INEN 420 – Final Review
Office Hours:
Mon, May 2 -- 2:00 - 3:00 p.m.
Tues, May 3 -- 12:45-2:00 p.m.
(Project Report/Critiques due on Thurs, May 5 by 5:00 p.m.)
Tuesday, April 28, 2005
L. Ntaimo (c) 2005 INEN420 TAMU
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Final Exam: Wednesday, May 11, 8:00 – 10:00 a.m.
• Closed book, closed notes, closed neighbor!
• You will be required to answer 5 problems out of 6
• Final exam will not be returned to you
• However, you can stop by to see how you did on the final
exam on Thurs, May 12.
L. Ntaimo (c) 2005 INEN420 TAMU
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Modeling Linear Programs (Chapter 3)
ƒ Basic linear algebra (preliquisite)
ƒ LP Assumptions
ƒ Proportionality, additivity, divisibility, certainty
ƒ LP Formulation
ƒ Decision variables
ƒ Objective function: Max/Min
ƒ Constraints
ƒ Sign restrictions
ƒ Lots of Applications:
ƒ Transportation (airlines, railway, …), chemical processes,
farming, diet, finance, inventory control, scheduling,
blending, etc.
L. Ntaimo (c) 2005 INEN420 TAMU
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Basic Polyhedral Theory (Chapter 3)
ƒ Convexity: Convex sets, convex functions
ƒ Feasible region: Polyhedron
ƒ Extreme points (corner points)
ƒ Extreme directions
ƒ Bounded, unbounded polyhedra
L. Ntaimo (c) 2005 INEN420 TAMU
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Solving Linear Programs (Chapter 4)
ƒ The Graphical Method
ƒ Two decision variables
ƒ Min: Isocost line / Max: Isoprofit line
ƒ Special cases: unique, alternative/multiple,
unbounded, infeasible solutions
L. Ntaimo (c) 2005 INEN420 TAMU
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Solving Linear Programs (Chapter 4)
ƒ The Simplex Method
ƒ Converting an LP to standard form
ƒ Basic and nonbasic variables
ƒ Finding an initial bfs
ƒ Adjacent bfs
ƒ Entering variable, ratio test, pivoting, etc
ƒ Special cases: unique, unbounded,
alternative/multiple solutions
ƒ Convergence, degeneracy
ƒ The Big-M Simplex Method
ƒ No readily available initial bfs
ƒ The Two-Phase Simplex Method
ƒ No readily available initial bfs
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Sensitivity Analysis and Duality (Chapter 6)
Two of the most important topics in Linear Programming
(How changes in the LP parameters affect the current optimal solution)
ƒ Important Formulas
ƒ Optimality condition
ƒ Feasibility Condition
ƒ Changing Parameters of an LP
ƒ Effect on current basis
ƒ Objective function coefficients (nonbasic, basic vars)
ƒ RHS
ƒ Adding a new activity
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Sensitivity Analysis and Duality (Chapter 6)
ƒ Finding the dual of an LP
ƒ Normal max LP, normal min LP
ƒ Basic Duality Theory
ƒ Weak duality
ƒ Strong duality
ƒ Economic Interpretation: dual/shadow prices
ƒ Complementary Slackness (CS)
ƒ binding, nonbinding constraints (primal/dual
problems)
ƒ Using CS to compute an optimal solution to the
primal/dual given the optimal solution to the other
ƒ Dual Simplex Method (not discussed)
ƒ Taught in INEN 622 – Linear Programming
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Special Problems (Chapter 7)
ƒ Transportation Problems
ƒ Balancing
ƒ Northwest corner method (provides an initial bfs)
ƒ Transportation simplex method
ƒ Transshipment Problems
ƒ Convert to transportation problem
ƒ Apply the transportation simplex method
ƒ Assignment problems
ƒ Balancing
ƒThe Hungarian method
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Network Models (Chapter 8)
ƒ Basic Definitions
ƒ Graph/network
ƒ Shortest Path Problems
ƒ Dijkstra’s Algorithm
ƒ Minimum Spanning Trees
ƒ MST algorithm (Greedy algorithm)
ƒ Maximum Flow Problems
ƒ The Ford-Fulkerson method
ƒ Add costs on the arcs:
ƒ Minimum Cost Network Flow Problem
ƒ Network Simplex Method
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Other Topics to Learn
ƒ Project Management: CPM, PERT (Chapter 8)
ƒ Integer Programming (Chapter 9 – INEN 668)
ƒ Linear Programming (Chapter 10 – INEN 622)
ƒ Game Theory (Chapter 11)
ƒ Nonlinear Programming (Chapter 12 – INEN 623)
ƒ Dynamic Programming (Chapter 13 – INEN 623)
ƒ Heuristic Techniques (Chapter 14 – INEN 689)
ƒ …and many more!
L. Ntaimo (c) 2005 INEN420 TAMU
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My Research Interests
Stochastic Programming
The Certainty Assumption No Longer Holds!
Operations Research I
Programming Skills
Probability and Statistics
INEN 420
C/C++
STAT 610
Linear Programming
Application Area
INEN 622
Integer Programming
INEN 668
Large-Scale Optimization
of Interest
Stochastic Programming
Software Engineering
Stochastic Integer Programming
Concepts
Probability and Statistics
Linear Programming
INEN 689 - Large-Scale Stochastic Optimization
Coming this Fall 2005!
L. Ntaimo (c) 2005 INEN420 TAMU
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