Undergraduate Course: Fundamentals of Operational Research (MATH10065)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||This course covers some core areas of Operational Research, namely Dynamic Optimisation, Integer Optimisation and Game Theory. Emphasis will be placed both on the mathematical techniques and on problem formulation through examples from applications.
Dynamic Optimisation is a neat way of solving sequential decision problems based on recursion. Its power comes from the fact that some important classes of optimisation problems that "ought to be difficult" can be reformulated as a recursive optimisation problem and thus made tractable. Examples are network optimisation problems, allocation problems and inventory problems.
Integer Optimisation provides a general method of solving problems with logical or integrality constraints. Solution methods include Branch-and-Bound and Gomory Cuts. Much emphasis will be placed on how to express various types of restrictions that may appear in optimisation problems (like logical conditions) can be expressed using integer variables.
Game Theory is concerned with mathematical modelling of behaviour and optimal decision making in competitive strategic situations in which the success of strategic choices of one individual (person, company, server, ...) depends on the choices of other (intelligent) "players" that each have their own (possibly conflicting) agenda.
Note that Dynamic Optimisation and Integer Optimisation were historically called "Dynamic Programming" and "Integer Programming" respectively (the term "programming" in these words did not mean "computer programming" but rather decision making).
Multistage decision processes; principle of optimality. Applications: network problems; inventory problem; resource allocation problem; knapsack problem; stochastic problems.
Modelling: set-up costs, batch production, limited number of production methods. Logical constraints; set covering problems; systematic conversion of logical expression to IP constraints. Solution techniques: branch and bound; Gomory pure integer cuts.
Optimal strategies in face of uncertainty (minimax and maximin). Two-person zero sum games, dominated strategies, saddle points, non=zero sum games, reaction curves and Nash equilibria.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| Student must not have taken :
MATH09002 Discrete Programming & Game Theory or MATH11089 Dynamic and Integer Programming.
There are no specific pre-requisites, but some previous exposure to optimisation (such as Linear Programming/Simplex algorithm) may be useful.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2023/24, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||Hours & Minutes
|Main Exam Diet S1 (December)||Fundamentals of Operational Research MATH10065||2:00|
On completion of this course, the student will be able to:
- Formulate and solve a sequential decision optimization problem.
- Formulate and solve optimization problems with logical constraints.
- Find optimal and equilibrium strategies for zero and nonzero-sum 2x2 matrix games.
- Master the theory underlying the solution methods.
|Introduction to Operations Research, F. S. Hillier and G. Lieberman, McGraw-Hill Higher Education, 9th edition. ISBN-10: 0071267670|
|Graduate Attributes and Skills
|Course organiser||Dr Sergio Garcia Quiles
Tel: (0131 6)50 5038
|Course secretary||Mrs Alison Fairgrieve
Tel: (0131 6)50 5045