Courses

DESCRIPTION
Multiple Criteria Decision Making (MCDM) is a subfield of Operational Research that focuses on methods and tools to support decision-making in problems involving multiple, often conflicting, criteria. It has broad applications across domains such as business, supply chain management, energy, healthcare, sustainability, and logistics. This course introduces the theory and principles of MCDM, including preference modelling and goal programming, and explores various approaches for analysing multi-criteria decision problems and solving multi-objective optimisation models.

Main contributors:
• Dr Banu Lokman (Course Leader), University of Portsmouth (banu.lokman@port.ac.uk)
• Professor Dylan Jones, University of Portsmouth (dylan.jones@port.ac.uk)
• Dr Nikolaos Argyris, Loughborough University (N.Argyris@lboro.ac.uk)

PRE-REQUISITES
The basics of mathematical programming

AIMS OF THE COURSE
The course aims to develop knowledge of the theory of MCDM and develop skills in building and solving optimisation problems with multiple objectives.

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
• Develop and solve mathematical models to obtain nondominated solutions of multi-objective optimisation
problems
• Understand and apply the goal programming method to solve decision problems with multiple goals
• Understand and apply preference modelling and interactive methods in MCDM

PRINCIPAL TOPICS OF STUDY

• Introduction to Multiple criteria decision making (MCDM)
• Efficiency and Nondominance
• Scalarization Techniques in Multi-objective Optimisation
• Exact & Approximate Solution Methods
• Goal Programming
• Preferences in MCDM: Foundations
• Preferences in MCDM: Interactive Methods

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 (Banu Lokman)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 A Review of Linear and Integer Programming (Banu Lokman)

Day 2
9.00 – 10.30 Scalarization Techniques in Multi-objective Optimisation – Part 1 (Banu Lokman)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Scalarization Techniques in Multi-objective Optimisation – Part 2 (Banu Lokman)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Exact & Approximate Solution Methods (Banu Lokman)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Case Study 1: A Real-life Sales Territory Construction Problem (Banu Lokman)

Day 3
9.00 – 10.30 Goal Programming: Theory and Applications – Part 1 (Dylan Jones)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Goal Programming: Theory and Applications – Part 2 (Dylan Jones)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Case Study 2: Goal programming and the Analytical Hierarchy Process (AHP) in the offshore wind sector (Dylan Jones)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Case Study 2 Discussion (Dylan Jones)

Day 4
9.00 – 10.30 Preferences in MCDM: Foundations (Nikolaos Argyris)
10.30 – 11.00 Tea/Coffee Break
11.00 – 12.30 Preferences in MCDM: Interactive Methods – Part 1 (Nikolaos Argyris)
12.30 – 13.30 Lunch Break
13.30 – 15.00 Preferences in MCDM: Interactive Methods – Part 2 (Nikolaos Argyris)
15.00 – 15.30 Tea/Coffee Break
15.30 – 17.00 Case Study (Nikolaos Argyris)

Day 5
9.00 – 10.00 Closing Session (Banu Lokman)
10.00 – 11.00 Assessment

The course is led by Martin Kunc who chairs the special interest group of the OR Society on OR and Strategy, has published numerous papers and edited books on System Dynamics and is an Editor-in-Chief of JORS. The course will be held mostly over five afternoons, commencing 6th July 2026.

System Dynamics will focus on behavioural modelling with a systems perspective. Modelling is a common core for both parts, with behavioural modelling following the field of Behavioural OR by focusing on behavioural aspects of operations, and the systems perspective will emphasise modelling and simulation of systems. In addition to sessions by the two course staff, there will also be sessions by guest academics who are leaders in their respective fields.

Purpose
The Nottingham NATCOR course covers the main techniques for heuristic optimisation algorithms (local search, meta-heuristics, multi-objective heuristics, hyper-heuristics, evolutionary algorithms) as well as an insight into complexity theory, automated configuration of heuristics, automated algorithm design, big data science and machine learning in the context of heuristic optimisation. The course is delivered by experts in the field with strong publication records and experience in the design and deployment of these methods on real-world problems in various business and industry scenarios.

Description
Heuristic Optimisation and Learning are cornerstone methodologies from the disciplines of Operational Research and Computer Science. These methods have been very successful in providing solutions to real-world problems across a wide range of application areas. Heuristic algorithms include a range of techniques from simple ‘rules of thumb’ to more sophisticated methods inspired on physical and natural processes like energy flow, evolution, and swarm intelligence. Heuristics can provide good-quality solutions (although not necessarily optimal) in practical computational time to otherwise intractable problems. Heuristics can be applied and tailored to a wide range of optimisation problems. Heuristic algorithms can also be combined with exact optimisation algorithms to form a rich variety of hybrid methodologies capable of performing with high effectiveness and efficiency when tackling complex problems. Big data usually refers to data that has large volume, variety, and complexity so that specialised modern techniques are required to analyse it and extract valuable knowledge from it. With the widespread availability of big data in many research problems and real-world applications, learning from it presents more challenges than traditional data science. There are many facets of big data science including acquisition, storage, computing infrastructure, visualisation, security, privacy, analysis, mining, machine learning etc. There are exciting interactions between big data science, machine learning and optimisation, and one of these is learning from evolutionary algorithms which is one of the topics covered in this course.

The course is suitable for participants from a wide range of backgrounds, from those that are new to optimisation to those that already have knowledge in some of the main topics (optimisation, heuristics, evolutionary computation, big data science, machine learning) but want to learn about the other topics and their interactions. The course is also effective to provide a full picture of heuristic optimisation and its interactions to big data science and machine learning.

In terms of techniques, the course covers a good number of them, giving a comprehensive view of heuristic optimisation and learning. The course starts with a gentle introduction to the fundamentals of optimisation and complexity theory. It then moves to cover key concepts and design principles of constructive and local search heuristics. Then, the course studies some metaheuristic techniques and evolutionary algorithms focusing on the main mechanisms from the single and multi-objective perspectives. This is followed by sessions on hyper-heuristic techniques, their origins, classification, and insights into variants of these methods. The automated configuration of heuristics and automated design of algorithms are also covered. The course also includes sessions on big data science and machine learning as well as some of the links to optimisation with evolutionary algorithms.

In terms of practice, the course describes the application of some of the optimisation and learning techniques covered in the course and others, to tackle real-world problems in areas like air transportation, airport operations, vehicle and personnel operational logistics, energy consumption prediction and others. Practical work with some of the techniques covered is also a feature of the course. Participants are organised in teams to work of various practical tasks where optimisation and learning are applied following the concepts and techniques covered in the course. There are plenty of opportunities for course participants to network and discuss interests and ideas.

Delivery Method
This residential course is planned to be delivered in-person. However, online tools like Microsoft Teams will also be used to enrich the learning experience and communication for course participants. Some course materials will be made available for downloading during the course.

The course will be delivered using a mix of lectures, discussions, and practical work. For some parts of the course, participants will be asked to undertake some tasks individually or in groups and use some freely available or trial software. Emphasis will be put on making the course a rich experience where theory and practical work are blended. In addition to the instructors, there will be teaching assistants to help with managing the course and its logistics.

Pre-requisites
Basics of complexity and optimisation theory as well as computer algorithms and data structures. Some reading material is provided to students a couple of weeks in advance to the start of the course.

Aim
On completion of the course, students should have a working knowledge of the theory, design, implementation, configuration, and application of the main heuristic methods, as well as an insight into their interplay with data science and machine learning in the context of optimisation scenarios.

Learning Outcomes
Understanding of the fundamental theory underlying the main heuristic optimisation methods (e.g. local search, metaheuristics, hyper-heuristics, evolutionary algorithms, etc.). Awareness of the strengths and limitations of different heuristic optimisation methods. Ability to critically evaluate the applicability and quality of different heuristic optimisation methods. Understanding the fundamentals of automated algorithm design in the continuous and discrete spaces. Capability for designing and developing heuristic methods for some optimisation problems. Awareness of some software tools for the rapid prototyping of heuristic optimisation methods. Understanding the fundamentals of data science and machine learning in the context of heuristic optimisation. Awareness of the key concepts in the application of some optimisation techniques to real-world airport and air transportation operations.

Assessment
A few formative assessments throughout the course in the form of quizzes and practical exercises, in addition to a simple summative test at the end of the course.

The summative test at the end of the course is in the format of multiple-choice questions spanning the various topics covered in the course. Undertaking this assessment is a requisite given the mechanism by which the delivery of the course is funded. However, it is emphasised that the degree of difficulty of this summative assessment in moderate. Engaging with the sessions and activities of the course should be sufficient to be able to do well in this assessment.

Previous Runs of the Course
The Nottingham NATCOR course has been delivered every two years since 2010. Each time as a residential course, except in 2020 when it was delivered online using Microsoft Teams due to the covid-19 pandemic. In past runs of the course, the number of participants has been between 50 and 90 and from several countries around the world. The course has attracted participants from diverse academic backgrounds including mathematics, business, computer science, industrial engineering, economics, statistics, operations management, management science, transportation logistics, psychology, etc. This is a course with a strong track record of success and being able to deliver it again in-person is a great excitement!

Some comments from previous participants in the course include the following:

• “I appreciate the overview of different techniques given in a very organised manner.”
• “Well organised and loved the real-life applications and case studies addressed; these were my favourite.”
• “The lectures included a lot of interesting topics and case examples. Lecturers were very experienced and keen to respond our questions.”
• “The environment between attendees was really good and allowed an understanding of the wide applicability of these methods.”
• “I have really enjoyed the course. It made me feel a lot more confidence concerning the approach to my research work.”
• “Overall thoroughly enjoyed, very interesting; most enjoyed the case studies and looking at the research that the lecturers have performed using what we are learning.”
• “Exceptional organization, sufficient related courses, high level professors and lecturers, valuable, amazing and interesting experience, nice to meet new people and exchange ideas.”
• “Well-organised in a logical way to connect all the ‘knowledge dots’ I had before into a clearer picture.”
• “I really liked the course. It was very well organized and overall, very interesting. I liked how we were going deeper into the topics throughout the week, and mainly how the topics were so connected to the research of the lecturers.”

PRE-REQUISITES:

1. Undergraduate level knowledge of linear algebra (e.g. the relevant chapter in Winston’s textbook on OR) and calculus (e.g. basic notions of continuity and differentiability).
2. The students are expected to have familiarized themselves with the material marked with an asterisk in the teaching schedule and with other directed reading.

AIMS OF THE COURSE

1. To develop knowledge of different aspects of convex optimization and its applications.
2. To develop an ability to model real life problems as mathematical programming problems and an ability to adapt industry standard solvers to process them.
3. To develop an ability to analyze optimization algorithms for their merits and shortcomings.
4. To develop an ability to work independently as well as in a peer group with limited supervision.

LEARNING OUTCOMES FOR THE COURSE

The course provides opportunities for students to develop and demonstrate knowledge and understanding, qualities, skills and other attributes in the following areas:

(A) Knowledge and Understanding

On successful completion of this course, the students will have

1. knowledge of theoretical underpinning of convexity in optimization and of general nonlinear programming methods. This knowledge will act as a foundation to understand an advanced graduate textbook or a research paper without significant help.
2. understanding of linear programming methods and related theoretical issues.
3. knowledge of semi-definite programming.
4. ability to use an industry standard optimization software system for processing optimization models.

(B) Cognitive Skills

On successful completion of this course, the students will be able to

5. formulate realistic industrial problems as mathematical programming problems.
6. analyze critically the choice of algorithms for solving different classes of a particular optimization model regarding their computational effectiveness.
7. construct elementary proofs related to the properties of optimization methods.

(C) Other Skills and Attributes (Practical/Professional/Transferable)

On successful completion of this course, the students will be able to

8, plan and execute a solution to an optimization problem as a group and will be able to present the results to peers and tutors.

PRINCIPAL TOPICS OF STUDY:

Foundations of Convexity: affine and convex sets, convex functions, composition of convex functions.

General Convex Optimization: examples of convex optimization problems, duality, unconstrained minimization, steepest descent method, first and second order optimality conditions in unconstrained minimization, Newton’s method and convergence analysis, norm approximation problems.

Linear Programming: simplex method, duality for LP, interior point methods for LP.

Convex Quadratic Programming: simplex method for quadratic programming, application in finance, KKT conditions for convex QP.

Semi-definite Programming: formulation, extension of interior point methods to SDP, quadratically constrained convex quadratic programs.

A case study of convex optimization in industry.

Numerical Linear Algebra: algorithm complexity, Cholesky factorization, sparsity.

The latter part of this course will be run in two parallel streams: an application stream (A stream) and a theory stream (T stream). The lectures and workshops for the two streams will differ for the two streams for a part of the course, and the students will need to choose beforehand which stream they prefer to follow. Most of the topics of study are the same for both the streams, apart from the topics mentioned below:

A stream: Use of Industry Strength Solver Systems for LP/QP to process industrial problems.

T stream: advanced topics in optimization including interior point methods for convex quadratic optimisation, complexity analysis via self-concordance, interior point methods for second order cone programming, Nesterov’s method for smooth and non-smooth programming.

REFERENCES

[1] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. As of June 2009, this text is freely available to download at http://www.stanford.edu/~boyd/cvxbook/ . The chapters relevant to this course are 2-5 and 9-11.
[2] D.G. Luenberger, Linear and Nonlinear Programming, Kluwer, 2003. The chapters relevant to this course are 2-10.
[3] R. Fourer, .M. Gay, B.W. Kernighan, Ampl: A Modeling Language for Mathematical Programming, Brooks Cole, 2002.
[4] Hillier and Lieberman, Introduction to Operations Research, McGraw Hill, 2002. The chapter relevant to this course is 13.

TIMETABLE

Sessions that are common to all the students are shown in black font.
Sessions only for the theory stream are shown in italics.
Sessions only for the modelling stream are shown in bold.

Monday 10 June
12:00-13:00 Registration and welcome lunch
13:00-13:30 Welcome and introduction
13:30-15:30 Linear programming + HiGHS: Open-source convex optimization software (0.5h)
15:30-16:00 Coffee break
16:00-17:00 HiGHS: Structure and matrix sparsity – Part 1
18:30-20:30 Social activities: Campus woodland walk, followed by hot buffet

Tuesday 11 June
9:30-10:30 Structure and matrix sparsity – Part 2
10:30-11:00 Coffee break
11:00-12:00 Foundations of convexity
12:00-13:30 Lunch (on your own)
13:30-15:00 Foundations of convexity (0.5h) + Role of convexity in optimization (1h)
15:00-15:30 Coffee break
15:30-17:30 Role of convexity in optimization (0.5h) + Convex relaxations of nonconvex optimization problems

Wednesday 12 June
9:30-10:30 Interior point methods for linear programming – Part 1
10:30-11:00 Coffee break
11:00-12:00 Interior point methods for linear programming – Part 2
12:00-13:00 Lunch (on your own)
13:00-15:00 Interior point methods for quadratic programming
15:00-15:30 Coffee break
15:30-16:30 Interior point methods for second order cone programming
16:30 – 21:00 Social activities: Visit to Lancaster + Course Dinner

Thursday 13 June
9:30-10:30 Introduction to conic and semidefinite Optimization. Max-cut formulations, relaxations and approximations – Part 1
9:30-10:30 Introduction to modelling with Xpress – Part 1
10:30-11:00 Coffee break
11:00-12:00 Introduction to conic and semidefinite Optimization. Max-cut formulations, relaxations and approximations – Part 2
11:00-12:00 Introduction to modelling with Xpress – Part 2
12:00-13:30 Lunch (on your own)
13:30-15:00 Polynomial optimization and the Lasserre hierarchy
13:00-15:00 Modelling with Xpress
15:00-15:30 Coffee break
15:30-17:00 Polynomial optimization and the Lasserre hierarchy (0.5h) + Exercise Session (1h)
15:30-17:00 Modelling with Xpress

Friday 14 June
9:00-10:00 Xpress Presentations
10:00-11:00 Lectures assessment
9:30-11:00 Lectures assessment
11:00-11:30 Round-up, feedback and farewell

Predictive analytics as a general term uniting methods of forecasting and data mining is at the heart of almost all OR projects. Recent years have seen rapid developments in new methods, stimulated by increasing computing power and the growth of ‘big data’. The course’s objectives are to introduce students to these two key areas, important both for research and applications: (1) data mining where the dramatic growth in data availability has meant new methods have been developed with many applications in OR, statistics and operations, and (2) forecasting, which has a major role in many if not most OR modelling.

In this course, we will start with the discussion of basic forecasting principles then move to the time series analysis and introduce conventional statistical models for demand forecasting, such as ETS, ARIMA and regression. After that we will introduce some of machine learning techniques (such as k Nearest Neighbour and Decision Trees) that can be used for classification, discuss principles behind neural networks and also touch on the main clustering techniques that can be used for a variety of purposes. We will also discuss the ideas behind the Artificial Intelligence and how it can be used in predictive analytics.

The course will consist of interactive lectures and workshops. The latter will be done in R, the course participants will be provided all the necessary materials to make sure that everyone is on the same level and can learn without any delays.

This course is also supported by DataCamp

Course Leader: Ivan Svetunkov

Pre-requisites
The main pre-requisite is having a basic understanding of the main statistical concepts. Undergraduate level knowledge of statistics will suffice.

Aims
1. To develop knowledge of basic forecasting and data mining principles;
2. To develop an ability to analyse data using conventional statistical tools implemented in R;
3. To develop an ability to select the appropriate techniques for forecasting and data mining and to learn how to apply them in practice;
4. To be able to understand the basic principles behind artificial intelligence and machine learning.

Assessment
Assessment will consist of two parts:
1. Multiple choice test based on the lecture material;
2. Group coursework in the form of a case study, relying on the approaches introduced in the course.

Timetable
The course will last for 5 days, starting at 1pm on Monday and ending at 1pm on Friday. The course will be delivered by the members of the Centre for Marketing Analytics and Forecasting of Lancaster University Management School and invited speakers, experts in areas of forecasting and data mining.

The exact timetable will be confirmed closer to the beginning of the course.

A presentation by Filotas Theodosiou will also be included on the course:

Bio: Filotas Theodosiou is a senior applied researcher and lecturer at the Research Group of Predictive AI and Digital Shift at VIVES University of Applied Sciences. His research focuses on designing, modeling, and effectively communicating machine learning-based forecasting solutions for complex business problems. With strong technical and engineering expertise evidenced by his contributions to multiple Python packages, Filotas brings practical implementation knowledge to theoretical concepts. His multi-dimensional ML-based forecasting experience spans diverse business challenges, including hierarchical forecasting systems, demand prediction models that perform well with limited historical data, interpretable and actionable prediction frameworks, and specialized forecasting solutions for highly perishable products requiring unique optimization approaches. Furthermore, he actively evaluates the rapidly evolving landscape of AI, with a keen focus on critically assessing the potential and limitations of LLMs and their applicability on forecasting tasks.

Title: Applied Machine Learning in Practice: Insights from Real-World Predictive Analytics Case Studies

Abstract: In today’s data-rich environment, the core objective for businesses is to translate vast amounts of information into a competitive advantage through smarter decisions. A fundamental step in that process is generating accurate and reliable predictions of future conditions. This is achieved through Predictive Analytics, a discipline where Machine Learning (ML) models serve as the engine, systematically learning from historical data to produce the predictions that enable efficient downstream optimization. This talk provides a practical introduction to applied Machine Learning, framing it as an algorithmic process for uncovering meaningful patterns within historical data to predict future outcomes. Beyond the fundamental theoretical concepts, we will explore how these tools are used in the real world to solve concrete business challenges. We will look at the entire toolbox of predictive models—from simple, transparent methods that are easy to explain, to powerful but complex “black box” systems. We will focus on the crucial trade-offs involved and highlight how choosing the wrong tool for the job can lead to costly business mistakes. Additionally, we will touch upon the current wave of AI, critically evaluating where powerful tools like Large Language Models (LLMs) offer groundbreaking solutions versus where they might be an inefficient or inappropriate choice. Drawing on real-world case studies, this talk provides a practical introduction for developing predictive machine learning models to solve complex business tasks.

Simulation is one of the most widely used operational research techniques. It involves the development of an imitation on a computer of the system under study, followed by experimentation to understand and investigate improvements to the system. This course provides an understanding of simulation, with a focus on the mathematical and statistical principles of stochastic simulation modelling. The main technique of interest is discrete-event simulation, although other simulation techniques will be introduced.

PRE-REQUISITES
An understanding of the basic principles of statistics including confidence intervals and hypothesis testing.
It would be useful to read some parts of the following books.

LECTURERS
Dr Steffen Bayer, University of Southampton
Prof Christine Currie, University of Southampton
Prof Kathy Kotiadis, University of Kent
Dr Thomas Monks, University of Exeter
Dr Lucy Morgan, Analytics Manager, The Strategy Unit; Visiting Researcher, Lancaster University Management School
Prof Stephan Onggo, University of Southampton
Dr Luke Rhodes-Leader, University of Lancaster
Please not this may be subject to change.

Statistical Aspects
Krzanowski, W.J. 2010. An Introduction to Statistical Modelling. Wiley, Chichester, UK.
Makridakis, S. Wheelwright, S.C. and Hyndman, R.J. 1998. Forecasting: Methods and Applications. 3rd ed., New York, Wiley.

Simulation Concepts
Pidd, M. (2005). Computer Simulation in Management Science, 5th ed. Wiley, Chichester, UK.Robinson, S. (2014). Simulation: The Practice of Model Development and Use. 2nd ed., Palgrave, UK.
Banks et al. (2010) Discrete Event System Simulation by (5th edition), Prentice Hall.
Law, A.M. (2015) Simulation Modeling and Analysis (5th edition).
Nelson, B.L. (2013) Foundations and Methods of Stochastic Simulation: A First Course.

Anylogic
Arash Mahdavi, The Art of Process-Centric Modeling with AnyLogic, http://www.anylogic.com/resources/books/the-art-of-process-centric-modeling-with-anylogic/

AIMS
The aim of the course is to provide an understanding of the mathematical and statistical principles of stochastic simulation modelling. The specific objectives are as follows:
• To understand the alternative simulation methods and the requirements for simulation studies
• To develop skills in simulation modelling and simulation computer packages
• To understand the nature of, and approaches to, input data modelling
• To be able to analyse the output from a simulation model using appropriate methods

LEARNING OUTCOMES
Subject Knowledge and Understanding
On completion of the course students will be expected to:
• Understand the basic principles of simulation and performing simulation studies.
• Understand the basic theory of simulation analysis including input data analysis, experimentation and output analysis.
• Understand the key stages in developing and using simulation models
• To be aware of the strengths and limitations of the approaches covered.

Intellectual Skills
On completion of the course students will be expected to:
• Be able to develop and use a simulation model for a given problem situation.
• Be able to evaluate the quality of a simulation analysis

Practical Skills
On completion of the course students will be expected to:
• Be familiar with the use of a simulation software package (Anylogic) as well code (Python) for DES modelling.
• Be able to follow an appropriate life-cycle for the development and use of simulation models

PRINCIPAL TOPICS OF STUDY

• basics of DES modelling
• modelling process
• input modelling
• model validation
• experimentation
• output analysis
• modelling in Python and Anylogic
• simulation optimisation
• simulation applications in industry and healthcare

COVERAGE OF WEB-BASED MATERIAL AVAILABLE IN ADVANCE
Material intended for preliminary reading discussing basics of the statistical aspects of simulation

The preliminary timetable is as follows:
7th -11th July 2025

Monday
12.15 – 13.00 Lunch provided & Registration
13.00 – 13.30 Welcome
13.30 – 14.30 Overview Modelling Approaches (Kathy Kotiadis)
14.30 – 15.30 Modelling Process (Kathy Kotiadis)
15.30 – 16.30 Intro DES (Kathy Kotiadis)

16.45 – 17.30 check-in Glen Eyre student residence
18.00 – 20.00 Dinner & Social Event (Glen Eyre student residence)

Tuesday
9.00 – 10.00 AnyLogic 1 (Steffen Bayer)
10.00 – 11.00 Anylogic 2
11.00 – 11.30 Break (Refreshments)
11.30 – 12.30 AnyLogic 3
12.30 – 13.30 Lunch break
13.30 – 14.30 Input Modelling 1 (Lucy Morgan)
14.30 – 15.30 Input Modelling 2
15.30 – 16.00 Break (Refreshments)
16.00 – 17.00 Input Modelling 3

Wednesday
9.00 – 10.00 SymPy (Tom Monks)
10.00 – 11.00 SymPy
11.00 – 11.30 Break (Refreshments)
11.30 – 12.30 SymPy
12.30 – 13.30 Lunch break
13.30 – 14.30 Output Analysis 1 (Christine Currie)
14.30 – 15.30 Output analysis 2
15.30 – 16.00 Break (Refreshments)
16.00 – 17.00 Validation (Stephan Onggo)

19.00 Dinner (Brewhouse)

Thursday
9.00 – 10.00 Group work
10.00 – 11.00 Group work
11.00 – 11.30 Break (Refreshments)
11.30 – 12.30 Group work
12.30 – 13.30 Lunch break
13.30 – 14.30 Simulation Optimisation 1 (Luke Rhodes-Leader)
14.30 – 15.30 Simulation Optimisation 2
15.30 – 16.00 Break (Refreshments)
16.00 – 17.00 Simulation Optimisation 3

Friday
9.00 – 10.00 Guest lecture (TBC)
10.00 – 11.00 Group work
11.00 – 11.30 Break (Refreshments) + Assessment
11.30 – 12.30 Groupwork presentation
12.30 – 13.00 Reflections and Closure

Combinatorial optimisation problems typically involve finding the best arrangement, ordering, or selection of objects. There are numerous applications in Operational Research including scheduling of orders on machines in production industries, routing of vehicles to deliver goods to customers, and assigning of personnel such as nurses or airline crew to work periods. This course provides the main approaches and techniques required to tackle combinatorial optimisation problems. The main topics include computational complexity, types of algorithms, optimisation problems in networks, branch-and-cut, and branch-and-price.

Main contributors: Melih Celik (University of Bath), Eun-Seok Kim (Queen Mary University of London), Gunes Erdogan (University of Bath), Antonio Martinez-Sykora (University of Southampton), Bo Chen (University of Warwick), Adam Letchford (Lancaster University), Carlos Lamas Fernandez (University of Southampton)

PRE-REQUISITES
Basics of linear and integer programming

AIMS
The course aims at providing an appreciation of the types of combinatorial problems that arise in Operational Research and providing knowledge of the main approaches for tackling such problems.

LEARNING OUTCOMES
On completion of the course, the student will be expected to:
• understand the basics of complexity theory and be able to provide proofs that certain problems are NP-hard.
• have knowledge of a range of algorithms for shortest path, minimum spanning tree and network flow problems.
• analyse the worst-case running time of an algorithm.
• have an appreciation of the main types of approaches that can be used for tackling combinatorial optimization problems, together with their limitations.
• understand the principles behind branch-and-cut and branch-and-price and be able to apply these approaches to new problems.
• have an overview of how combinatorial optimization techniques can be applied in an area such as data science.

PRINCIPAL TOPICS OF LEARNING
1. Introduction. Types of problems (e.g., machine scheduling, vehicle routing and the travelling salesman problem, cutting and packing, set covering and partitioning). Integer programming formulations.
2. Computational complexity. Analysis of worst-case running time of algorithms (sorting, matrix multiplication, divide and conquer, dynamic programming). NP-completeness, reducibility.
3. Shortest path and minimum spanning tree algorithms. Label setting shortest path algorithms (Dijkstra’s algorithm and its variants). Label correcting shortest path algorithms (Bellman-Ford algorithm and its variants). Greedy algorithms for the minimum spanning tree (Kruskal, Prim).
4. Network flow algorithms. Maximum flow problem, augmenting paths, max-flow min-cut, Ford-Fulkerson algorithm and its variants. Minimum cost flow problem.
5. General solution approaches. Branch-and-bound, dynamic programming, constraint satisfaction, Lagrangean relaxation.
6. Branch-and-cut, branch-and-price, and Benders decomposition. Valid inequalities, polyhedra and facets, separation, computational aspects. Formulations using column generation, pricing algorithms, branching strategies.
7. Applications of combinatorial optimisation. Integer programming methods for data science. Case study and computer lab sessions. Combinatorial optimisation in practice.