04/02/2024
By Hung Phan
The Kennedy College of Sciences, Department of Mathematics and Statistics, invites you to attend the Master’s thesis defense by Julia Koron on "Linear Programming and Applications."
Candidate Name: Julia Koron
Degree: Master of Science in Mathematics
Defense Date: Tuesday, April 9, 2024
Time: 11 a.m. to noon
Location: TBA, please contact the Department of Mathematics and Statistics, UMass Lowell
Thesis Title: Linear Programming and Applications
Committee Members:
- Hung Phan, Ph.D., (Advisor) Department of Mathematics and Statistics, UMass Lowell
- Sedi Bartz, Ph.D., Department of Mathematics and Statistics, UMass Lowell
- Daniel Glasscock, Ph.D., Department of Mathematics and Statistics, UMass Lowell
Brief Abstract:
Linear programming is an optimization technique used to find the optimal solution of a system of linear equations. It is widely agreed that the development of linear programming has been ranked among the most important scientific advances of the mid-20th century. Today it is a standard tool that has saved thousands, if not millions, of dollars for businesses around the world. The purpose of this thesis is to provide a brief introduction to linear programming and its various applications. In the first part of the thesis, we will define terminology and how to formulate linear programs. Different methods for solving a linear program will be presented, such as the Graphical Method and the Simplex Method. Next, the primal and dual problems of a linear program will be defined. In particular, the proofs for the Weak Duality and Strong Duality Theorems will be given. The two theorems provide important implications in linear programming. Finally we show two, out of the various ways, linear programming can be applied to the real world: The Transportation Problem and the Assignment Problem.