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Operations Research: a Mathematical Way to Optimise your World

Operations Research: a Mathematical Way to Optimise your World

During computer practicals you will gain hands-on experience with up-to-date software applied to practical cases.

Course description

This course will introduce you to the most successful models and algorithms from operations research, such as linear optimisation, combinatorial optimisation, network optimisation, dynamic optimisation, Markov chains, queueing, simulation, and reinforced learning. Not only will you learn some of the beautiful but basic mathematics behind them, but also during computer practicals you will gain hands-on experience with up-to-date software applied to practical cases in such domains as logistics, revenue management, and financial engineering. The course will enable you to recognise and exploit opportunities for mathematically supported decision-making and can help you prepare for an MSc in Operations Research.

Our registration deadline has passed, it is no longer possible to apply. You can leave your contact details to be added to our summer 2023 newsletter.
 

About this course

Course level

  • Master / Advanced

Course coordinator

  • A.A.N. Ridder

Credits

  • 3 ECTS

Contact hours

  • 45

Language

  • English

Tuition fee

  • €650 - €1150

Additional course information

  • Requirements

    Undergraduate courses in linear algebra, analysis, and probability theory/statistics. Computer programming skills preferably in Python, R or Matlab/Octave.

  • Learning objectives

    By the end of this course, students will:

    • have an overview of the field of Operations Research;
    • be able to model a practical optimisation problem into an appropriate mathematical formulation;
    • be able to solve the mathematical model using advanced optimisation software;
    • have learnt how to work in teams on a quantitative oriented and how to present the results.
  • Course structure

    Week 1 focusses on deterministic optimisation techniques, while week 2 is centered around stochastic modelling.

    In week 1 we start with the basic technique of linear programming (LP). The emphasis will be on modelling practical problems into the framework of LP, and solving them with software such as Gurobi. It will be demonstrated what mathematical principles lie behind the solution method. Many interesting and practical LP problems involve integer variables, which lead to the topics integer linear programming (ILP), and combinatorial optimisation (ILP). We will discuss why these are more difficult than LP and highlight some solution methods. Next, we will consider optimisation problems in network models which is relevant for logistical, distributional, and supply chain systems. The most famous problems are the ones with the  shortest paths, which are easy to solve by Dijkstra's algorithm, and the traveling salesman, which is hard to solve. These problems can be solved as special cases of ILP, but have, in most cases, their own algorithm. Week 1 is concluded by generalising to dynamic optimisation. In practice, once you have made a decision (or action), the system evolves to a new state and a new optimisation problem that requires an action, etc. We will show you how to get an overall optimal solution by considering the appropriate single decision problems and solve these. 

    During week 1, students will work on an optimisation project that could be (I)LP or network model. The necessary input data are obtained from various sources, then the model is constructed and validated. The output is generated by solving the model with Gurobi.

    Week 2 starts off with discussing Markov chains. These are relevant stochastic processes with properties that make them suitable for modelling operational systems. For instance, Google pagerank is based on Markov chains. Moreover, it is relatively easy to analyse long-run behaviour of systems when modelled as Markov chains. Another approach for modelling and analysis of operational systems is by executing simulation experiments. Stochastic simulation (also called Monte Carlo simulation) is the second topic of this week. We will discuss the basic principles of generating random numbers and random variables, will give ample examples, and elaborate on statistical analysis of simulation output. Next, we will discuss queueing systems, a typical Operations Research topic.  Queueing and waiting are phenomena that one encounters in, for example, service centres, ticket lines, hospitals, communication systems, and many others. In this lecture, we will discuss the mathematical theory that describes these phenomena in a conceptual model which enables to execute performance analysis and run numerical computations. The purpose is to find system designs that may reduce waiting times or increase utilisation. The last topic is reinforced learning. Reinforced learning is a computational approach for determining optimal decisions in a dynamic system by means of learning (exploiting) from previous decisions and experimenting  (exploring) with new decisions. The exploiting stage uses techniques from dynamic programming, whereas the exploring stage uses Monte Carlo simulation. Typically, reinforced learning is applied to reach a certain goal. This lecture will discuss the basic principles of this method, and will supply successful examples and applications.

    During week 2, students will work on a simulation project for queueing optimisation or reinforced learning. The necessary input data are obtained from various sources, then the model is constructed and validated. Finally, the model is solved with Python (or other language) programming.

  • Course schedule

    Classes will take place from Monday 18 July until Friday 29 July. In general classes will be during the week between 9am and 17pm (please take exceptions into account). Wednesday afternoons and weekends will be off for optional social activities or personal time. Good to be aware that self-study will be required in your private time (nights and weekends). Sunday 17 July and Sunday 31 July are arrival and departure days (in case you arrange accommodation via our housing service). More details will be shared in the course syllabus which will be shared with the participants in June. 

  • About the course coordinator

    Ad Ridder is an associate professor of operations research at the department of Operations Analytics, at Vrije Universiteit, Amsterdam, where he teaches courses on Numerical Methods, Stochastic Operations Research, and Simulation. He obtained his MSc in mathematics at the University of Amsterdam, and his Ph.D. in operations research from Leiden University. His previous affiliations include the University of California at Berkeley and the Erasmus University.  His research interests are in efficient simulation methodologies for complex stochastic systems, and in modelling and analysis of counting distributions.

Team VU Amsterdam Summer School

We are here to help!

+31 20 59 86429

Skype: by appointment via amsterdamsummerschool@vu.nl

Contact

  • Bianca
  • Programme Coordinator
  • Celia
  • Summer and Winter School Officer
Celia VU Amsterdam Summer & Winter School
  • Helena
  • Summer and Winter School Support Assistant
Helena VU Amsterdam Summer and Winter School