## MA50087: Optimisation methods of operational research

[Page last updated: 05 August 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Description: Aims & Learning Objectives:
Aims:
To present methods of optimisation commonly used in OR, to explain their theoretical basis and give an appreciation of the variety of areas in which they are applicable. To facilitate an in-depth understanding of the topic.
Objectives: On completing the course, students should be able to:
* Recognise practical problems where optimisation methods can be used effectively.
* Implement appropriate algorithms, and understand their procedures.
* Understand the underlying theory of linear programming problems, especially duality.
* Demonstrate an in-depth understanding of the topic.

Content:

* The Nature of OR: Brief introduction.
* Linear Programming: Basic solutions and the fundamental theorem. The simplex algorithm, two phase method for an initial solution. Interpretation of the optimal tableau. Applications of LP. Duality.
* Topics selected from: Sensitivity analysis and the dual simplex algorithm. Brief discussion of Karmarkar's method. The transportation problem and its applications, solution by Dantzig's method. Network flow problems, the Ford-Fulkerson theorem.
* Non-linear Programming: Revision of classical Lagrangian methods. Kuhn-Tucker conditions, necessity and sufficiency. Illustration by application to quadratic programming.

Programme availability:

#### MA50087 is Optional on the following programmes:

Department of Mathematical Sciences

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.