Posts by Collection




Graph Coloring With Decision Diagrams: An Analysis Of Variable Ordering


A decision diagram approach was recently introduced to generate lower bounds for the graph coloring problem. It uses compilation via iterative refinement, which requires a variable ordering to be specified in advance. Oftentimes no single variable ordering dominates all others for a set of problem instances. This work provides an analysis and experimental evaluation of different variable ordering strategies including using portfolios of variable orderings.

Graph Coloring using Decision Diagrams with Zykov Branching


A recent work by van Hoeve introduced a decision diagram based iterative refinement algorithm for finding multi-path solutions to optimization problems. We study the addition of branch and bound to this algorithm, including the well-known Zykov branching rule for graph coloring.

Comparing Column Elimination and Column Generation


A method called Column Elimination was recently introduced to generate both lower bounds and optimal solutions for the graph coloring problem. Based on dynamic programming and decision diagrams, this exact method begins with a relaxed state space and refines this space at each iteration. Our work provides methodological and computational comparisons between Column Elimination and Column Generation; it uses the Capacitated Vehicle Routing Problem (CVRP) as a case study.


MBA Math Bootcamp TA

Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2021

TA for MBA Math Bootcamp focusing on Calculus and Probability

45-751 Optimization (MBA) Spring 2022

Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2022

TA for MBA Optimization course that covers fundamental optimization tools for quantitative analysis in the management sciences. The central topics of study are linear integer and nonlinear programming. Special emphasis is placed on linear programming particularly on modeling business applications and on sensitivity analysis. The course follows a practical spreadsheet-based approach to provide hands-on experience with software such as Excel Solver.

46-888 Optimization for Prescriptive Analytics (MBA) Summer 2022

Teaching Assistant, Carnegie Mellon University, Tepper School of Business, 2022

TA for MBA Optimization course that focuses on developing such optimization models for operational and strategic decision making. We will consider applications such as resource allocation, network design, and capacity planning, in a variety of business areas including finance, operations, logistics, and marketing. We will primarily focus on deterministic optimization models (i.e., we don’t use probability models or stochastic processes), and use linear, integer, and nonlinear programming as optimization methodologies. We solve problems in these fields using CPLEX in Python.

70-460 Mathematical Models for Consulting (Undergrad) Fall 2022

Instructor, Carnegie Mellon University, Tepper School of Business, 2022

Instructor for upper-level undergraduate optimization elective course. Fulfilled my teaching requirement for Tepper PhD students by teaching this class of 22 students. The course material includes column generation, integer programming, robust optimization, and a project where teams use these advanced modeling techniques to solve a real world problem. Models are implemented in both Excel and Python using Gurobi.