Fall Semester 2020

Operations Research (CO-583)

Syllabus

Quick Links:

Class space on Teams
Class space on Moodle (For homework assignments and submissions)
Homework sheets (only backup, please submit via Moodle)
Informal lecture notes
Exams and solutions
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, Th 15:45-17:00 in the Campus Center East Wing

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:

See Class space on Teams for installation instructions
Pyomo Online Documentation

Grading:

The module grade will be determined by the written module examination. Time and place are centrally scheduled.
Homework and "Mock Midterm" can each provide a grade bonus of up to 0.33 grade points (5% on the percentage scale), for a maximal total bonus of 10% on the percentage scale.
The two worst homework sets will be removed from the bonus computation.
The bonus is applied as follows: The portion of the percentage score above 50%, divided by 10, will be added to the module exam percentage score, for a maximum total of 110%
Scores above 100% will be capped at 100%.
The bonus cannot change a failing grade into a non-failing grade.
The full provisions of the Code of Academic Integrity apply not only to the module examination, but to all bonus work, of course, and will be enforced. That said, the bonus for learning and retention of the material from consistent and honest homework is far greater than any possible bonus to your final score. If you invest time on homework and midterm preparation, you will succeed in the final module examination!

Class Schedule (subject to change!)

01/09/2020:	Introduction, Simple linear programming problems
03/09/2020:	Linear Programming: Graphical Solution R. Larson, Elementary Linear Algebra, Chapter 9.2
08/09/2020:	Review: Underdetermined linear systems Old class handout on Gaussian elimination
10/09/2020:	Standard form of an LP problem, slack variables, geometry of feasible region
15/09/2020:	Solving a simplex tableau Class notes, Section 1
17/09/2020:	Introduction to Pyomo Modeling Ipython notebooks as shown in class
22/09/2020:	Sensitivity, shadow prices, and duality Van Roy and Mason, Section 4.1
24/09/2020:	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)
29/09/2020:	Strong Duality Theorem Class notes, Theorem 2 with proof
01/10/2020:	Network Optimization I: Transportation Problem Hillier and Lieberman, Chapter 8
06/10/2020:	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)
08/10/2020:	Network Optimization III: Network duals and their interpretation; Minimum cost flow problem Hillier and Lieberman, Section 9.6
13/10/2020:	Network Optimization IV: Pyomo implementations; arbitrage detection. Project management, critical path, project crashing Hillier and Lieberman, Section 10.3, 10.5
15/10/2020:	Two player zero sum games (Van Roy and Mason, Section 4.4) Arbitrage detection (example graph, code)
20/10/2020:	TBA
22/10/2020:	Review
27/10/2020:	Mock Midterm Exam
29/10/2020:	Dynamic Programming I: Shortest path revisited, "Local Job Shop" problem Hillier and Lieberman, Section 11.1, Section 11.3 Example 4
03/11/2020:	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
05/11/2020:	Inventory Theory I: EOQ model and variants Hillier and Lieberman, Sections 19.2 and 19.3
10/11/2020:	Inventory Theory II: EOQ with stochastic demand, stochastic single-period model for perishable products Hillier and Lieberman, Sections 19.5 and 19.6
12/11/2020:	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
17/11/2020:	TBA
19/11/2020:	Decision analysis, decision trees, and the expected value of information Selected topics from Hillier and Lieberman, Chapter 15
24/11/2020:	Nonlinear Programming I: Basic examples; using Ipopt as a solver for linear and nonlinear programming problems Hillier and Lieberman, Section 13.1
26/11/2020:	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
01/12/2020:	TBA
03/12/2020:	Review for final exam
TBA:	Final Exam

Last modified: 2020/12/19
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2020/CO-583/index.html
Marcel Oliver (m.oliver@jacobs-university.de)