Here is an overview of mixed integer linear programming via the Solver.

## Introduction to Mixed Integer Linear Programming

**Mixed Integer linear programming** is a type of mathematical method that consists of integer variables and linear objective functions and equations. The mixed-integer linear programming has both continuous and integer variables. With the help of linear programming, we can determine the minimum or maximum outcome of a given problem with some conditions. It is a tool that can be used to achieve a way to apply limited resources in the best possible manner. It uses:

**Decision Variables:**The decision variables that minimize or maximize the objective function.**Objective Function:**This is a function that helps us to determine the decision variables. It expresses the relation between the result and the variables.**Constraints:**Constraints are also functions that denote different conditions on possible solutions.

## Perform Mixed Integer Linear Programming in Excel: Step-by-Step Procedures

We have to set your objective function and the constraints.

**Objective Function**

**Z=2.79X**_{1}**+2.19X**_{2}**+2.99X**_{3}**+400Y**_{1}**+500Y**_{2}**+600Y**_{3}

**Constraints**

**X**_{1}+X_{2}+X_{3}=1050**X**_{1}-420Y_{1}<=0**X**_{2}-550Y_{2}<=0**X**_{3}-650Y_{3}<=0

Here, **X _{1}**,

**X**, and

_{2}**X**are integers. On the other hand,

_{3}**Y**,

_{1}**Y**, and

_{2}**Y**are binary numbers. We need to find the

_{3}**minimum value**of

**Z**.

### Step 1 – Insert Details

- Create three separate tables like below. The tables should include:
- Decision Variables
- Constraints
- Objective

### Step 2 – Load the Solver Add-in in Excel

- Click on the
**File**tab.

- Select
**Options.**

- This will open the
**Excel**Options. - Select
**Add-ins**. - Select
**Excel Add-ins**and click on**Go**in the**Manage**.

- The
**Add-ins**message box will pop up. - Check
**Solver Add-in**and select**OK**from the message box.

- You will see the
**Solver**feature in the**Analysis**section of the**Data**tab.

**Read More:** How to Use Excel Solver for Linear Programming

### Step 3 – Type the Mixed Coefficients of Objective Function and Constraints

- Write down the coefficients of the objective function in the
**B17:G17**range. - Input the coefficients of the constraints in the
**B6:J13**range. - Keep the
**Total**column empty for now. - Your worksheet should look like this.

### Step 4 – Calculate the Totals

- Go to
**H10**and enter the following formula

`=SUMPRODUCT($B$6:$G$6,B10:G10)`

- Press
**Enter**to get the output.

- Use the
**Fill Handle**to**AutoFill**up to**H13**.

### Step 5 – Measure the Dependent Variable of Objective Function

- Go to
**H6**and insert the following formula.

`=SUMPRODUCT(B17:G17,B6:G6)`

- Hit Enter.

### Step 6 – Apply the Solver Add-in

- Go to the
**Data**tab. - Select
**Solver**.

- A
**Solver Parameters**window will appear. - Set the objective
**H6**to be minimum. - Set the variables that
**Excel**is going to change. - Select
**Add**to set the constraints.

- After clicking
**Add**, an**Add Constraint**box will appear. - Set the
**Cell Reference**and the condition from the drop-down list. - Click
**Add**.

**Excel**has added a constraint.

- Add other constraints.
- Select a solving method.
- Click
**Solve**.

- The
**Solver Result**box will appear. - Click
**OK**.

### Step 7 – Show Final Output

After clicking **OK**, **Excel** will solve the problem for you. The outputs are shown below.

**Read More:** How to Find Optimal Solution in Linear Programming Excel

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