set ARCS within NODES cross NODES;
# Elements of ARCS must have both elements in NODES

If you need a multi-dimensional set, but don't have the 1-dimensional sets to construct it yet you can use the dimen keyword:

set ROUTES dimen 2;

{'HOST', 'DEVICE', 'SWITCH', 'HUB', 'LINK', 'SUPERLINK'}

param start;
param end > start;
param step;
set NUMBERS := start .. end by step;

set NUMBERS := 1..5; # NUMBERS = {1, 2, 3, 4, 5}

set NUMBERS := 1 2 3 4 5; # NUMBERS = {1, 2, 3, 4 5}

{ <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 cros 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            -          -         -      -       -      +    + ;
   

3. 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 ...
   

set MONTHS ordered;

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)};

set ARCS within NODES cross NODES;

    ( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )};

display {(m, n) in ARCS : Supply[m] > 0}; # Display all arcs from supply nodes

var UnderProduction {(n, t) in TIME_NODES : Supply[n, t] > 0} >= 0, integer;

subject to ConserveFlow {(n, t) in TIME_NODES}:
   sum {(m, s) in TIME_NODES: (m, s, n, t) in TIME_ARCS}
     Shipment[m, s, n, t] + Supply[n, t] -
     if Supply[n, t] > 0 then UnderProduction[n, t] = ... 

set TIME_ARCS within TIME_NODES cross TIME_NODES;

set TIME_ARCS := (Youngstown, April, Albany, April)
                  (Youngstown, April, Youngstown, May) ... ;

set TIME_ARCS : =
(*, May, *, May)  Cincinnati 'Kansas City' Albany ... :=
Youngstown         +          +            +      ...
Pittsburgh         +          +            -      ...
... ;

set TIME_ARCS := (*, May, *, May) (Youngstown, Cincinnati) ... ... ;

set TIME_ARCS := (Youngstown, May, *, May) Cincinnati 'Kansas City' ... ... ;

# 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, (m, n) in ARCS} {(m, t, n, t)};
set STORAGE_ARCS := union {t in MONTHS, (m, n) in ARCS : t <> last(MONTHS)}
   {(m, t, n, next(t, MONTHS)};

set TIME_ARCS within TIME_NODES cross TIME_NODES :=
  TRANSPORT_ARCS union STORAGE_ARCS;