| Unit name | Optimisation & Algorithms |
|---|---|
| Unit code | MGRCM0021 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Kremantzis |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
None |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Management - Business School |
| Faculty | Faculty of Social Sciences and Law |
Why is this unit important?
Optimisation, which is also referred to as mathematical programming, is among the most widely used techniques in operational research and management science. In many cases, its application has been so successful that its use has passed out of operational research departments to become an accepted routine planning tool. Mathematical programming, which is related to computer programming only in the sense of “planning”, becomes involved with computing as practical problems almost always involve big data and arithmetic that can only be tackled by the calculating power of a computer.
Building on the modelling analytics unit of the first teaching block, students will be exposed to different problem formulations and more mathematical algorithmic techniques to solve real-life problems; in this way, they will be able to convey the results from modelling a managerial situation to the relevant stakeholders and to respond to their concerns.
How does this unit fit into your programme of study?
Building on the modelling analytics in the first teaching block, the two units embrace a comprehensive and sought-after skillset to students, who would be interested in pursuing a PhD degree or a specialist career in management science-related fields. This unit is elective and if selected by students, it will offer them the opportunity to deepen into well-established, and in some cases, efficient algorithms for solving linear, integer, non-linear, and dynamic (mathematical) programming problems. They will also be more familiar with the process of building optimisation models to reveal the interconnections of elements within more challenging real-life applications.
An overview of content:
Students will be given the chance to thoroughly explore widely used topics in effectively solving optimisation models such as the simplex algorithm and its variants to effectively solve Linear Programming (LP) models; the sensitivity analysis and simplex algorithm; duality and LP problems; the branch-and-bound and the cutting plane algorithms to solve integer programming models; the Dantzig-Wolfe and the Benders decomposition algorithms for solving large-scale optimisation problems; the gradient descent and Newton’s method to deal with non-linear programs; and the dynamic programming. More advanced and special applications will also be considered in the unit’s teaching portfolio with respect to gaining experience on more complicated model building processes.
How will students, personally, be different as a result of the unit:
On completion of this unit, students will realise that the knowledge of consolidated and efficient optimisation algorithms and techniques to formulate and solve real-life problems, plays a key role in various sectors involving marketing, finance, operations, and supply chain management. They will be able to select appropriate and powerful (mathematical programming) techniques for different contexts with the aim to obtain the desired results, interpret them into useful insights, and communicate them to key stakeholders.
Learning Outcomes:
On completion of this unit, students will be able to:
ILO1: utilise principles to build mathematical models and learn about the functioning of systems,
ILO2: demonstrate a sound knowledge of various sets of mathematical rules (algorithms) for solving linear, integer, non-linear, and dynamic programming models,
ILO3: apply appropriate optimisation techniques and algorithms to model and solve a wide range of managerial problems,
ILO4: utilise a variety of digital platforms which support computer-based prescriptive analytics,
ILO5: convey the results from modelling a managerial situation to the relevant stakeholders and to respond to their concerns.
Teaching will be conducted through ten lectorial sessions of 3 hours (total 10*3 = 30 hours). These will comprise a combination of lecture talks, problem-solving workshops focusing on the practical aspects discussed in the lecture, small group computer lab sessions for further practice, and optional advice and feedback hour sessions for addressing more questions (if any). Additional online quizzes and contemporary case studies will be provided on Blackboard to support self-directed learning; you will, thus, cover the basic building blocks of the unit and deepen your understanding of the material covered in the main supervised sessions. The amount of time necessary to spend in the self-directed study will be dependent on how deeply you wish to understand the concepts covered, but 120 – 170 hours over the TB2, may be taken as a ballpark figure. All learning materials, apart from the core textbooks, will be available on Blackboard. You will also be more than welcome to start exploring the discussion board and its utility to strengthen peer interaction and accommodate issues that are not discussed in detail within the classroom. At the beginning of each week, set aside time to review the tasks and materials for the week and plan when you will work through them. Planning will allow you to learn in an efficient and organised manner and can prevent you from stress and anxiety in the long-term run.
Tasks which help you learn and prepare you for summative tasks (formative):
There will be weekly practical exercises and case studies (in workshops and computer labs) to be completed by students either individually or collectively to improve their analytical skills. Answers and feedback will be available to students for self-assessment (ILOs 1-4). In addition, students will be offered the opportunity to answer online quizzes found on Blackboard, typically at the end of the main (online asynchronous) lecture talk, to check their understanding of the respective week’s content. Finally, in class and/or online polling questions will also be delivered to students via the Mentimeter response system to further check their understanding of various discussed topics (ILOs 1-2).
During the lab sessions, small-group assessments will be undertaken which will involve the formulation of a model-based solution to a given managerial problem. This activity will require access to computer software (MS Excel, Python) which enables the solution to be reached. Formative feedback will be given and will aid the students to complete their summative project assessments (ILOs 1-5).
Tasks that count towards your unit mark (summative):
Individual Assignment (100% of the overall unit mark):
Students will work individually and independently to evaluate the past efforts of a real firm of their liking to apply appropriate principles and optimisation techniques and algorithms to formulate and solve a business problem. A discussion should be generated on the problematic area identified, the type of optimisation model built, the solution mathematical algorithm selected, the various insights from the interpretation of the outcomes, and any assumptions and limitations made. The student should also consider involving a discussion on alternative methodologies that could have been implemented instead (by the firm) to obtain even more effective and realistic outcomes. This assessment is related to all intended learning outcomes. The student is required to submit a 2500-word project report to communicate their findings (ILOs 1-5).
When assessment does not go to plan:
If the assessment does not go to plan, then the resit will consist of an individual case study, no more than 2500 words (100%) covering the various topics of the unit, discussed in detail throughout the semester.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MGRCM0021).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
