Fall Semester 2017

Operations Research

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets
Class handouts
Ipython notebooks and data files

Summary:

Operations Research applies mathematical optimization and modeling techniques to decision and planning tasks in diverse fields of application such as business, engineering, finance, the military, and public services. This course covers fundamental techniques of operations research, beginning with linear programming, integer and mixed integer programming, nonlinear programming, and stochastic programming. Although there will be some theory, the class emphasizes the study of concrete application contexts. Moreover, all models will be implemented and studied using the Pyomo optimization and modeling framework.

Contact Information:

Instructor:	Marcel Oliver
Email:	m.oliver@jacobs-university.de
Phone:	200-3212
Office hours:	Tu 11:00, We 10:00 in Research I, 107
TA:	TBA

Time and Place:

Lectures:

Tu 8:15-9:30, Tu 9:45-11:00 in the Research I Lecture Hall

Textbook/Further Reading:

F.S. Hillier and G.J. Lieberman, Introduction to Operations Research, 9th ed., McGraw-Hill, 2010.
W.E. Hart, C. Laird, J.-P. Watson, and D.L. Woodruff, Pyomo - Optimization Modeling in Python, Springer, 2012.
Course notes on linear programming from a different class; note that the standard form of an LP problem and associated simplex tableau is different from the presentation in Hillier and Lieberman.
Chapter 4 on Duality by Benjamin Van Roy and Kahn Mason, Stanford University, is one of the few good introductions to duality theory as it contains a clean conceptual motivation as well as elegant mathematics.

Python/Pyomo Resources:

Download page for the Anaconda Python distribution
Download page for the GLPK Solver (Windows only - on Linux and MacOS you can use native or Anaconda-bundled installer scripts)
Pyomo Online Documentation

Grading:

The final grade will be determined as follows:

Homework: 30%

Midterm Exam: 30%

Final Exam: 40%
The scores will be averaged as percentage grades with the given weights.
Homework will be given every week, it is due in class the following Wednesday.
I reserve the right to substitute in-class Quizzes for part of the homework score.

Class Schedule (subject to change!)

decisions under uncertainty, rev, Sections 15.2-3iew of Bayes' rule
Dynamic Programming IV: The value of information; "Hit-and-Miss Manufacturing Co." as a further example of decision analysis
Hillier and Lieberman, Section 15.3 (finish); Section 11.4 Example 6

05/09/2017:	Introduction, Simple linear programming problems
05/09/2017:	Linear Programming: Graphical Solution R. Larson, Elementary Linear Algebra, Chapter 9.2
12/09/2017:	Review: Underdetermined linear systems Old class handout on Gaussian elimination
12/09/2017:	Standard form of an LP problem, slack variables, geometry of feasible region
19/09/2017:	Solving a simplex tableau Class notes, Section 1
19/09/2017:	Introduction to Pyomo Modeling Ipython notebooks as shown in class
26/09/2017:	Sensitivity, shadow prices, and duality Van Roy and Mason, Section 4.1
26/09/2017:	Another simplex method example; weak duality theorem Van Roy and Mason, Section 4.2.1 Duals in a transportation network Class notes, Section 3 (start)
10/10/2017:	Strong Duality Theorem Class notes, Theorem 2 with proof
10/10/2017:	Network Optimization I: Transportation Problem Hillier and Lieberman, Chapter 8
17/10/2017:	Network Optimization II: Shortest path, minimum spanning tree, and maximum flow problems; linear programming formulation for shortest path and maximum flow Hillier and Lieberman, Sections 9.1-9.5 (focus on LP formulation of these problems)
17/10/2017:	Network Optimization III: Network duals and their interpretation; Minimum cost flow problem Hillier and Lieberman, Section 9.6
24/10/2017:	Network Optimization IV: Pyomo implementations; arbitrage detection. Project management, critical path, project crashing Hillier and Lieberman, Section 10.3, 10.5
24/10/2017:	Two player zero sum games (Van Roy and Mason, Section 4.4) Arbitrage detection (example graph, code)
27/10/2017:	Midterm Exam, 11:15-12:30, Campus Center East Wing
07/11/2017:	Dynamic Programming I: Shortest path revisited, "Local Job Shop" problem Hillier and Lieberman, Section 11.1, Section 11.3 Example 4
07/11/2017:	Dynamic Programming II: Distribution of effort problem, "Hit-and-Miss Manufacturing Co." Hillier and Lieberman, Section 11.3 Example 2, Section 11.4 Example 6
14/11/2017:	Inventory Theory I: EOQ model and variants Hillier and Lieberman, Sections 19.2 and 19.3
14/11/2017:	Inventory Theory II: EOQ with stochastic demand, stochastic single-period model for perishable products Hillier and Lieberman, Sections 19.5 and 19.6
21/11/2017:	Inventory Theory III: Deterministic periodic review model; Review of Bayes' rule Hillier and Lieberman, Section 19.4; for Bayes' rule see, e.g., these MIT open courseware notes, Section 7
21/11/2017:	Discussion of midterm exam
28/11/2017:	Decision analysis, decision trees, and the expected value of information Selected topics from Hillier and Lieberman, Chapter 15
28/11/2017:	Nonlinear Programming I: Basic examples; using Ipopt as a solver for linear and nonlinear programming problems Hillier and Lieberman, Section 13.1
05/12/2017:	Special types of nonlinear programs, turning nonlinear programs into linear programs, convexity; Using Pyomo to solve nonlinear programs Selected topics from Hillier and Lieberman, Chapter 13
05/12/2017:	Review for final exam
21/12/2017:	Final Exam, 16:00-18:00, Campus Center East Wing

Last modified: 2017/12/19
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2017/ilme202/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

Homework:	30%
Midterm Exam:	30%
Final Exam:	40%