## What Is Zero-One Integer Programming?

Zero-one integer programming (which can also be written as 0-1 integer programming) is a mathematical method of using a series of binary, yes (1) and no (0) answers to arrive at a solution when there are two mutually exclusive options. In the world of finance, such programming is often used to provide answers to capital rationing problems, as well as to optimize investment returns and assist in planning, production, transportation, and other issues.

### Key Takeaways

- Zero-one integer programming relies on mutually exclusive yes (1) and no (0) decisions to find solutions.
- In zero-one integer problems, each variable is represented only by 0 or 1 and could represent selecting or rejecting an option, turning on or off some switches, a yes or no answer or various other applications.
- This type of programming can be useful for companies making decisions on issues like what to invest in, or which of two proposed products are easiest to manufacture.

## The Basics of Zero-One Integer Programming

Integer programming is a branch of mathematical programming or optimization, which involves creating equations to solve problems. The term "mathematical programming" is connected with the fact that the goal of solving various problems is choosing programs of action. Assigning a simple yes/no value can be a powerful way to establish a linear problem-solving framework to identify inefficiencies.

## Real World Example of Zero-One Integer Programming

A simple example of how zero-one integer programming might be used in capital rationing would be in determining the number of product development projects that can be completed by a company by a certain date or within a certain budget. For example, a number of variables for each project can be given values that ultimately result in a 1 (yes) or 0 (no) binary decision about whether or not to include the project in a budget. This can be helpful to companies that are unsure about a specific business decision and are looking for a straightforward way to assess the possibilities.