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MATH3141: OPERATIONS RESEARCH III

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

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 Combinations of Modules

  • None.

Aims

  • To introduce some of the central mathematical models and methods ofoperations 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 theapplication of the theory to practical examples.
  • Assignments for self-study develop problem-solving skills andenable students to test and develop their knowledge andunderstanding.
  • Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week in Michaelmas and Epiphany; 2 in Easter1 Hour42 
Problems Classes8Fortnightly in Michaelmas and Epiphany1 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

Formative Assessment

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

More information

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