Introduction
Maximizing profit, minimizing loss, optimizing resources: these are the buzzwords of business. Before the Second World War, though, businesses would use only basic mathematical equations, estimations, and even intuition to maximize profit, minimize loss, and optimize resources. The underlying principles of linear programming have been around a long time; these are not revolutionary algorithmic concepts. Yet the industrial age and its models and methods of mass production meant increasing demands for calculations that would help solve complex operational and financial challenges. Linear programming allows for the introduction of several decision variables into the equation, allowing specialists in a wide range of fields to help companies improve their overall operations, with the ultimate goal of making calculated decisions based on math instead of guesswork. In this paper, I will discuss multiple methods for applying linear equations to the real world. For example, I will show how linear equations are used in human resources and personnel management in firms with fluctuating needs. Next, I will show how linear programming is used to maximize investment portfolios for businesses and individuals. Finally, I will show how linear programming is used in novel and creative ways, particularly in inventory management and logistics.
Background
Linear programming evolved around the Second World War, when the American military used basic mathematical functions to plan military deployments in ways that optimized manpower, resources, and time constraints (Lewis, 2008, p. 4). After the war, Air Force officer George Dantzig developed the first branded optimization algorithm known as Simplex, with the goal of providing “an efficient algorithm for solving programming problems that had linear structures,” (Lewis, 2008, p. 4). Reflecting on his work, Dantzig (2002) states that linear programming evolved as “part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to ‘best’ achieve its goals when faced with practical situations of great complexity,” (p. 42). Simply put, linear programming has become so ubiquitous since the days of simplex that...
References
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Dantzig, G.B. (2002). Linear programming. Operations Research 50(1): 42-47
Lewis, C. (2008). Linear programming: theory and applications. https://www.whitman.edu/Documents/Academics/Mathematics/lewis.pdf
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