The @MIN and @MAX functions are used to find the minimum and maximum of an expression over members of a set.

Again, consider the model:

MODEL:

SETS:

  VENDORS: DEMAND;

ENDSETS

DATA:

  VENDORS, DEMAND =  V1,5 V2,1 V3,3 V4,4 V5,6;

ENDDATA

END

To find the minimum and maximum DEMAND, all one need do is add the two expressions:

MIN_DEMAND = @MIN( VENDORS( J): DEMAND( J));

MAX_DEMAND = @MAX( VENDORS( J): DEMAND( J));

The resulting model with the new statements in bold would then be as follows:

MODEL:

SETS:

  VENDORS: DEMAND;

ENDSETS

DATA:

  VENDORS, DEMAND =  V1,5 V2,1 V3,3 V4,4 V5,6;

ENDDATA

  MIN_DEMAND = @MIN( VENDORS( J): DEMAND( J));

  MAX_DEMAND = @MAX( VENDORS( J): DEMAND( J));

END

As with the @SUM example, we can use an implied index list since the attributes are defined on the index set. Using implied indexing, we can recast our expressions as:

MIN_DEMAND = @MIN( VENDORS: DEMAND);

MAX_DEMAND = @MAX( VENDORS: DEMAND);

In either case, when we solve this model, LINGO returns the expected minimum and maximum DEMAND of:

Variable           Value

MIN_DEMAND        1.000000

MAX_DEMAND        6.000000

For illustration purposes, suppose we had just wanted to compute the minimum and maximum values of the first three elements of DEMAND. As with the @SUM example, all we need do is add the conditional qualifier J #LE# 3. We then have:

MIN_DEMAND3 =

  @MIN( VENDORS( J) | J #LE# 3: DEMAND( J));

MAX_DEMAND3 =

  @MAX( VENDORS( J) | J #LE# 3: DEMAND( J));

with solution:

Variable           Value

MIN_DEMAND3        1.000000

MAX_DEMAND3        5.000000