Login for PhD students/staff at UCPH      Login for others
Advanced Operations Research: Stochastic Programming
Provider: Faculty of Science

Activity no.: 5635-23-07-31 
Enrollment deadline: 24/04/2023
PlaceDepartment of Mathematical Sciences
Date and time24.04.2023, at: 08:00 - 23.06.2023, 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
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 detailsApproval of one project report is a prerequisite for enrolling for examination.
Exam aidsOnly certain aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures28.00
Theory exercises14.00
Project work55.00
Exam1.00
Preparation28.00
Eksamensforberedelse80.00
Sum206.00
Content
In countless real-life situations, decision makers are required to make decisions under uncertainty, that is while relevant information is uncertain, noisy, imprecise. Examples are investments in assets or projects with uncertain returns, scheduling of taks with uncertain duration, or production of goods with uncertain demand. Decision problems with these features are central in the modern finance, energy, and logistics sector, to name a few.

This course introduces the students to optimization in conditions of uncertainty by means of stochastic programming. 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 sound input data (scenarios). The students of this course will independently handle practical problems in project work and exercises, hereby gaining the practical experience necessary to work on complex decision problems under uncertainty. 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 and the value of information.

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.
E2. Solution of several practical exercises.

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.

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.