Exploration of Multi-Objective, Piecewise Benefit Function Linear Program Solution Algorithms
Date
2016
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Producer
Director
Performer
Choreographer
Costume Designer
Music
Videographer
Lighting Designer
Set Designer
Crew Member
Funder
Rehearsal Director
Concert Coordinator
Advisor
Moderator
Panelist
Alternative Title
Department
Swarthmore College. Dept. of Engineering
Type
Thesis (B.A.)
Original Format
Running Time
File Format
Place of Publication
Date Span
Copyright Date
Award
Language
en_US
Note
Table of Contents
Terms of Use
Full copyright to this work is retained by the student author. It may only be used for non-commercial, research, and educational purposes. All other uses are restricted.
Rights Holder
Access Restrictions
Terms of Use
Tripod URL
Identifier
Abstract
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.