D'Math University | Computing & Interdisciplinary Mathematics

MSc Optimisation & Operations Research

Mathematical decision-making at scale — linear programming, integer optimisation, game theory, stochastic programming, and metaheuristics — applied to the logistical, economic, and engineering challenges that shape modern organisations.

Postgraduate 1 Year Applied Decision Science
10
Taught Modules
£65k
Avg Graduate Salary
40+
Industry Partners
Capstone
Industry Project

Programme Overview

What You Will Study

Operations Research is mathematics applied to the optimal allocation of scarce resources — from airline scheduling and hospital capacity planning to portfolio optimisation and supply chain design. This programme builds the full toolkit from theory to implementation.

  • Deterministic Optimisation: linear, integer, combinatorial, and network programming
  • Stochastic Methods: stochastic programming, simulation, queuing theory
  • Advanced Topics: multi-objective optimisation, robust optimisation, game theory
  • Industry Capstone: a real-world OR project with an industry partner organisation

Programme Highlights

OR graduates are among the most in-demand quantitative professionals in the world — sought by logistics giants, airlines, consultancies, financial firms, and technology companies to improve operations and drive strategic decisions.

  • Industry Capstone: a live project with one of 40+ partner organisations
  • Software Suite: Gurobi, CPLEX, Python (PuLP, SciPy), Julia (JuMP) throughout
  • Broad Application: modules span supply chain, revenue management, healthcare, and finance
  • PhD Pathway: strong preparation for doctoral study in mathematical optimisation or OR
Course Catalogue

Click any course to view its objective and learning outcomes.

OPT 501 Linear & Integer Programming +

Objective

To master modern LP and IP solution methods.

Learning Outcomes

  • Apply simplex and revised simplex.
  • Use branch-and-cut.
  • Apply Lagrangian relaxation.
  • Use column generation.
  • Solve large MIPs.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
Interactive Activity — Simplex Method on 2D LP
A small 2-variable LP is shown with its feasible polygon. Press Step to walk along vertices increasing the objective. Highlights the current vertex.
OPT 502 Convex Optimisation +

Objective

To solve convex problems efficiently and analyse their structure.

Learning Outcomes

  • Apply convex analysis.
  • Use interior-point methods.
  • Apply duality and KKT conditions.
  • Solve SDPs and SOCPs.
  • Use CVX or similar tools.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
Interactive Activity — Gradient Descent on a 2D Loss Surface
Click anywhere on the surface to drop a starting point. Animation traces the descent path on the chosen loss function. Adjust the learning rate to see how step size affects convergence.
Loss: η = 0.10
Click on the loss surface to drop a starting point.
OPT 503 Nonlinear Optimisation +

Objective

To solve nonlinear optimisation problems globally and locally.

Learning Outcomes

  • Apply gradient and Newton methods.
  • Use SQP and interior-point methods.
  • Apply trust-region methods.
  • Solve nonconvex problems.
  • Use global optimisation methods.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
OPT 504 Stochastic Optimisation +

Objective

To optimise under uncertainty.

Learning Outcomes

  • Apply two-stage stochastic programs.
  • Use scenario generation.
  • Apply chance-constrained programming.
  • Use robust optimisation.
  • Apply stochastic gradient methods.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
OPT 505 Combinatorial Optimisation +

Objective

To solve discrete optimisation problems.

Learning Outcomes

  • Apply graph algorithms.
  • Use matroid theory.
  • Apply approximation algorithms.
  • Use heuristics and metaheuristics.
  • Solve TSP and scheduling.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
OPT 506 Network Optimisation +

Objective

To model and solve network problems.

Learning Outcomes

  • Apply shortest path algorithms.
  • Use max flow / min cut.
  • Apply minimum cost flow.
  • Use assignment algorithms.
  • Solve facility location.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
OPT 507 Optimal Control +

Objective

To find optimal trajectories for dynamical systems.

Learning Outcomes

  • Apply Pontryagin's minimum principle.
  • Use dynamic programming.
  • Apply Hamilton-Jacobi-Bellman.
  • Use linear-quadratic control.
  • Apply model predictive control.
OPT 508 Operations Research Applications +

Objective

To apply OR to industry problems.

Learning Outcomes

  • Apply OR to supply chain.
  • Use OR in healthcare.
  • Apply OR to energy systems.
  • Use OR in transportation.
  • Apply OR to finance.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
OPT 509 Simulation Optimisation +

Objective

To optimise systems described by simulations.

Learning Outcomes

  • Apply ranking and selection.
  • Use response surface methodology.
  • Apply metamodelling.
  • Use stochastic approximation.
  • Apply Bayesian optimisation.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
OPT 510 Algorithmic Game Theory +

Objective

To compute equilibria and design mechanisms.

Learning Outcomes

  • Compute Nash equilibria.
  • Apply correlated equilibria.
  • Use mechanism design.
  • Apply auction theory.
  • Discuss algorithmic mechanism design.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
OPT 511 OR Software +

Objective

To use industrial OR software effectively.

Learning Outcomes

  • Use AMPL/GAMS modelling.
  • Apply Gurobi or CPLEX.
  • Build OR pipelines in Python.
  • Use distributed solvers.
  • Document models for stakeholders.
OPT 512 Master's Project +

Objective

To complete an original optimisation research project.

Learning Outcomes

  • Identify a real optimisation problem.
  • Apply rigorous methods.
  • Implement large-scale solvers.
  • Write a research-quality dissertation.
  • Present to OR practitioners.

Core Modules

🔢

Linear & Convex Optimisation

Simplex method, interior point methods, duality theory, KKT conditions, and convex programming fundamentals.

📈

Integer & Combinatorial Optimisation

Branch and bound, cutting planes, Gomory cuts, travelling salesman problem, and integer programming applications.

🧮

Stochastic Programming

Two-stage recourse models, chance constraints, sample average approximation, and scenario-based decision making.

💻

Metaheuristics

Genetic algorithms, simulated annealing, ant colony optimisation, particle swarm, and hyper-heuristic frameworks.

📐

Game Theory & Mechanism Design

Nash equilibria, cooperative games, auction theory, mechanism design, and applications in economics and networks.

🌐

Network Flows & Logistics

Maximum flow, minimum cost flow, shortest path algorithms, and vehicle routing and scheduling problems.

📊

Multi-Objective Optimisation

Pareto optimality, scalarisation, evolutionary multi-objective algorithms, and decision support for conflicting objectives.

🔬

Robust Optimisation

Uncertainty sets, robust counterparts, min-max formulations, and applications in supply chain and portfolio management.

🌍

Dynamic Programming

Bellman equations, value iteration, policy iteration, Markov decision processes, and reinforcement learning connections.

🏗️

Applied OR Project

An industry-partnered capstone project applying OR methodology to a real-world optimisation or logistics challenge.

Career Outcomes

📊

Operations Research Analyst

Apply mathematical modelling and optimisation to improve decision-making in airlines, logistics, healthcare, and defence.

🌐

Supply Chain Optimiser

Design and optimise global supply chains, warehouse networks, and distribution systems for major corporations.

📈

Management Consultant

Deliver data-driven strategic recommendations using OR methods for clients in finance, retail, and public sector.

🔢

Logistics Engineer

Optimise routing, scheduling, and capacity planning for transport networks, last-mile delivery, and aviation operations.

💻

Revenue Management Analyst

Maximise revenue through dynamic pricing, capacity allocation, and demand forecasting in airlines, hotels, and e-commerce.

🤖

Data Scientist

Build optimisation-driven machine learning pipelines and decision support systems across a broad range of industries.

Where Our Graduates Go & Top Global Universities

MIT Georgia Tech Carnegie Mellon Cornell Imperial College London University of Southampton NUS Singapore TU Eindhoven University of Waterloo Ghent University

Why D'Math University — Our 4-Step Approach

01

Mathematical Modelling

Students learn to translate messy real-world problems into precise mathematical programmes — the foundational skill of every OR practitioner.

02

Solver Proficiency

Hands-on labs with industrial solver software (Gurobi, CPLEX, JuMP) build the technical implementation skills employers require.

03

Breadth of Application

Case studies span healthcare, aviation, energy, finance, and logistics — ensuring graduates can apply OR across diverse sectors.

04

Industry Capstone

The year culminates in a real-world project with a partner organisation, delivering measurable impact and employment-ready evidence.

Enrol in MSc Optimisation & Operations →

Applications open year-round — optimise the decisions that drive the world's most complex systems.