DESCRIPTION
Decision making in many applications usually involves multiple conflicting criteria and uncertain factors. This course will cover these two important aspects of decision making. In the first half of the course, the theory of Multiple Criteria Decision Making (MCDM) and various approaches to deal with decision and optimisation problems with multiple criteria will be covered. In the second half of the course, optimisation under uncertainty, especially robust optimisation will be covered. Multi-objective optimisation under uncertainty which considers both aspects of multiple criteria and uncertainty in decision making will also be discussed.
Main contributors:
• Dr Banu Lokman (Course Leader), University of Portsmouth
• Dr Xuan Vinh Doan, University of Warwick
• Professor Dylan Jones, University of Portsmouth
• Dr Nikolaos Argyris, Loughborough University
PRE-REQUISITES
The basics of mathematical programming
AIMS OF THE COURSE
The course aims to develop knowledge of decision making with multiple criteria and uncertainty and develop skills in building and solving optimisation problems with multiple objectives and uncertainty.
LEARNING OUTCOMES
On completion of the course, students will be expected to:
• Understand the properties of efficient solution alternatives in decision problems with multiple
objectives
• Build and solve mathematical models to find nondominated solutions of multi-objective optimisation
problems and identify preferred solutions
• Understand and apply the goal programming method to solve decision problems with multiple goals
• Understand the concepts of optimisation under uncertainty
• Formulate and solve mathematical models for robust optimisation problems
PRINCIPAL TOPICS OF STUDY
• Introduction to Multiple Criteria Decision Making (MCDM)
• Efficiency and Nondominance
• Scalarization Techniques in Multi-objective Optimisation
• Preferences in MCDM: Foundations
• Preferences in MCDM: Interactive Methods
• Goal Programming
• Introduction to Optimisation Under Uncertainty
• Robust Optimisation: Concepts and Reformulation
• Multi-Objective Optimisation Under Uncertainty
ASSESSMENTS
Assessment, a summative assessment exercise, will be held in the last day. It will typically last about an-hour. Feedback will be provided at the end of the course.
OUTLINE
Day 1
12.30 – 13.30 Registration and lunch
13.30 – 15.00 Introduction to MCDM: Efficiency and Nondominance (Dr Banu Lokman)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 A Review of Linear and Integer programming (Dr Banu Lokman)
Day 2
9.00 – 10.30 Scalarization Techniques in Multi-objective Optimisation – Part 1 (Dr Banu Lokman)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Scalarization Techniques in Multi-objective Optimisation – Part 2 (Dr Banu Lokman)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Preferences in MCDM: Foundations (Dr Nikolaos Argyris)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Preferences in MCDM: Interactive Methods (Dr Nikolaos Argyris)
Day 3
9.00 – 10.30 Goal Programming: Theory and Applications – Part 1 (Professor Dylan Jones)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Goal Programming: Theory and Applications – Part 2 (Professor Dylan Jones)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Introduction to Optimisation under Uncertainty (Dr Vinh Doan)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Review of Linear Duality (Dr Vinh Doan)
Day 4
9.00 – 10.30 Robust Optimisation – Part 1 (Dr Vinh Doan)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Robust Optimisation – Part 2 (Dr Vinh Doan)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Case Study: Robust Optimisation (Dr Vinh Doan)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Multi-Objective Optimisation under Uncertainty (Dr Vinh Doan)
Day 5
9.00 – 10.00 Closing Session (Dr Banu Lokman)
10.00 – 11.00 Assessment
11.00 – 11.30 Round-up, feedback and farewell