In this post, you’ll learn what is shortest path problem and how to solve a **shortest path problem in Excel** using the solver tool.

## Shortest Path Problem

As the name says this problem is about finding the shortest path between two points or destinations comparatively, which minimizes the cost of transportation or production.

Lets look at a example of this problem. Look at the screenshot attached below.

A problem has been framed, the diagram gives us the map of the transportation and the cost units required to reach destinations. We are required to find the path which will cost us the least.

In the solution space, the **outgoing** is the** sum of the respective rows** similarly the **Incoming** is the **sum of the respective columns**. And the** Out-In** is the** difference between the Out and In** accordingly to its column and row.

**RHS** is the **condition for the nodes** that go out from that point, since Z is the starting position it’s assigned to 1, similarly to the other points.

The **Optimal solution** is the sum and product of the given values and the changing variables, so use the formula **=SUMPRODUCT()**.

## Shortest Path Problem Using Excel Solver

- Go to the
**Data tab**and under**Analyze group**select the**Solver tool**.

- When the
**Solver parameters**dialog box opens up, set the**objective**to**Min**.**By changing variables**are the**variables**in the**Solution space**. **Subject to the constraints**are**Out-In = RHS**and the**Changing variables**are**Binary numbers**.- The
**solving method**is**Simplex LP**. - After making all the changes click on
**Solve.**

When the **Solver results dialog box **opens up, click on **Keep the Solver solution**< **OK** and the solution gets displayed.

This is how you find the shortest path in a problem in Excel using Solver tool.

## Leave a Review