Spring Semester 2016

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:	We, Th 10:00 in Research I, 107
TA:	Ciprian Blindu
Email:	c.blindu@jacobs-university.de

Time and Place:

Lectures:

We 11:15, Fr 9:45 in the Research I (CS) 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.
Slides from a previous instance of this class, by Asvin Goel, Kühne Logistics University

Python/Pyomo Resources:

Download page for the Anaconda Python distribution (please use the Python 3.x Version)
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 computed as a grade point average with the following weights:

Homework: 30%

Midterm Exam: 30%

Final Exam: 40%
Each of the individual scores will be converted to Jacobs grade points before the overall weighted grade point average is computed.
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!)

03/02/2016:	Introduction, Simple linear programming problems
05/02/2016:	Linear Programming: Graphical Solution R. Larson, Elementary Linear Algebra, Chapter 9.2
10/02/2016:	Introduction to Pyomo Modeling Ipython notebooks as shown in class
12/02/2016:	Review: Underdetermined linear systems Old class handout on Gaussian elimination
17/02/2016:	Standard form of an LP problem, slack variables, geometry of feasible region
19/02/2016:	Solving a simplex tableau Class notes, Section 1
24/02/2016:	Sensitivity, shadow prices, and duality Van Roy and Mason, Section 4.1
26/02/2016:	Review Session
02/03/2016:	Strong Duality Theorem Van Roy and Mason, Section 4.2.2 and 4.2.3
04/03/2016:	Network Optimization I: Transportation Problem Hillier and Lieberman, Chapter 8
09/03/2016:	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)
11/03/2016:	Network Optimization III: Network duals and their interpretation Class notes, Section 3 (start) and other sources Minimum cost flow problem Hillier and Lieberman, Section 9.6
16/03/2016:	Network Optimization IV: Pyomo implementations; arbitrage detection. Project management, critical path Hillier and Lieberman, Section 10.3
18/03/2016:	Network Optimization V: Project crashing Hillier and Lieberman, Section 10.5 Pyomo implementations; Midterm Review (I)
30/03/2016:	Two player zero sum games Van Roy and Mason, Section 4.4; Midterm Review (II)
01/04/2016:	Midterm Exam
06/04/2016:	Dynamic Programming I: Shortest path revisited, "Local Job Shop" problem Hillier and Lieberman, Section 11.1, Section 11.3 Example 4
08/04/2016:	Dynamic Programming II: Distribution of effort problem, decisions under uncertainty, review of Bayes' rule Hillier and Lieberman, Section 11.3 Example 2, Sections 15.2-3
13/04/2016:	Dynamic Programming III: Decision trees; turning nonlinear programs into dynamic programs Hillier and Lieberman, Section 15.4; Exercise 11.3-20
15/04/2016:	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
20/04/2016:	Nonlinear Programming I: Basic examples; using Ipopt as a solver for linear and nonlinear programming problems Hillier and Lieberman, Section 13.1
22/04/2016:	Midterm discussion
27/04/2016:	Nonlinear Programming II: Separable and fractional programming - converting nonlinear programs into linear programs Hillier and Lieberman, Sections 13.8 and 13.8
29/04/2016:	Inventory Theory I: EOQ model and variants Hillier and Lieberman, Sections 19.2 and 19.3
04/05/2016:	Inventory Theory II: Deterministic periodic review model, serial two-echelon model Hillier and Lieberman, Sections 19.4 and 19.5
06/05/2016:	Review I; Linear and integer programming in Pyomo
11/05/2016:	Inventory Theory III: EOQ with stochastic demand, stochastic single-period model for perishable products Hillier and Lieberman, Sections 19.5 and 19.6
13/05/2016:	Review II
21/05/2016:	Final Exam, 9:00-11:00, Conference Hall, IRC

Last modified: 2016/02/01
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2016/ilme202/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

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