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Master’s in Optimisation under Uncertainty

Online master's programme of 1,900 hours in optimisation under uncertainty: robust and stochastic optimisation, scenarios and trade-offs. 12 modules covering stochastic programming, robust optimisation, chance constraints and risk, reliability-based design, Bayesian optimisation and sequential decision-making, with ISO 31000, ISO 2394 and the GUM, and an assigned technical tutor.

Duration12–14 months
ModeOnline
LanguageEnglish
Start datesSet by the faculty
AwardSEIUM Institute diploma
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Learning outcomes

What you will be able to do

01

Characterise the uncertainty present in engineering decision problems.

02

Formulate linear, integer and nonlinear optimisation models.

03

Apply two-stage and multi-stage stochastic programming.

04

Design solutions that are robust against uncertainty sets.

05

Incorporate risk measures and chance constraints.

06

Optimise expensive-to-evaluate systems using Bayesian methods.

07

Solve real cases in energy, logistics and design under uncertainty.

Profile

Who it's for

  • Optimisation engineers who need their models to hold up when data and demand are uncertain.
  • Operations researchers moving from deterministic models to stochastic and robust formulations.
  • Quantitative risk analysts looking to embed risk measures directly into decisions.
  • Energy planners working on dispatch, storage and grid expansion with renewables.
  • Supply chain engineers designing resilient networks and inventory policies.
  • Decision scientists who combine forecasting, simulation and optimisation.
  • Engineering or science graduates looking to enter the energy sector.
Standards & tools

What you'll work with

  • ISO 31000 (risk management — guidelines)
  • ISO 2394 (general principles on reliability for structures)
  • ISO/IEC Guide 98-3 (GUM — guide to the expression of uncertainty in measurement)
  • JCGM 101 (propagation of distributions using the Monte Carlo method)
  • EN 1990 (Eurocode 0 — basis of structural design)
  • ISO 22301 (business continuity management)
  • Pyomo
  • Gurobi
  • CPLEX
  • BoTorch
  • MATLAB Optimization Toolbox
Syllabus

12 modules

  1. 1.1Aleatory and epistemic uncertainty
  2. 1.2Variability in loads, materials and demand
  3. 1.3Probability and basic inference
  4. 1.4Common distributions in engineering
  5. 1.5Scenarios and decision trees
  6. 1.6Expected value and risk aversion
  7. 1.7Value of information
  8. 1.8Examples in energy, logistics and design
  9. 1.9Errors of deterministic decision-making
  10. 1.10Case study: impact of uncertainty on a design
  1. 2.1Linear programming and duality
  2. 2.2Mixed-integer programming
  3. 2.3Nonlinear optimisation and KKT conditions
  4. 2.4Convexity and why it matters
  5. 2.5Gradient methods
  6. 2.6Commercial and open-source solvers
  7. 2.7Algebraic modelling with Pyomo
  8. 2.8Sensitivity and parametric analysis
  9. 2.9Scaling and efficient formulation
  10. 2.10Lab: planning model in Pyomo
  1. 3.1Two-stage models with recourse
  2. 3.2Value of the stochastic solution
  3. 3.3Multi-stage programming
  4. 3.4Scenario trees
  5. 3.5Benders decomposition
  6. 3.6L-shaped method and progressive hedging
  7. 3.7Sample average approximation
  8. 3.8Scenario reduction
  9. 3.9Implementation in mpi-sppy
  10. 3.10Practical exercise: capacity expansion under uncertain demand
  1. 4.1Uncertainty sets
  2. 4.2Soyster and Bertsimas-Sim robustness
  3. 4.3Tractable robust counterpart
  4. 4.4Adjustable robust optimisation
  5. 4.5Affine decision rules
  6. 4.6Price of robustness
  7. 4.7Distributional robustness
  8. 4.8Data-driven uncertainty sets
  9. 4.9Comparison with stochastic approaches
  10. 4.10Lab: robust logistics network
  1. 5.1Individual and joint chance constraints
  2. 5.2Convex approximations
  3. 5.3Value at Risk and CVaR
  4. 5.4Optimisation with risk measures
  5. 5.5Stochastic dominance
  6. 5.6Reliability constraints
  7. 5.7Scenarios and sampling
  8. 5.8Calibrating the risk level
  9. 5.9Interpretation for management
  10. 5.10Practical exercise: energy dispatch with CVaR
  1. 6.1Taguchi design
  2. 6.2Reliability-based design optimisation (RBDO)
  3. 6.3FORM and SORM methods
  4. 6.4Monte Carlo uncertainty propagation
  5. 6.5Polynomial chaos
  6. 6.6Surrogate models in optimisation
  7. 6.7Multi-objective optimisation under uncertainty
  8. 6.8Manufacturing tolerances and variability
  9. 6.9Validating the robust design
  10. 6.10Case study: robust design of a structural component
  1. 7.1Problems with expensive simulation
  2. 7.2Gaussian processes
  3. 7.3Acquisition functions
  4. 7.4Constrained Bayesian optimisation
  5. 7.5Evolutionary algorithms and NSGA-II
  6. 7.6Optimisation with noise
  7. 7.7Parallelising evaluations
  8. 7.8BoTorch and Optuna tools
  9. 7.9Stopping criteria
  10. 7.10Lab: tuning a process with Bayesian optimisation
  1. 8.1Markov decision processes
  2. 8.2Stochastic dynamic programming
  3. 8.3SDDP for hydrothermal planning
  4. 8.4Stochastic model predictive control
  5. 8.5Reinforcement learning as optimisation
  6. 8.6Approximate policies
  7. 8.7Inventory problems
  8. 8.8Maintenance under uncertainty
  9. 8.9Policy evaluation through simulation
  10. 8.10Practical exercise: multi-period inventory policy
  1. 9.1Unit commitment with renewables
  2. 9.2Bidding in electricity markets
  3. 9.3Grid expansion planning
  4. 9.4Storage management
  5. 9.5Microgrids and self-consumption
  6. 9.6Demand-side management
  7. 9.7Probabilistic forecast data
  8. 9.8Implementation with industrial solvers
  9. 9.9Interpreting results
  10. 9.10Case study: operating a hybrid plant with batteries
  1. 10.1Robust supply chain design
  2. 10.2Production planning
  3. 10.3Vehicle routing with uncertain travel times
  4. 10.4Capacity management
  5. 10.5Project planning under risk
  6. 10.6Multi-echelon inventory management
  7. 10.7Disruptions and resilience
  8. 10.8Integration with ERP and APS
  9. 10.9Communicating results
  10. 10.10Workshop: resilient distribution network
  1. 11.1Probabilistic forecasting
  2. 11.2Predict-then-optimise
  3. 11.3Contextual optimisation
  4. 11.4Learning uncertainty sets
  5. 11.5End-to-end optimisation
  6. 11.6Out-of-sample validation
  7. 11.7Optimiser's bias
  8. 11.8Integrated software tools
  9. 11.9Governance of decision models
  10. 11.10Practical exercise: decision driven by demand forecasting
  1. 12.1Defining the decision problem
  2. 12.2Characterising the uncertainty
  3. 12.3Formulating the model
  4. 12.4Choosing a stochastic or robust approach
  5. 12.5Implementation and solution
  6. 12.6Validation through simulation
  7. 12.7Sensitivity and risk analysis
  8. 12.8Decision recommendations
  9. 12.9Written thesis report
  10. 12.10Master's Thesis: defence before a panel
Methodology, software & labs

How you'll learn

100% online training on the SEIUM campus, with downloadable material, recorded classes and an assigned technical tutor. There are no fixed timetables: you progress at your own pace within each intake, so the programme fits around your job.

Each module combines theory, guided reading of the original standard and applied exercises. The working software is Pyomo, Gurobi, CPLEX, BoTorch and MATLAB Optimization Toolbox, in free, academic or evaluation versions. Testing is studied through real procedures: Monte Carlo simulation of optimal solutions, out-of-sample evaluation with historical data and scenario sensitivity analysis. Assessment is continuous for each module, plus the final Master's Thesis.

Standards covered: ISO 31000, ISO 2394, ISO/IEC Guide 98-3 (GUM), JCGM 101 (Monte Carlo), EN 1990 (Eurocode 0), ISO 22301.

Assigned technical tutor:every module ends with a deliverable that your tutor marks individually.
Standards-based learning:guided reading of ISO 31000, ISO 2394 and ISO/IEC Guide 98-3 (GUM) applied to real cases, not as a theoretical annex.
Industry software:Pyomo, Gurobi, CPLEX, BoTorch and MATLAB Optimization Toolbox, in free, academic or evaluation versions.
Master's Thesis with defence:A real engineering decision problem modelled and solved under uncertainty, from characterising the uncertainty to risk-informed recommendations, defended before a panel.
Flexible format:100% online, no fixed timetables, compatible with full-time work.
Capstone project

Build it end to end

Your final project follows the real engineering workflow, step by step, reviewed by your tutor.

Planning model in Pyomo
Formulate and solve a deterministic planning model as the baseline for the project.
Stochastic capacity expansion
Extend the model to a two-stage stochastic programme under uncertain demand.
Robust network design
Design a robust logistics network and quantify the price of robustness.
Risk-aware dispatch
Optimise energy dispatch with CVaR and calibrate the acceptable risk level.
Master's Thesis
A real decision problem solved under uncertainty and validated through simulation, defended before a panel.
Career opportunities

Where this takes you

Optimisation engineerOperations researcherQuantitative risk analystEnergy plannerSupply chain engineerDecision scientist
Admissions & scholarships

Requirements

  • University degree in engineering, science or architecture, or equivalent demonstrable professional experience.
  • Internet connection and a computer capable of running the programme software.
  • English sufficient to read technical standards.

Ready to start?

Send your application today. Our admissions team replies within 72 hours with your study plan and funding options.

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FAQ

Frequently asked questions

The programme totals 1,900 hours over 12–14 months. You set your own pace within each intake, and your tutor helps you plan the workload around your job.

You work with Pyomo, Gurobi, CPLEX, BoTorch and MATLAB Optimization Toolbox, using free, academic or evaluation versions. Your tutor indicates the free alternative wherever one exists.

A SEIUM Institute diploma, awarded on passing the continuous assessment and the Master's Thesis. It is SEIUM's own qualification, not an official state degree; its recognition depends on the programme completed and the regulations of each country.

Yes. Modules passed in a course or postgraduate diploma in the same area are recognised in the higher programme. Ask about the recognition policy when you enrol.

A university degree in engineering, science or architecture (or equivalent professional experience), a computer able to run the software, and English sufficient to read technical standards.

Start dates are set by SEIUM's faculty for each intake. Our admissions team will confirm the next available date when you apply.

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