Undergraduate Programme and Module Handbook 2017-2018 (archived)

# Module MATH4251: OPERATIONS RESEARCH IV

## Department: Mathematical Sciences

### MATH4251: OPERATIONS RESEARCH IV

Type | Open | Level | 4 | Credits | 20 | Availability | Not available in 2017/18 | Module Cap | Location | Durham |
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#### Prerequisites

- Core Mathematics A (MATH 1012) AND a minimum of 40 credits of Mathematics modules at Level 3.

#### Corequisites

- None.

#### Excluded Combination of Modules

- Operations Research III (MATH3141)

#### Aims

- To introduce some of the central mathematical models and methods of operations research.

#### Content

- Introduction to Operations Research.
- Linear programming: primal/dual simplex algorithm, sensitivity analysis, transportation algorithm.
- Optimisation on networks.
- Introduction to Markov chains.
- Inventory theory.
- Markov decision processes.
- Further topics chosen from: integer programming, iterative non linear programming, dynamic programming.
- Reading material on a topic related to: integer programming, queueing theory.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve novel and/or complex problems in Operations Research.
- have a systematic and coherent understanding of theoretical mathematics in the fields Operations Research.
- have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Linear programming and the simplex algorithm.
- Duality and sensitivity analysis for L.P.
- Optimisation on network models.
- Brief treatment of finite state Markov chains.
- Deterministic and probabilistic dynamic programming.
- Markov decision processes, including policy-improvement algorithms.
- Inventory Theorem.
- Knowledge and understanding of a topic in the following areas: integer programming, queueing theory.

Subject-specific Skills:

- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling, Computation.

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 40 | 2 per week for 19 weeks and 2 in term 3 | 1 Hour | 40 | |

Preparation and Reading | 160 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

three hour written examination | 100% |

#### Formative Assessment:

Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University