Undergraduate Programme and Module Handbook 2024-2025

# Module MATH3141: OPERATIONS RESEARCH III

## Department: Mathematical Sciences

### MATH3141: OPERATIONS RESEARCH III

Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) AND Probability I (MATH1597) AND Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071).

#### Corequisites

- None.

#### Excluded Combination of Modules

- None.

#### Aims

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

#### Content

- Introduction to Operations Research.
- Linear programming: simplex algorithm, duality, post-optimal analysis.
- Deterministic and stochasitc dynamic programming.
- Optimisation in Markov chains and Markov decision processes.
- Further topics chosen from: intenetwork optimisation problems (transportation problem, shortest path problem, maximal flow problem, etc.), reinforcement learning, inventory theory.

#### Learning Outcomes

Subject-specific Knowledge:

- Ability to solve novel and/or complex problems in Operations Research.
- Systematic and coherent understanding of the theoretical mathematics underlying Operations Research.
- A coherent body of knowledge, demonstrated through one or more of the following topic areas: linear programming and the simplex algorithm; duality and post-optimal analysis; optimisation on network models; deterministic and stochastic dynamic programming; Markov decision processes, including policy-improvement algorithms.

Subject-specific Skills:

- Specialised mathematical skills which can be used with minimal guidance in the following areas: 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 | 42 | 2 per week in Michaelmas and Epiphany; 2 in Easter | 1 Hour | 42 | |

Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

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

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

Written examination | 3 Hours | 100% |

#### Formative Assessment:

Eight assignments to be submitted.

■ 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