General Information

Mountain View
Student: Kajal Chokshi
Office: CORE 448
School: Loyola University Chicago
E-mail: kchokshi[at]luc[dot]edu
Project: Optimal Train Scheduling Problem

Project Description

This project searches to find an optimal scheduling model for trains. A dataset from Union Pacific was provided regarding single track trains. I plan to analyze the dataset, visualize the data with the various constraints, generate data using a probability distribution, and ultimately minimize cost and delay by providing a model to schedule these trains.

Week 1:
This week, I spent my time reading several papers on optimal scheduling of trains with various constraints in order to gain a better understanding of my project. Additionally, I familiarized myself with the data given to me by my mentor, Dr. Guo. We met several times and came up with weekly goals. As I have never created my own website, I attended a workshop on using LaTeX and HTML. I ended the week working on my website and presentation for next Monday.
Week 2:
I worked hard to visualize my data this week. Using SAS programming, I coded to produce several different types of bar graphs. Some examples of the graphs are Category of the Train vs. Frequency and Day of the Week vs. Frequency. However, these graphs were not accurate as frequency was not the appropriate label. Instead, I must find the average unique trains. This became a challenge because I had to filter the document and I am still working on it. I am in the process of learning R now as well to see if this will make the process smoother as my mentor is proficient in R and she could assist me better. Additionally, I have been reading up on Empirical Distributions, which will lead to the next step of my research.
Week 3:
This week I worked in R programming to understand the dataset. I have never worked with R so it was a bit of a challenge to start up with a new programming software. My mentor ran some examples with me to help me understand which commands to use. I processed some of her old code to understand various functions which I then implemented into my code. Next week, I plan to continue this code. I hope to have the dataset filtered by the number of unique trains, day of the week and train category.
Week 4:
During the last week, I became very familiar with the R programming language. My mentor and I came up with an efficient code that produces various visualizations for my dataset. It was challenging at first because we were implement several set loops and there were many errors. We worked through the logic of it together and finally got our program to work. Next week, she is going on vacation, so I am to produce all visualizations of the data.
Week 5:
I was able to successfully create almost all of the graphs needed to visualize my data. Much of my time was spent researching various examples on how to complete this process in an efficient code. Additionally, I spent time reading articles on empirical distributions. Next week, we start working on my probability distribution.
Week 6:
This past week, I read over the book that Dr. Guo gave me to read. I read about empirical modeling and looked at a few examples. There is a specific model that I am to emulate in order to put into my final presentation. I am meeting with Dr. Guo again next week to discuss this model and our future goals. The graphs are a success and I will be working on my abstract and final paper in general this weekend.
Week 7:
Over the course of this last week, I worked mainly on my final presentation and poster. I worked hard to analyze my graphs and data that I received from my code to find significant trends. In addition, I worked hard to finish my poster that I can bring to future conferences. I hope to eventually have a simulated empirical distribution model that mimics the real data set. We leave on Monday for Prague so we spent much of the time saying goodbye this week to the other students.
Week 8:
This week, we arrived to Prague! We left on Monday evening and arrived on Tuesday afternoon. We spent Tuesday exploring with the Czech students. Quickly we learned that Czech cuisine was delicious! Lectures began on Wednesday morning by the Charles University professors. It was very interesting to be in a classroom in a different country and learn about the experiences of students in Prague. Dr. Jiri Fiala gave us a very interesting lecture on interval graphs which I found the most interesting. It related Hamiltonian Paths to interval graphs, which has many real life applications. After recovering from jet lag, we spent quite a bit of time exploring Prague and having adventures with the Czech group. I can't wait to see how the conference will be. I am most excited for Tuesday for a talk about the talk "Selecting mappings of large girth graphs" because it is most simialr to the research I did last year.
Week 9:
The Mathematics of Jiri Matousek conference was this week in Prague. It has been an interesting experience.



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