# Advanced Operations Research: Stochastic Programming

### Course 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 mathematical 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 applications:

• E1. Solution of case studies from e.g., the energy, finance, or logistics sector, using optimization software such as GAMS, Cplex or Gurobi.
• E2. Solution of several practical exercises.
Education

MSc Programme in Mathematics-Economics

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

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

Lecture notes provided by the teacher (see Absalon).

Operations Research 1 (OR1) or similar is required.
Recommended but not required: Applied Operations Research.

Academic qualifications equivalent to a BSc degree is recommended.

Oral

Lecturer's oral or written feedback (collective and/or individual) on the project work.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
30 minutes oral examination with 30 minutes preparation time.
Aid
Only certain aids allowed

All aid can be used during the preparation time.

No aid can be used during the exam.

Marking scale
Censorship form
No external censorship
Several internal examiners
##### Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

• Category
• Hours
• Lectures
• 28
• Preparation
• 28
• Theory exercises
• 14
• Project work
• 55
• Exam Preparation
• 80
• Exam
• 1
• English
• 206

### Kursusinformation

Language
English
Course number
NMAK15004U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 4
Schedulegroup
A
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Giovanni Pantuso   (2-767f4f7c7083773d7a843d737a)
Saved on the 28-02-2022

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