**Introduction**

The basic assumption of many optimization models in operations research is that the variables are continuous. But in many real problems, decision variables are discrete. These problems are called integer programming models. If all decision variables are integer variables, the resulting model is called **all integer programming model**.

To solve these problems, there are limited softwares that need to be installed and know the programming language of those softwares. In order to make it easy to solve all integer programming models, the **Optimization City** group has designed and developed an online solver. In the following, we will review how to use this online solver.

**Instruction of using online solver of all integer programming **

The **GUI** of the online solver of the all integer programming is as follows.

**Problem input**

To find the optimal solution of the all integer programming problem, the required inputs are as follows:

**n:** number of decision variables

**m:** number of constraints

**dist:** This matrix has m+n+1 rows and n+2 columns. The coefficients of the objective function are in dist[0,j] where j=1,…,n; and dist[i,j] where i=1,…,m and j=1,…,n are the coefficients of the constraints, and dist[i, n+1] are the values on the right hand side of the constraints. The rest of the components of this matrix are considered equal to zero.

**Note:** Limits should be defined as less-than-equal.

**Note:** The problem should be defined as minimization.

**Example: **To teach how to use this solver, we use the following example. An integer programming model with three variables and two constraints is defined as follows.

**Solution****:** The input information for the given model is as follows.

Entering information in the online solver for the all integer programming is as follows.

After entering the data, we click on the **RUN** button.

The result of running the algorithm is as follows.

In the output, the phrase “**Optimal solution found”** means that the model has a limited optimal solution.

In front of Solution, the optimal values of the decision variables are reported, which in this example we have:

In the last part of the output, the value of the optimal objective function is reported, which is equal to **17 **in this example.