Below are details of our courses which will be running in the current academic year and details on how to apply.

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

The basics of mathematical programming

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.

On completion of the course, students will be expected to:
• Understand the properties of efficient solution alternatives in decision problems with multiple
• 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

• 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

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.

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

This NATCOR course consists of two parts – the more established system dynamics modelling part and a newer part (only taught once before) on behavioural modelling. The two parts are inter-related and it is recommended that students enrol in both, although it is possible to enrol in either one of the two.

The course is led by academic staff from the University of Southampton, Konstantinos Katsikopoulos who chairs the OR Society’s special interest group on Behavioural OR and has recently single-authored a monograph on the topic (published by Palgrave Macmillan), and Martin Kunc who chairs the special interest group of the OR Society on OR and Strategy and is an Editor-in-Chief of JORS. The two parts will be held back-to-back: First, the Behavioural OR part will focus on operational decision making and then the System Dynamics part will focus on behavioural modelling with a strategic perspective. Modelling is a common core for both parts, with Behavioural OR focusing more on mathematical modelling and machine learning and System Dynamics focusing more on computer modelling and simulation. In addition to sessions by the two course staff, there will also be sessions by guest academics who are leaders in their respective fields.

Description and value: Behavioural modelling
This two-and-a-half-day course will focus on those domains of OR in which mathematical modelling has been mostly developing and yielding intellectual and practical benefits, including decision analysis, game theory, classification and prediction. The course will be founded on a key feature of behavioural science—the distinction among normative, descriptive and prescriptive models. The course will be valuable to all of those OR students who have noticed the limits of approaches that are insensitive to how (i) human behaviour is modelled in models, (ii) clients interact with models and (iii) policy makers utilize models in their decision making—these aspects map to the Behavioural-OR taxonomy of behaviour in/with/beyond models. The course will be especially valuable to OR students looking to critically apply their skills and explore possibilities in areas adjacent to OR, such as economics and operations management, where human behaviour is since long being modelled. The sessions will be interactive, and there will also be plenty of time for informal interactions and networking.

Description and value: System modelling
Nowadays, there is an increasing integration of methods from economics and psychology in simulation that allow more rigorous approaches to address behavioural issues. One of these approaches is the use of laboratory and field experiments of individual and group decision making concerning human judgment and decision-making under uncertainty. System Dynamics, as a simulation methodology, has been employed successfully as a behavioural experimental tool as well as to represent bounded decision making. Some researchers suggest that System Dynamics models are behavioural models of business systems which uncover intended rationality (theories in use) in business decision making. The two and a half days will cover the basic principles of System Dynamics, System Dynamics to model behaviour, useful approaches to perform research using System Dynamics together with other OR methods.

Structure and content: Behavioural modelling
Monday (July 15, 2024)
10:30 – 11:00 Welcome and registration
11:00 – 12:30 Session 1: Foundations (normative/descriptive/prescriptive models and behaviour in/with/beyond models; Konstantinos Katsikopoulos)
12:30 – 13:30 Lunch
13:30 – 15:00 Session 2: Behavioural decision theory and some of its myths (hands-on group exercises and review of basic results; Konstantinos Katsikopoulos)
15:00 – 15:30 Coffee and tea
15:30 – 17:00 Session 3: Behavioural game theory (hands-on group exercises and review of basic findings; João Ferreira, University of Southampton Department of Economics)

Tuesday (July 16, 2024)
09:00 – 10:30 Session 4: Transparent machine learning: Fast-and-frugal decision trees (hands-on group exercises and review of basic findings; Özgür Şimşek, Head of AI group at University of Bath)
10:30 – 11:00 Coffee and tea
11:00 – 12:30 Session 5: Transparent machine learning: Other models (hands-on group exercises and review of basic findings; Özgür Şimşek)
12:30 – 13:30 Lunch
13:30 – 15:00 Session 6: Behavioural forecasting (Kostas Nikolopoulos, Durham University)
15:00 – 15:30 Coffee and tea
15:30 – 17:00 Session 7: Discussion: Publishing top journal articles in Behavioural OR (Kostas Nikolopoulos and Konstantinos Katsikopoulos)

Wednesday (July 17, 2024)
09:00 – 10:30 Session 8: Behavioural inventory control (Konstantinos Katsikopoulos)
10:30 – 11:00 Coffee and tea
11:00 – 12:30 Session 9: Wrap-up and connection to System Dynamics (Konstantinos Katsikopoulos and Martin Kunc)
12:30 – 13:30 Lunch

Structure and content: Systems modelling
Wednesday (July 17, 2024)
13:30-15:00 Introduction to the system dynamics field (Martin Kunc)
15:00-15:30 Tea break
15:30-17:00 Introduction to System dynamics software (Martin Kunc)
17:00-17:30 Summary for the Day – Q&A

Thursday (July 18, 2024)
9:00-10:30 Rules for modelling and basic structures in System Dynamics (Martin Kunc)
10:30-11:00 Coffee break
11:00-12:30 Quantitative behavioural modelling: approaches using SD (Martin Kunc)
12:30-13:30 Lunch
13:30-15:00 System dynamics models using R (Jim Duggan, University of Galway)
15:00-15:30 Tea break
15:30-17:00 System dynamics models using R (Jim Duggan, University of Galway)

Friday (July 19, 2024)
9:00-10:30 Qualitative behavioural modelling: using SD as a problem structuring method (Martin Kunc)
10:30-11:00 Coffee break
11:00-12:30 System Dynamics and Hybrid modelling (Martin Kunc)
12:30-13:30 Lunch
13:30-15:00 Research applications and publishing articles in SD (Martin Kunc)
15:00-15:30 Tea break
15:30-17:00 Using System Dynamics in industry (TBD)

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.

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.

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.

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.

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.”


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.


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.


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.


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.


[1] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. As of June 2009, this text is freely available to download at . 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.


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 and the methods of forecasting and data mining and are 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: 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 forecasting, which has a major role in many if not most OR modelling. In both these fields there have been many recent advances not least in the area of machine learning (building on data availability).

The first stage in any analysis of data is to explore the data to identify key components such as seasonality or to cluster the data to understand different segments (for example customer behaviour). After this introduction we then revisit regression, perhaps the single most used method for analysing multi-dimensional data. Here explanatory variables are linked through a model to the variable(s) of interest: various models of the data can then be developed and evaluated. Our emphasis is on model building rather than the mechanics of regression, which most participants will have been exposed to. Alternatively, where the aim is to understand the features of the data, these can be clustered into segments and the individual segments analysed to understand what features distinguishes one segment from another.

Where the data are collected over time, exploratory analysis of time series data decomposes the time series into certain key components such as trend and seasonality. simple models such as exponential smoothing have proved the workhorses of OR over many years. But often researchers will need to develop explanations of the forces that drive the focus variable. Regression (which most students have learnt something of) will be covered in some detail, both in its applications to model building including its use of testing theory but also in forecasting The type of application affects which methods are most suitable and lecturers will discuss how the nature of the data affects the choice of method. Finally, the course will examine the new methods of data mining and forecasting including neural networks, a flexible method which has the capacity to capture non-linearities in any data set.

Theoretical model building only takes us so far. The last two days of the course emphasize hands-on experience of these various methods through a group project analysing complex data. A short assessment of participants’ understanding completes the course.

The course assumes knowledge only of basic statistics. This course will be taught by members of Lancaster’s Centre for Marketing Analytics and Forecasting, led by Dr Nicos Pavlidis. The many data based exercises in the course rely on computer packages. We have chosen to use R which some but we quite understand not all of you will be familiar with it. But this is not a programming course. Participants will be given access to a self-learning course in R where participants can learn the basics quickly. But in exercises and the group workshops help will be at hand and the aim is for each group to include an R ‘expert’ to ensure that the analysis emphasizes model building rather than computing.

This course is supported by DataCamp

Dr Nicos Pavlidis: Course Leader
Dr Anna Srogonis: Course Coordinator
Dr Kandrika Pritularga: Course Coordinator

Timetable (to be confirmed)

Day 1 Monday
Start Finish
1:00:00 PM 1:30:00 PM Registration
1:30:00 PM 2:15:00 PM Welcome and Introduction: Predictive analytics and Forecasting
2:15:00 PM 2:45:00 PM Break
2:45:00 PM 3:30:00 PM Data Exploration & Decomposition
3:30:00 PM 4:15:00 PM Exercise
4:15:00 PM 4:20:00 PM Break
4:20:00 PM 5:05:00 PM Simple forecasting methods
6:30:00 PM 8:00:00 PM Social events, woodland walks

Day 2 Tuesday
Start Finish
9:00:00 AM 9:45:00 AM Intro to Forecasting
9:45:00 AM 10:30:00 AM Exponential smoothing
10:30:00 AM 11:15:00 AM Exercise (ETS)
11:15:00 AM 11:45:00 AM Break
11:45:00 AM 1:15:00 PM Forecast evaluation and selection​
1:15:00 PM 2:15:00 PM Lunch
2:15:00 PM 3:00:00 PM Exercise
3:00:00 PM 3:45:00 PM Autoregressive models
3:45:00 PM 4:15:00 PM Break
4:15:00 PM 5:00:00 PM Autoregressive models (tbc)
5:00:00 PM 5:45:00 PM ARIMA exercise

Day 3 Wednesday
Start Finish
9:00:00 AM 9:45:00 AM Regression modelling intro: Explanation and prediction
9:45:00 AM 10:30:00 AM Regression modelling II
10:30:00 AM 11:00:00 AM Break
11:00:00 AM 11:45:00 AM Exercise
11:45:00 AM 12:30:00 PM Dummy variables in regression
12:30:00 PM 1:30:00 PM Lunch
1:30:00 PM 2:15:00 PM Regression models for time series
2:15:00 PM 3:00:00 PM Exercise
3:00:00 PM 3:30:00 PM Break
3:30:00 PM 4:15:00 PM Classification: k-NNs, Cross validation
4:15:00 PM 5:00:00 PM Classification workshop
7:00:00 PM 9:00:00 PM Social dinner (Indian restaurant on China Street)

Day 4
Start Finish
9:00:00 AM 9:45:00 AM Introduction to Clustering
9:45:00 AM 10:30:00 AM Clustering Workshop
10:30:00 AM 11:00:00 AM Break
11:00:00 AM 11:45:00 AM Introduction to Artificial Intelligence/Machine Learning in Analytics;
11:45:00 AM 12:30:00 PM AI/ ML in Forecasting
12:30:00 PM 1:30:00 PM Lunch
1:30:00 PM 2:15:00 PM ML methods
2:15:00 PM 3:00:00 PM Workshop
3:00:00 PM 3:30:00 PM Break
3:30:00 PM 4:15:00 PM Group project
4:15:00 PM 5:00:00 PM Group project
5:00:00 PM 5:15:00 PM Break
5:15:00 PM 6:00:00 PM Group project

Day 5
Start Finish
9:00:00 AM 9:45:00 AM Group project
9:45:00 AM 10:30:00 AM Guest lecture (Alex)
10:30:00 AM 11:00:00 AM Break
11:00:00 AM 12:15:00 PM Group presentation
12:15:00 PM 12:45:00 PM Closing Remarks

Stochastic Modelling is concerned with using probability concepts and techniques for capturing uncertainty in order to describe situations, predict performance and support decision making. Many activities in real-life situations are not deterministic in nature, but rather have an unknown or uncertain element attached to them. The Operational Research literature abounds with applications of Stochastic Modelling, with Healthcare, Transportation, Computing and Communications, Business and Finance being just a few examples. In the recent years, Stochastic Modelling has become a key component of interdisciplinary research between Operational Research and Statistics and Machine Learning.

This course will present some of the theory behind such modelling processes, but consideration will also be given to applications by means of case studies. The topics covered are: Stochastic Processes, Queueing Systems and Networks, Maintenance and Reliability, Inventory Control and Revenue Management. This course will be taught by members of Lancaster University, especially from its research groups on Simulation and Stochastic Modelling, Optimisation and Centre for Transport & Logistics, complemented with speakers from other institutions and companies.

Dr. Rob Shone: Course Leader

Much of the material needed as background reading for this course will be provided on-line. The preparatory material will cover basics of probability, random variables, probability distributions and stochastic processes, and introductions to maintenance & reliability, queueing theory, inventory control and revenue management.

The course aim is to provide an appreciation of the theory which has been developed to model real-life situations using probability concepts and techniques. On completion of the course, participants should be better prepared to understand the more sophisticated models that appear in the literature.

On completion of the course, students will be expected to:
– understand the basics of probability concepts and techniques, with particular relevance to queueing systems and networks, maintenance and reliability, inventory control and revenue management
– be aware of the rich diversity of scenarios to which stochastic modelling may be applied,
– be conscious of the relationships and complementarities between analytic and simulation modelling.

Stochastic Processes: Markov chains in discrete and continuous time, renewal processes, applications to queueing systems.
Queueing Systems and Networks: Queues with general arrival and service patterns, queues in series and in parallel, batch arrivals and services, phase-type service distributions, numerical approaches to transient behaviour.
Maintenance and Reliability: Replacement decisions (age, preventative, block, etc), inspection criteria, stochastic comparisons of system reliabilities and maintenance policies, scheduling and sequencing decisions, continuous and discrete renewal and repair processes and their computational requirements.
Inventory Control: Review of deterministic models as approximations to stochastic situations, Newsboy-type problems, time-varying demands, stochastic demand with constant lead-times, stochastic lead-times.
Revenue Management: stochastic modelling of demand, models of perishable products, strategies of decisions making, discrete-time Markov decision processes, stochastic dynamic programming algorithms, curse of dimensionality, optimisation/learning trade-off.
Case studies. The above topics will be illustrated by case studies of applications from fields such as business and finance, computing and communications, transportation, or healthcare.

All students who attend a NATCOR course will be required to undergo a (relatively light) summative assessment exercise. This will normally take the form of a multiple-choice test, though exceptions may be permitted in some cases

A copy of the full timetable can be found here

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.

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.

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.

Arash Mahdavi, The Art of Process-Centric Modeling with AnyLogic,

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

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


• 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

Material intended for preliminary reading discussing basics of the statistical aspects of simulation

A preliminary copy of the course timetable can be found here

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: Antonio Martinez-Sykora (University of Southampton), Trivikram Dokka (Lancaster University), Bo Chen (University of Warwick), Adam Letchford (Lancaster University), Chris Potts (University of Southampton), Stefano Coniglio (University of Southampton)

The basics of linear and integer programming

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.

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.

1.Introduction. Types of problems (for example, 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.  Valid inequalities, polyhedra and facets, separation, computational aspects.

7.Danzig Wolfe Decomposition.  Formulations using column generation, pricing algorithms, branching strategies.

8.Benders Decomposition.

9.Applications in Data Analysis and Visualisation.  Models from regression and classification, clustering and visualisation.