Fall Semester 2017

Operations Research


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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:  We, Th 10:00 in Research I, 107

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

Textbook/Further Reading:

Python/Pyomo Resources:


Class Schedule (subject to change!)

05/09/2016: Introduction, Simple linear programming problems
05/09/2016: Linear Programming: Graphical Solution
R. Larson, Elementary Linear Algebra, Chapter 9.2
12/09/2016: Review: Underdetermined linear systems
Old class handout on Gaussian elimination
12/09/2016: Standard form of an LP problem, slack variables, geometry of feasible region
19/09/2016: Solving a simplex tableau
Class notes, Section 1
19/09/2016: Introduction to Pyomo Modeling
Ipython notebooks as shown in class
26/09/2016: Sensitivity, shadow prices, and duality
Van Roy and Mason, Section 4.1
26/09/2016: Another simplex method example; weak duality theorem
Van Roy and Mason, Section 4.2.1
29/09/2016: Duals in a transportation network
Class notes, Section 3 (start)
10/10/2016: Strong Duality Theorem
Class notes, Theorem 2 with proof; Network Optimization I: Transportation Problem
Hillier and Lieberman, Chapter 8
10/10/2016: 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)
17/10/2016: Network Optimization III: Network duals and their interpretation; Minimum cost flow problem
Hillier and Lieberman, Section 9.6
17/10/2016: Network Optimization IV: Pyomo implementations; arbitrage detection.
Project management, critical path, project crashing
Hillier and Lieberman, Section 10.3, 10.5
TBA: Midterm Exam
24/10/2016: Two player zero sum games (Van Roy and Mason, Section 4.4)
Arbitrage detection (example graph, code)
24/10/2016: Dynamic Programming I: Shortest path revisited, "Local Job Shop" problem
Hillier and Lieberman, Section 11.1, Section 11.3 Example 4
07/11/2016: 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
07/11/2016: Dynamic Programming III: Decision trees; turning nonlinear programs into dynamic programs
Hillier and Lieberman, Section 15.4; Exercise 11.3-20
14/11/2016: 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
14/11/2016: Nonlinear Programming I: Basic examples; using Ipopt as a solver for linear and nonlinear programming problems
Hillier and Lieberman, Section 13.1
21/11/2016: Nonlinear Programming II: Separable and fractional programming - converting nonlinear programs into linear programs
Hillier and Lieberman, Sections 13.8 and 13.8
21/11/2016: Nonlinear Programming III: Review of unconstrained smooth optimization, Lagrange multipliers, introduction to the KKT conditions
28/11/2016: Nonlinear Programming IV: Quadratic programming; Integer programming in Pyomo
28/11/2016: Inventory Theory I: EOQ model and variants
Hillier and Lieberman, Sections 19.2 and 19.3
05/12/2016: Inventory Theory II: Deterministic periodic review model, serial two-echelon model
Hillier and Lieberman, Sections 19.4 and 19.5
05/12/2016: Inventory Theory III: EOQ with stochastic demand, stochastic single-period model for perishable products
Hillier and Lieberman, Sections 19.5 and 19.6
TBA: Final Exam

Last modified: 2017/09/04
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2017/ilme202/index.html
Marcel Oliver (m.oliver@jacobs-university.de)