d/msgid/or-tools-discuss/84279f8b-eb5b-4028-99ee-894973d9a2a1n%40googlegroups.com.

[Alexander Leiser]

I think the problem is that there is no possible implication when you start scheduling. You will only find out later.

If it would be clear in task 0, that for example only that machine is needed I think it`ll be no problem.

But I have can't figure out how to model it and string everything together with the alternatives...