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Advanced Operations Research: Stochastic Programming
Provider: Faculty of Science

Activity no.: 5635-22-07-31 
Enrollment deadline: 25/04/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time25.04.2022, at: 08:00 - 24.06.2022, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserGiovanni Pantuso    E-mail address: gp@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formOral examination, 30 minutes
Exam form30 minutes preparation, 30 minutes oral examination including grade determination
Exam details Approval of two project reports is a prerequisite for enrolling for examination (failed project reports can be resubmitted) Aid Written aids allowed
Exam aidsWriten aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures28.00
Theoretical exercises14.00
Project work55.00
Exam1.00
Eksamensforberedelse80.00
Preparation28.00
Sum206.00
Content
This course introduces the students to optimization under uncertainty by means of stochastic programming. In many real-life situations, decisions have to be made while relevant data is uncertain, noisy, imprecise. Examples are investments in assets with uncertain returns or production of goods with uncertain demand. For these problems, the course presents different mathematical formulations, illustrates the corresponding mathematical properties, shows how to exploit these properties in various solution methods, and discusses how uncertain parameters can be transfortmed into input data (scenarios). Furthermore, the students of this course will independently handle practical problems in project work. The content can be summarized as follows.

A. Stochastic programming problems:
A1. Decision making under uncertainty.
A2. Formulations of stochastic programming problems.

B. Approximations and scenario generation:
B1. Monte Carlo techniques.
B2. Property matching.
B3. Assessing the quality of a solution.

C. Properties of stochastic programming problems:
C1. Structural properties of stochastic programs.
C2. The value of stochastic programming: EVPI and EEV.

D. Solution methods:
D1. Decomposition techniques for two-stage stochastic programs (e.g., L-shaped decomposition).
D3. Decomposition techniques for multistage stochastic programs (e.g., Dual decomposition).

E. Practical aspects and applications:
E1. Solution of case studies from e.g., Energy planning, Finance, Transportation, using optimization software such as GAMS, Cplex or Gurobi.

Learning outcome
Knowledge:

Formulations of stochastic programming problems
Scenario generation methods
Properties of stochastic programming problems
Solution methods for stochastic programming problems


Skills:

Formulate different types of stochastic programming problems
Recognize and prove properties of stochastic programs
Represent/approximate the uncertain data by means of scenarios
Evaluate the benefits of using stochastic programming
Apply the solution methods presented in the course to solve stochastic programs
Implement a (simplified version of a) solution method using optimization software


Compentences:

Recognize and structure a decision problem affected by uncertainty and propose a suitable mathematical formulation
Design a solution method for a stochastic program based on an analysis of its properties and justify the choice
Identify a suitable way of representing the uncertain data of the problem, and its effect on the solutions obtained
Quantify the benefit of using stochastic programming in a particular decision making problem

Literature
See Absalon.

Teaching and learning methods
2x2 hours of lectures per week, 2 hours of classroom exercises or project work supervision. Individual or group-based project work throughout the course.

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