This theorem provides an easy method for determining which

solution procedures to IDM's are worth analyzing and which are not. If

there are no decision variables (decision indices actually) involved,

the analysis is even simpler. For a variable index defined by a list

with no decisions, letting L.=U. proves there is only one list element.

Thus for the index there is a full precedence ordering. For a variable

index defined by a range, four cases must be considered. First consider

L. and U. offset from L. and U. by the same factor (to result in no
3 3 1 1
decisions). In this case a solution procedure does not extend since,

for any blocking factor k, k-1 tears are made in the first block and k

tears must be made in the second block. Next consider L. offset from L.
 -7
and U. offset from i, again by the same factor. A full precedence
 3
ordering exists as this results in a lower triangular IDM. Similarly L

offset from i and U. offset from U. results in full precedence order.
 -7 .7
With both limits offset from i by the same amount the IDM is diagonal

and fully precedence orders.

 Knowledge of the behavior of solution procedures from index

 definitions is very useful in choosing among the various solution

 procedures. Many possible solution procedures can be rejected without

 extensive analysis because they are known to be inefficient for the

 problem at hand.