Operations Research
The course will introduce fundamental topics in operations research at the undergraduate level. Some specific topics to be covered are: Formulations, Linear Programming, Simplex Method, Duality, Sensitivity Analysis, Transportation, Assignment Problems, Network Optimization Problems, Integer Programs, Nonlinear Optimization, and Game Theory.Prerequisites: Mathematical maturity at the level of a junior undergraduate student will be assumed. Prior coursework in Linear Algebra, Calculus and familiarity with Matrices is required.
Homeworks, Exams
 Midterm and Final will be inclass written exams. No cheat sheets.
 We will have about 10 to 12 homeworks (one per week).
 Homeworks will be assigned on Wednesdays. Solutions will be due the following week before the beginning of the lecture. Strict due dates will be enforced.
 Homework submisions should have each problem starting in a fresh page. State the problem number clearly. The problems should appear in order.
 Staple and write your name in your submission. Unstapled/unnamed submissions will not be graded.
 Electronic submission will be accepted provided it is in a "single file pdf" format. Submissions should be through the Compass2g website. Email submissions will NOT be accepted.
 You are encouraged to discuss the course material, especially the practice problems and the review problems, with each other, but no collaboration or other solution sources are allowed on the problems assigned for homework, midterm or final.
 Write clearly. Illegible submissions will not be graded.
 Plagiarism will be dealt with severely. No credit for the homework, midterm or final.
Lectures
The following is a tentative list of lectures. Subject to change.Lecture slides will be posted a day before the lecture in Compass2g.
 Week 1
 Aug 22: Introduction, Formulations
 Aug 24: Linear Programming, Standard Form
 Aug 26: Graphic Method, Corner Points
 Week 2
 Aug 29: Simplex Method: Augmented LP, Basic Variables
 Aug 31: Simplex Method: Basic Feasible Solution, Intuition and Overview
 Sep 2: Simplex Method: Initialization, big M method, Iteration Steps, Termination
 Week 3
Sep 5: Labor day Sep 7: Simplex Method: Degeneracy, Bland's rule, Algebraic form
 Sep 9: Simplex Method: Tabular form
 Week 4
 Sep 12: Shadow prices
 Sep 14: Dual linear program, PrimalDual connections
 Sep 16: Strong and Weak Duality, Complementary Slackness
 Week 5
 Sep 19: Dual solution from Simplex tableau, Dual Simplex Method
 Sep 21: LP in matrix form, Simplex method in matrix form
 Sep 23: Simplex method: Connections between matrix form and tabular form, Sensitivity Analysis: changing objective
 Week 6
 Sep 26: Sensitivity Analysis: changing RHS, addition of a constraint
 Sep 28: Sensitivity Analysis: addition of a variable, Game Theory: 2person 0sum games
 Sep 30: Game Theory: Maxmin, Minmax problems, Dominant strategies, Saddle point
 Week 7
 Oct 3: Game Theory: Graphical Method, LP method
 Oct 5: Game Theory: Duality interpretations, Minmax theorem, Nash equilibrium, Review, Transportation Problem: LP formulation
 Oct 7: Transportation Problem: Initial Basic Feasible Solution, Northwest rule, Vogel and Russell rules
 Week 8
 Oct 10: Transportation Simplex Method: Loop, Degeneracy, Iterations
 Oct 12: Transportation Simplex Method: Reasoning for optimality, integral solutions property, unbalanced transportation problem
 Oct 14: Assignment Problem: Formulation, Unbalanced case, Intro to the Hungarian Method
 Week 9
 Oct 17: Midterm, Time: 11:50pm (usual class hours)
Venue: 103 Transportation Building and 217 Noyes Lab (seating chart posted in Compass2g)  Oct 19: Assignment Problem: Hungarian Method, Network Terminologies, Minimum Spanning Tree Problem: Prim's Algorithm
 Oct 21: Shortest Path Problem: Dijkstra's Algorithm
 Week 10
 Oct 24: Max Flow Problem: Augmenting Path Algorithm
 Oct 26: Dynamic Programming: backward induction
 Oct 28: Dynamic Programming: Bellman's principle
 Week 11:
 Oct 31: Dynamic Programming: Continuous states and decision variables
 Nov 2: Dynamic Programming: Probabilistic
 Nov 4: Dynamic Programming: Probabilistic, Nonlinear Optimization: Convex functions
 Week 12
 Nov 7: Nonlinear Optimization: Convex functions, Unconstrained single variable: Bisection Search
 Nov 9: Nonlinear Optimization: Unconstrained single variable: Newton Search
 Nov 11: Nonlinear Optimization: Unconstrained single variable: Golden Section Search, Unconstrained multivariable: Gradient Search
 Week 13
 Nov 14: Midterm solutions
 Nov 16: Nonlinear Optimization: Unconstrained multivariable: Newton Search, Constrained multivariable: Lagrangian
 Nov 18: Nonlinear Optimization: Constrained multivariable: KKT Conditions

Week 14: Thanksgiving Break (Nov 21, 23, 25)  Week 15
 Nov 28: Integer Programming: Formulations, Integer Variables
 Nov 30: Integer Programming: Combinatorial Explosion, Variable Fixing, Branch and Bound
 Dec 2: Integer Programming: LPs with Integral Solutions
 Week 16
 Dec 5: Discrete Optimization and Integer Programming
 Dec 7: Review
 Week 17
 Final Exam
Date: Wed, 14 Dec
Time: 78pm
Venue: 151 Loomis Laboratory