Definition

Noun: A mathematical technique used in operations research and economics for optimizing a linear objective function, subject to a set of linear equality or inequality constraints. It is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

Usage

"Linear programming" is used as a singular, uncountable noun. It refers to the overall technique or field of study. * The factory used linear programming to optimize its production schedule and minimize costs. * Linear programming is a fundamental tool for solving resource allocation problems. * She wrote her thesis on applications of linear programming in supply chain management.

Examples

• The operations team applied linear programming to determine the most efficient shipping routes.
• Linear programming problems can be solved using the simplex method.
• Understanding linear programming is essential for many careers in data analysis and logistics.

Advanced Usage

• As a field of study: "He specializes in linear programming and combinatorial optimization."
• In software/algorithm context: "The software uses a linear programming solver to find the optimal solution."

Variants and Related Words

• Linear program (noun): The specific mathematical model or problem instance to be solved. (e.g., "We formulated the budget allocation as a linear program.")
• LP (noun): A common abbreviation for both "linear programming" and "linear program."
• Integer linear programming (noun): A related technique where some or all variables are restricted to integer values.
• Linear optimizer (noun): A tool or algorithm that performs linear programming.

Synonyms

• Linear optimization: A direct synonym, often used interchangeably.
• Mathematical programming: A broader category that includes linear programming as a subset.

Related Concepts (Not Phrasal Verbs or Idioms)

• Objective function: The linear function (e.g., profit, cost) that is to be maximized or minimized.
• Constraints: The linear equations or inequalities that define the limitations of the problem.
• Feasible region: The set of all possible points that satisfy the constraints.
• Simplex method: A classic algorithm for solving linear programming problems.

Noun

1. a mathematical technique used in economics; finds the maximum or minimum of linear functions in many variables subject to constraints