Brooks Emerick

matH 362 — Operations research II

Independent Instruction

Course Materials:

• Syllabus (updated Jan 27)

• Schedule (updated Jan 27)

lecture notes:

• Chapter 4 — Simplex Method Revisited

• Chapter 6 Part 1 — Sensitivity Analysis

• Chapter 6 Part 2 — Duality

• Chapter 7 — Transportation Problems

• Chapter 8 — Network Models

• Chapter 9 — Integer Programming Problems

• Chapter 14 — Game Theory

EXcel, Python, and Desmos Solvers

• S.7.1.P1 Solver

• S.7.1.P2 Solver

• Problem Set 1 Solver

• Problem Set 2 Solver

Worksheets:

• Review of Graphical Solutions and Simplex Algorithm (Solutions)

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

• S.6.1: Graphical Introduction to Sensitivity (Solutions)

• S.6.2.P1: Some Important Formulas (Solutions)

• S.6.2.P2: Some Important Formulas (Solutions)

• S.6.2.P3: Important Formulas in Python (python)

• S.6.3.P1: Sensitivity — Feasibility Ranges (Solutions)

• S.6.3.P2: Sensitivity — Feasibility Ranges (Solutions)

• S.6.3.P3: Sensitivity — Optimality Ranges (Solutions)

• S.6.3.P4: Sensitivity — New Activity (Solutions)

• S.6.4: The 100% Rule (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 Dual (Solutions)

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

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

• S.6.8: Shadow Prices & Feasibility Ranges (Solutions)

• S.6.9: Duality and Sensitivity for Cost Coefficients and New Activities (Solutions)

• S.6.10: Complimentary Slackness (Solutions)

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

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

• S.7.2: Finding a BFS of a Transportation Problem (Solutions)

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

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

• S.7.4: Sensitivity in Transportation Problems (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: Transformation Formulation of Shortest Path (Solutions)

• S.8.3: Maximum Flow Problems (Solutions)

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

• S.8.6: Minimum Spanning Tree (Solutions)

• S.9.2.P1: Formulating IP Problems (Solutions)

• S.9.2.P2: Formulating IP Problems (Solutions)

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

• S.9.3.P2: Branch and Bound for Pure IPs (Solutions)

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

• S.9.5: Knapsack Problems (Solutions)

• S.9.6.P1: Traveling Salesperson Problems (Solutions)

• S.9.6.P2: Heuristic Algorithms for TSP (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)

Problem Sets:

• Problem Set I (Solutions, Excel Solver)

• Problem Set II (Solutions)

• Problem Set III (Solutions, Excel Solver)

• Problem Set IV (Due May 8 by 11:59 PM on D2L)

Projects:

• Project I — Multi-Period Planning and Maintenance (Solutions)

• Project II — Transshipment Problem (Solutions)

Exams:

• Exam I (Solutions)

• Exam II (Solutions)