gams:model_predecessor_successor_relations

Q: *I have variables with two indices, e.g. x(d,h), where d and h are sets of days and hours.
My problem is to make a predecessor/sucessor relation between those x variables. E.g. I have to model the difference between two neighboring x variables like:
delta(d,h) =e= x(d,h) - x(pred(d,h)) ;
delta(d,h) =l= constant ; *

The GAMS lingo for this is lag and lead operators: `x(d,h-1)`

e.g. shows the previous hour.

The `-`

is not a numerical minus but a lag. Trouble
is that the predecessor for `x(d,'h1')`

is `x(d-1,'h24')`

. You also have
to decide what predecessor of `'d1`

',`'h1`

' is.

If you do a steady state
model you could have `'d365`

',`'h24`

' or you can decide that there is no
predecessor (meaning `delta('d1','h1') = x('d1','h1)`

). I am assuming
your sets look like this

Set d / d1*d365 / h / h1*h24 /;

Now here is what you can do:

delta(d,h) =e= x(d,h) - x(d-(1$sameas('h1')),h--1)) ;

Not so elegant, but it will work. I prefer working with an additional set of all hours in the year and a map between d,h and all hours in the year:

Set h /h1*h24/, d /d1*d365/, dh(d,h) /#d.#h/ Set t /t1*t8760/, tdh(t,d,h) /#t:#dh/, dht /#dh:#t/;

`.`

and `:`

are called matching operators.
Now I would have the variable `x`

and `delta`

over `t`

and then the
constraint looks simple:

delta(t) =e= x(t) - x(t-1); (or x(t--1) for steady state)

In case you have data by `d,h`

you can use the map `tdh`

, for example:
`delta(t) =l= sum(tdh(t,d,h), maxdeviation(d,h));`

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gams/model_predecessor_successor_relations.txt · Last modified: 2020/05/18 14:10 by Lutz Westermann