# AMPL Modeling Tips #1: Disjunctions

**URL:** <https://discuss.ampl.com/t/ampl-modeling-tips-1-disjunctions/166>\
**Category:** Announcements\
**Tags:** logical-constraints, modeling-tips\
**Created:** [December 1, 2022, 9:40am UTC](https://discuss.ampl.com/t/ampl-modeling-tips-1-disjunctions/166 "2022-12-01T09:40:39Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![fdabrandao](https://sea1.discourse-cdn.com/flex019/user_avatar/discuss.ampl.com/fdabrandao/32/63_2.png) [@fdabrandao](https://discuss.ampl.com/u/fdabrandao)\
**Post date:** [December 1, 2022, 9:40am UTC](https://discuss.ampl.com/t/ampl-modeling-tips-1-disjunctions/166/1 "2022-12-01T09:40:39Z")

</div>

**“Two variables x and y cannot be positive at the same time”** : how to model this constraint? For the new [MP Library-based drivers](https://amplmp.readthedocs.io/en/latest/rst/drivers.html) (e.g., [gurobi](https://ampl.com/products/solvers/solvers-we-sell/gurobi/), [highs](https://ampl.com/products/solvers/open-source-solvers/), [copt](https://ampl.com/products/solvers/solvers-we-sell/copt/)), as well as for Constraint Programming solvers (ilogcp, gecode, jacop), this goes via AMPL logical operators:

`x <= 0 or y <= 0`

#### Small complete examples:

1. With MP, using the `or` operator:

```python
var x >= -1000 <= 1000;
var y >= -1000 <= 1000;
maximize total: 5 * x + 2 * y;
s.t. only_one_positive: x <= 0 or y <= 0;

```

1. With MP, using implication:

```python
var x >= -1000 <= 1000;
var y >= -1000 <= 1000;
maximize total: 5 * x + 2 * y;
s.t. only_one_positive: x > 0 ==> y <= 0;

```

1. Without MP you would need to linearize the constraint using big-M:

```python
var x >= -1000 <= 1000;
var y >= -1000 <= 1000;
var b binary;
maximize total: 5 * x + 2 * y;
s.t. big_m_1: x <= b * 1000;
s.t. big_m_2: y <= (1-b) * 1000;

```

Solving any of the three models above using our new Gurobi 10 driver produces the following:

```ampl
ampl: option solver gurobi; solve; display x, y, total;
x-Gurobi 10.0.0: optimal solution; objective 5000
x = 1000
y = 0
total = 5000

```

Solving any of the three models above using our HiGHS driver produces the following:

```ampl
ampl: option solver highs; solve; display x, y, total;
HiGHS 1.2.2: optimal solution; objective 5000
1 branching nodes
x = 1000
y = 0
total = 5000

```

More examples and documentation are in the [MP Modeling Guide](https://amplmp.readthedocs.io/en/latest/rst/model-guide.html).

### [[On LinkedIn](https://www.linkedin.com/feed/update/urn:li:activity:7004145631782948864)] [[On Twitter](https://twitter.com/AMPLopt/status/1598376843027091460)]

---

<div class="post-metadata">

**Author:** ![marcos](https://sea1.discourse-cdn.com/flex019/user_avatar/discuss.ampl.com/marcos/32/154_2.png) [@marcos](https://discuss.ampl.com/u/marcos)\
**Post date:** [December 2, 2022, 12:22pm UTC](https://discuss.ampl.com/t/ampl-modeling-tips-1-disjunctions/166/2 "2022-12-02T12:22:47Z")

</div>

This new feature is awesome!! Looking forward to the next chapter 🙂