MAS1901 : Optimisation with Constraints (Inactive)
- Inactive for Year: 2024/25
- Module Leader(s): Prof. Sarah Rees
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
| European Credit Transfer System | |
Aims
To introduce the mathematical and computational methods required to maximise or minimise objectives subject to constraints on potential solutions
Module summary
Many problems require users how best to employ limited resources to obtain optimal cost-benefit. For example, a distribution company might have to decide what routes its vehicles should take around suppliers and customers. Or a financier might need to decide on whether to invest small amounts in lots of businesses or larger amounts in fewer businesses. Or a student preparing for several examinations might need to schedule revision time for each subjects.
Problems such as these can be expressed as optimisation (getting the best result) subject to constraints (finite or restricted resources). This module will introduce a variety of such problems and provide experience of some of the range of techniques available for solution from the array or modern operational research tools.
Outline Of Syllabus
Simple linear programming: graphical solutions; sensitivity analysis.
Linear programming: simplex algorithm; canonical form; sensitivity analysis; duality; integer programming; 0-1 problems.
Transportation and assignment problems: linear programming formulation; N-W corner algorithm; Hungarian algorithm.
Decision theory: problems with no data; decision trees; randomised actions; convex sets; problems with observations; decision rules; sequential decision problems.
Dynamic programming: shortest path problem; principle of optimality; forward and backward induction.
Inventories: economic order quantities; discounts; dynamic inventory models.
Introduction and application of Markov chains: transition probabilities; steady-state analysis; absorbing states, fundamental matrices.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 1 | 1:00 | 1:00 | Assignment laboratory |
| Scheduled Learning And Teaching Activities | Lecture | 1 | 1:00 | 1:00 | Class test |
| Scheduled Learning And Teaching Activities | Lecture | 3 | 1:00 | 3:00 | Problem classes |
| Guided Independent Study | Assessment preparation and completion | 1 | 6:00 | 6:00 | Revision for class test |
| Guided Independent Study | Assessment preparation and completion | 1 | 13:00 | 13:00 | Revision for unseen exam |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision lectures |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:00 | 2:00 | Unseen exam |
| Scheduled Learning And Teaching Activities | Lecture | 23 | 1:00 | 23:00 | Formal lectures |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 4 | 1:00 | 4:00 | Tutorials in the lecture room |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 12 | 0:10 | 2:00 | Office hours |
| Guided Independent Study | Independent study | 5 | 2:00 | 10:00 | Review of coursework assignments and course test |
| Guided Independent Study | Independent study | 4 | 4:00 | 16:00 | Preparation for coursework assignments |
| Guided Independent Study | Independent study | 1 | 17:00 | 17:00 | Studying, practising and gaining understanding of course material |
| Total | 100:00 |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 1 | A | 80 | N/A |
| Written Examination | 40 | 1 | M | 10 | Class test |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 1 | M | 10 | Coursework assignments |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class, therefore 40 minute) coursework test allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1901's Timetable