Undergraduate Programme and Module Handbook 2026-2027
Module MATH3141: Operations Research III
Department: Mathematical Sciences
MATH3141: Operations Research III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2026/2027 | Module Cap | Location | Durham |
|---|
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: Role of mathematical models, deterministic and stochastic OR.
- Linear Programming: linear algebraic model; convexity and optimality of extreme points; simplex method; duality and post-optimal analysis.
- Special types of linear programming problems in networks chosen from: Transportation problem; Shortest-path problem (Dijkstra’s algorithm); Maximum flow problem (Ford-Fulkerson algorithm).
- Deterministic dynamic programming: backwards induction; applications to non-linear and integer programming, e.g. knapsack problem.
- Stochastic dynamic programming: optimizing expected total return; optimizing probability of success.
- Markov Decision Processes: optimality equation; optimal policies; policy-improvement algorithms; criterion of discounted costs.
- Further topics chosen from: Reinforcement learning; Inventory theory; Queueing theory; Non-linear 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.
- Demonstrate systematic and coherent understanding of the theoretical mathematics underlying Operations Research.
- Apply a coherent body of mathematical knowledge, skills, and reasoning, including: 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:
- Students will have enhanced mathematical skills in the following areas: modelling, computation
Key Skills:
- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.
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 | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week in Michaelmas and Epiphany | 1 Hour | 40 | |
| Problem Classes | 10 | 4 in Michaelmas and Epiphany; 2 in Easter | 1 Hour | 10 | Yes ■ |
| Preparation and Reading | 150 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 70% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| On Campus Written Examination | 2 Hours | 100% | |
| Component: Summative Assignments | Component Weighting: 30% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Assignment | 100% | ||
Formative Assessment:
Four assignments to be submitted.
■ Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.