Fall Semester 2020

Operations Research (CO-583)


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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
Office hours:  Tu 11:00, We 10:00 in Research I, 107

Time and Place:
Lectures:  Tu, Th 15:45-17:00 in the Campus Center East Wing

Textbook/Further Reading:

Python/Pyomo Resources:


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)