Creating set of sets.

Question

Hi,
I'm making a model of flexible flow shop for academic project and I have a problem with declaring one set(or sets in fact). The set I'm talking about is a set of parallel machins which are bounded to specific stages. It looks more or less like this:
 
t - stage index, t = 1, 2, 3, . . . , k  
i - machine index, i = 1, 2, 3, . . . , mt (t is upper index) 
Do I have to specify every set of machines seperatly for each stage or is there some convinient way of doing it?

deannezhang · Accepted Answer

Hi,You do not need to specify every set of machines for each stage, what you can do is to introduce a parameter StageMachineMapping (t,i). If machine i belongs to stage t, then StageMachineMapping is 1, otherwise it's 0. Then when you declare your decision variables, for example, JobSchedule(t,i,j), which is to assign job j to machine i on stage t, you want to use StageMachineMapping (t,i) as domain condition of this variable, so for each job j the model will only use a machine i if it belongs to stage t.  You also need to use this parameter as domain condition for all variables and constrains when it applies. Hope this helps.

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