# When I set option substout 1, why doesn’t AMPL make the substitutions that I expect?

**URL:** <https://discuss.ampl.com/t/when-i-set-option-substout-1-why-doesn-t-ampl-make-the-substitutions-that-i-expect/58>\
**Category:** FAQs\
**Tags:** variables\
**Created:** [December 15, 2021, 5:33pm UTC](https://discuss.ampl.com/t/when-i-set-option-substout-1-why-doesn-t-ampl-make-the-substitutions-that-i-expect/58 "2021-12-15T17:33:35Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![megrobert](https://avatars.discourse-cdn.com/v4/letter/m/d07c76/32.png) [@megrobert](https://discuss.ampl.com/u/megrobert)\
**Post date:** [December 15, 2021, 5:33pm UTC](https://discuss.ampl.com/t/when-i-set-option-substout-1-why-doesn-t-ampl-make-the-substitutions-that-i-expect/58/1 "2021-12-15T17:33:35Z")

</div>

A variable is ineligible to be substituted out of a problem if (a) it is subject to any bounds or integrality conditions, or (b) it has already appeared on the right-hand side of a constraint that was used to make a substitution.

Case (a) includes bounds or integrality conditions specified in the variable’s declaration, and also bounds that are added by AMPL’s presolve phase. Thus turning presolve off (by setting `option presolve 0` ) may permit a greater number of substitutions.

For constraints indexed over a set, the incidence of case (b) may depend on the ordering of the set. Consider for example the constraints

```auto
var x {1..10}; 
subj to step {j in 1..9}: x[j] = x[j+1] + 1;

```

The first several constraints generated are

```auto
step[1]: x[1] = x[2] + 1 
step[2]: x[2] = x[3] + 1 
step[3]: x[3] = x[4] + 1 
step[4]: x[4] = x[5] + 1

```

Constraint `step[1]` may be used to substitute for `x[1]` . Constraint `step[2]` may not be used to substitute for `x[2]` , however, because `x[2]` has already appeared on the right-hand side of a constraint, namely `step[1]` , that was used to make a substitution. Similarly, `step[3]` may be used to substitute for `x[3]` , but `step[4]` may not be used to substitute for `x[4]` , and so forth. Only the odd-numbered constraints `step[j]` are eliminated by substitution in this case.

If instead you write the declaration with the ordered index set reversed,

```auto
subj to step {j in 9..1 by -1} x[j] = x[j+1] + 1;

```

then the constraints are generated as

```auto
step[9]: x[9] = x[10] + 1 
step[8]: x[8] = x[9] + 1 
step[7]: x[7] = x[8] + 1 
step[6]: x[6] = x[7] + 1

```

and case (b) does not occur. All of the constraints `step[j]` can be eliminated, and every variable except `x[10]` is substituted out as a result.

Close attention to formulation may thus be necessary to get the substitutions that you want. Set option `show_stats 1` to see how many substitutions are being made, and use AMPL’s constraint expansion commands to see the constraints (in order) before and after substitution.