Exploration of Multi-Objective, Piecewise Benefit Function Linear Program Solution Algorithms
Friske, Spencer
Given life's scarcity of resources, decision-making is an omnipresent component of both society and the human experience. Individually, we routinely face choices that range from mundane to life changing. As a society, we similarly must make decisions, but the scale and scope of these choices dramatically increase. Assuming the fundamental tenet of economics, that humans are rational, holds true, the question then becomes which choice will result in the fulfillment of our goals and ambitions. This question can be cripplingly difficult to answer, and any mistakes can have costly consequences.
In this paper, we will discuss a specific class of multi-objective optimization problems and a proposed novel solution algorithm. We begin with a discussion of linear programming as a whole before defining our problem class both through a relatable example and traditional mathematical formulation. Throughout this class definition, we will discuss the characteristic elements of the problems we are hoping to solve. Upon developing an understanding of our problem class, we will describe the proposed solution algorithm. The algorithm will be clearly defined, and it will be compared to current solution methods through a literature review. We will then present a case study that identifies an important application of the problem class as well as shows the solution algorithm in practice.
Following the derivation of the algorithm and the presentation of the case study, additional applications of the algorithm will be discussed. It is important to remember that multi-objective, linear piecewise benefit slope optimization problems are relevant across many disciplines, and we will explore some of their potential uses. Furthermore, we will explore the future steps of the algorithm, including further implementation and expansion. At the conclusion of the paper, the benefits of the algorithm over the Simplex Method for solving multi-objective, linear piecewise benefit slope optimization problems should be apparent through both mathematical proof and example.
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