Brooks Emerick

mat 362 — Operations research II

SECTION 010

Course Materials:

• Syllabus (updated Jan 22)

• Schedule (updated Jan 22)

lecture notes:

• Chapter 4 — Simplex Method Revisited

• Chapter 6 — Sensitivity and Duality (Part 1)

• Chapter 6 — Sensitivity and Duality (Part 2)

• Chapter 7 — Transportation Problems

• Chapter 8 — Network Models

• Chapter 14 — Game Theory

• Chapter 9 — Integer Programming

EXcel, Python, and Desmos Solvers

• S.7.1.P1 Solver

• S.7.1.P2 Solver

• S.8.2.P3 Solver

• S.8.3 Solver

• S.8.5 Solver

• S.14.3 Solver

Worksheets:

• S.4.14: Unrestricted-in-Sign Variables (Solutions)

• S.6.5.P1: Intro to the Dual Problem (Solutions)

• S.6.5.P2: Finding the Dual of an LP (Solutions)

• S.6.6: Economic Interpretation of the Dual LP (Solutions)

• S.6.7.P1: The Duality Theorem (Solutions)

• S.6.7.P2: The Duality Theorem (Solutions)

• S.6.8: Shadow Prices (Solutions)

• S.6.9: Sensitivity and Duality (Solutions)

• S.6.10: Complementary Slackness (Solutions)

• S.7.1.P1: Formulating Transportation Problems (Solutions)

• S.7.1.P2: Formulating Transportation Problems (Solutions)

• S.7.2: Starting bfs for Transportation Problems (Solutions)

• S.7.3.P1: Transportation Simplex Method (Solutions)

• S.7.3.P2: Transportation Simplex Method (Solutions)

• S.7.4: Sensitivity in Transportation LPs (Solutions)

• S.7.5: Assignment Problems (Solutions)

• S.8.1: Basic Definitions (Solutions)

• S.8.2.P1: Shortest Path Problem (Solutions)

• S.8.2.P2: Dijkstra’s Algorithm (Solutions)

• S.8.2.P3: Transportation Formulation of Shortest Path (Solutions)

• S.8.3: Maximum Flow Problems (Solutions)

• S.8.5: Minimum Cost Network Flow Problems (Solutions)

• S.14.1: Two-Person Constant-Sum Games — Saddle Points (Solutions)

• S.14.2: Two-Person Constant-Sum Games — Mixed Strategies (Solutions)

• S.14.3: Two-Person Constant-Sum Games — LP Formulation (Solutions)

• S.14.5: Three-Person Constant Sum Game (Solutions)

• S.9.2.P1: Formulating Integer Programming Problems (Solutions)

• S.9.2.P2: Formulating Integer Programming Problems (Solutions)

• S.9.3.P1: Branch and Bound Method for Pure IPs (Solutions)

• S.9.4: Branch and Bound Method for Mixed IPs (Solutions)

• S.9.5: Branch and Bound Method for Knapsack Problems (Solutions)

Problem Sets:

• Problem Set I (Solutions)

• Problem Set II (Solutions)

• Problem Set III (Solutions)

• Problem Set IV (Solutions)

• Problem Set V (Due May 3 at 11:59 PM on D2L)

Projects:

• Project I (Solver)

Exams:

• In-Class Exam (Solutions)

• Take-Home Exam (Solutions)

Lecture REcordings from 2021

• Unrestricted-in-Sign Variables

• Finding the Dual

• Interpreting the Dual Problem

• The Dual Theorem