Undergraduate Course: Fundamentals of Operational Research (MATH10065)
Course Outline
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 
SCQF Credits  10 
ECTS Credits  5 
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. 
Course description 
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 BranchandBound 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).
Dynamic Optimisation
Multistage decision processes; principle of optimality. Applications: network problems; inventory problem; resource allocation problem; knapsack problem; stochastic problems.
Integer Optimisation
Modelling: setup 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.
Game Theory
Optimal strategies in face of uncertainty (minimax and maximin). Twoperson zero sum games, dominated strategies, saddle points, non=zero sum games, reaction curves and Nash equilibria.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  Student must not have taken :
MATH09002 Discrete Programming & Game Theory or MATH11089 Dynamic and Integer Programming.
There are no specific prerequisites, but some previous exposure to optimisation (such as Linear Programming/Simplex algorithm) may be useful.

Information for Visiting Students
Prerequisites  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? 
Yes 
Course Delivery Information

Academic year 2019/20, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   2:00  

Academic year 2019/20, Partyear visiting students only (VV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   2:00  
Learning Outcomes
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 nonzerosum 2x2 matrix games.
 Master the theory underlying the solution methods.

Reading List
Introduction to Operations Research, F. S. Hillier and G. Lieberman, McGrawHill Higher Education, 9th edition. ISBN10: 0071267670 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  FuOR 
Contacts
Course organiser  Dr Andreas Grothey
Tel: (0131 6)50 5747
Email: Andreas.Grothey@ed.ac.uk 
Course secretary  Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk 

