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Durham University

Postgraduate Module Handbook 2021/2022

Archive Module Description

This page is for the academic year 2021-22. The current handbook year is 2022-23

Department: Mathematical Sciences

MATH30820: Operations Research

Type Tied Level 3 Credits 20 Availability Available in 2021/22
Tied to G1K509 Mathematical Sciences

Prerequisites

  • Probability and Linear Algebra

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: 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.

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.
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 42 2 per week for 20 weeks and 2 in term 3 1 Hour 42
Problems Classes 8 Four in each of terms 1 and 2 1 Hour 8
Preperation 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 written or electronic 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