What is integer zero-one programming?
Zero-one integer programming (which can also be written as ‘0-1’ integer programming) is a mathematical method of working with a series of binary functions; in particular, yes (‘1’) and no (‘0’) responses to arrive at a solution when there are two mutually exclusive options.
In the world of finance, integer zero-one programming is often used to provide answers to capital rationing problems, as well as to optimize returns on investment and help with planning, production, transportation and other problems.
Key points to remember
- Integer zero-one programming relies on mutually exclusive yes (1) and no (0) decisions to find solutions to logical problems.
- In zero-one integer problems, each variable is represented only by 0 (“no”) or 1 (“yes”), and can represent the selection or rejection of an option, the activation or deactivation of ‘electronic switches, or a simple yes or no response used in various other applications.
- This type of programming can be useful for companies making decisions on issues such as what to invest in or which of the two products on offer is easier to manufacture.
Understanding Integer Zero-One Programming
Integer programming is a branch of mathematical programming or optimization, which involves creating equations in order to solve problems. The term “mathematical programming” is related to the fact that the goal of solving various problems is to choose programs of action. Assigning a simple yes/no value can be a powerful way to establish a linear problem-solving framework for identifying inefficiencies.
Basically, the most basic instructions executed by a computer are binary codes, consisting only of ones and zeros. These codes are directly translated into the “on” and “off” states of the electricity flowing through the physical circuitry of the computer. Essentially, these simple codes form the basis of “machine language”, the most fundamental variety of programming languages. These on and off positions can also be interpreted as assigning a “yes” or a “no” to a logic function.
Of course, no human would be able to build modern software by explicitly programming ones and zeros. Instead, human programmers must rely on various layers of abstraction that can allow them to articulate their commands in a more human-intuitive format. Specifically, modern programmers issue commands in “high-level languages”, which use intuitive syntax such as whole English words and phrases, as well as logical operators such as “And”, “Or”, and “Else ” which are familiar to everyday use.
Ultimately, however, these high-level commands must be translated into machine language. Rather than doing it manually, programmers rely on assembly languages whose purpose is to automatically translate between these high-level and low-level languages.
Practical example of integer zero-one programming
A simple example of how zero one integer programming could be used in capital rationing would be to determine how many product development projects a company could complete on 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 binary 1 (yes) or 0 (no) decision on whether or not to include the project in a budget. This can be useful for businesses that are unsure of a specific business decision and are looking for an easy way to assess the possibilities.