{ <e> in <S>, [<f> in <T>, <g> in <U>, …] :   <logical expression involving e [f, g, …]>} 

set NODES := Youngstown Pittsburgh Cincinnati 'Kansas City' Chicago
             Albany Houston Tempe Gary ;

set KIND := {'HOST', 'DEVICE', 'SWITCH', 'HUB', 'LINK', 'SUPERLINK'};
set COMPONENT := {C in CLASSES : (kind[C] = 'HOST'  ) or
                                 (kind[C] = 'DEVICE') or
                                 (kind[C] = 'HUB'   ) or
                                 (kind[C] = 'SWITCH')};
set FABRIC := NODE union LINK;

set SEARCH within VERTICES;
let SEARCH := {v in VERTICES: (v, w) in EDGES};

1. Using a List You simply list the elements in the set. This is good for sparse sets.

      model;
      set ARCS within NODES cross NODES;
      data;
      set ARCS := (Youngstown, Albany), (Youngstown, Cincinnati), ... ;
      

2. Using a Table You give a table using the first index set for the rows and the second index set for the columns, then you place a + where an element exists and a - where there is no element. This is good for dense sets.

set ARCS:
              Cincinnati 'Kansas City' Chicago Albany Houston Tempe Gary :=
Youngstown    +           +            +       +      -       -     -
Pittsburgh    +           +            +       -      -       -     +
Cincinnati    -           -            -       +      +       -     -
'Kansas City' -           -            -       -      +       +     -
Chicago       -           -            -       -      -       +     +
 ;

1. Using an Array You define a list of column indices for each row index. This is a good for sets with a few elements for each row.

set ARCS :=
(Youngstown, *) Cincinnati ‘Kansas City’ Chicago Albany
(Pittsburgh, *) Cincinnati ‘Kansas City’ Chicago Gary
(Cincinnati, *) Albany Houston ...

ord(e, ORD_SET)   # The position of e in ORD_SET
first(ORD_SET)    # The first element in ORD_SET
last(ORD_SET)     # The last element in ORD_SET
prev(e, ORD_SET)  # The element before e in ORD_SET
next(e, ORD_SET)  # The element after e in ORD_SET
member(i, ORDSET) # The element at position i in ORD_SET

# The set of time-staged arcs
set TIME_ARCS within TIME_NODES cross TIME_NODES :=
  { (m, t) in TIME_NODES, (n, u) in TIME_NODES :
    ( ( (m, n) in ARCS) and (t = u) ) or # The transportation arcs
	( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )}; # The storage arcs

set TRANSPORT_ARCS := union {t in MONTHS} (union {(m, n) ARCS} {(m, t, n, t)});

set TRANSPORT_ARCS := union {t in MONTHS, (m, n) in ARCS} {(m, t, n, t)};