This course in Operations Research aims to teach students the fundamentals of optimization and decision-making. By the end of the course, learners will be able to model and solve various operations research problems using techniques such as linear programming, transportation problems, integer programming, and nonlinear programming. The course covers a wide range of topics including sensitivity analysis, primal and dual problems, network optimization, game theory, Markov chains, inventory models, and the implementation of optimization models using the AMPL software. The course employs a combination of theoretical lectures, practical examples, and hands-on exercises to help students develop the necessary skills to tackle complex real-world optimization problems. This course is designed for students and professionals interested in operations research, management science, industrial engineering, or related fields, who want to enhance their analytical and decision-making skills.
Overview
Syllabus
Operations Research 01: Operations Research Course Overview.
Operations Research 02: Introduction to Operations Research.
Operations Research 03A: Linear Function & Linear Inequality.
Operations Research 03B: Typical Linear Programming Problems.
Operations Research 03C: Linear Programming Feasible Region.
Operations Research 03D: Linear Programming Graphical Solution Technique.
Operations Research 03E: Binding & Nonbinding Constraints.
Operations Research 03F: Convex Set & Convex Function.
Operations Research 03G: Linear Programming Extreme Points.
Operations Research 03H: Linear Programming Staff Scheduling Problem.
Operations Research 03I: Linear Programming Blending Problem.
Operations Research 03J: Linear Programming Production Process Problem.
Operations Research 03K: Linear Programming Multiperiod Inventory Problem.
Operations Research 04A: Linear Programming Slack & Excess Variables.
Operations Research 04B: Simplex Method Basic Feasible Solution.
Operations Research 04C: Simplex Method Graphical Explanation.
Operations Research 04D: Simplex Method Entering & Leaving Variables, Pivoting.
Operations Research 04E: Simplex Method & The Big M.
Operations Research 04F: Simplex Method Unrestricted-in-Sign Variables.
Operations Research 04G: Goal Programming.
Operations Research 04H: Different Cases of Simplex Solutions.
Operations Research 05A: Sensitivity Analysis & Shadow Price.
Operations Research 05B: Primal & Dual Problems.
Operations Research 05C: Weak Duality & Strong Duality.
Operations Research 05D: Complementary Slackness.
Operations Research 05E: Dual Simplex Method.
Operations Research 06A: Transportation Problem.
Operations Research 06B: Transportation Northwest Corner Method.
Operations Research 06C: Transportation Minimum Cost Method.
Operations Research 06D: Transportation Vogel's Method.
Operations Research 07A: Transportation Loop & Pivoting.
Operations Research 07B: Transportation Simplex Method.
Operations Research 07C: Transshipment Problem.
Operations Research 07D: Assignment Problem & Hungarian Method.
Operations Research 08A: Directed & Undirected Networks.
Operations Research 08B: Shortest Path & Dijkstra’s Algorithm - Undirected Networks.
Operations Research 08C: Shortest Path & Dijkstra’s Algorithm - Directed Networks.
Operations Research 08D: Converting Shortest Path Problem to Transshipment Problem.
Operations Research 08E: Minimum Spanning Tree.
Operations Research 08F: Maximum Flow Problem Formulation.
Operations Research 08G: Maximum Flow Problem & Ford Fulkerson Method.
Operations Research 08H: Project Network.
Operations Research 08I: Early/late Event Time, Total Float, Critical Path.
Operations Research 08J: Program Evaluation & Review Technique PERT.
Operations Research 09A: Integer Programming vs Linear Programming Relaxation.
Operations Research 09B: Branch and Bound for Integer Programming.
Operations Research 09C: Knapsack Problem.
Operations Research 09D: Job Shop Scheduling Problem.
Operations Research 09E: Traveling Salesman Problem - Integer Programming.
Operations Research 09F: Traveling Salesman Problem - Hungarian Method.
Operations Research 09G: Traveling Salesman Problem - Nearest Neighbor Method.
Operations Research 10A: Derivatives of Basic, Trigonometric, Composite Functions.
Operations Research 10B: Hessian Matrix, Convex & Concave Functions.
Operations Research 10C: Nonlinear Convex Programming & KKT Conditions.
Operations Research 11: Decision Trees & Decision Making under Uncertainty.
Operations Research 12A: Zero-Sum Game & Pure Strategy.
Operations Research 12B: Rock, Paper, Scissors Game & Mixed Strategy.
Operations Research 12C: Nonconstant-Sum Game & Prisoner's Dilemma.
Operations Research 12D: More about Nash Equilibrium.
Operations Research 13A: Stochastic Process & Markov Chain.
Operations Research 13B: Markov Chain n-Step Transition.
Operations Research 13C: Ergodic Markov Chain.
Operations Research 13D: Markov Chain Steady-State Theorem.
Operations Research 13E: Markov Chain Mean First Passage Time.
Operations Research 13F: Absorbing Markov Chain.
Operations Research 14A: Economic Order Quantity (EOQ) Model with Zero Lead Time.
Operations Research 14B: Economic Order Quantity (EOQ) Model with Nonzero Lead Time.
Operations Research 14C: Economic Production Quantity (EPQ) Model.
Operations Research 14D: Newsvendor Inventory Model.
Operations Research 14E: Capacity-Controlled Fare (Early Bird Discount).
Operations Research 14F: Revenue Management & Airline Overbooking.
Operations Research 15A: AMPL - Download & Installation.
Operations Research 15B: AMPL - Quick Start Guide for Linear Programming.
Operations Research 15C: AMPL - Model and Data Separation.
Operations Research 15D: AMPL - Integer & Mixed Integer Programming.
Operations Research 15E: AMPL - Nonlinear Programming.
Operations Research 15F: AMPL - NEOS Server.
Taught by
Yong Wang
