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Master’s in Optimisation under Uncertainty Engineering

Online master's programme of 1,900 hours in optimisation under uncertainty: 12 modules covering uncertainty in decision-making, scenario models, two-stage and multi-stage stochastic programming, chance constraints, robust and distributionally robust optimisation, risk measures, design under uncertainty and learning-based decisions, with an assigned technical tutor.

Duration1900 h
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 sources of uncertainty in a decision problem.

02

Generate and reduce representative scenarios.

03

Formulate two-stage and multi-stage stochastic programming models.

04

Apply robust and distributionally robust optimisation.

05

Incorporate risk measures such as CVaR into optimisation.

06

Combine machine learning and optimisation under uncertainty.

07

Evaluate solutions out of sample in engineering problems.

Profile

Who it's for

  • Stochastic optimisation engineers working on planning under uncertain demand, prices or resources.
  • Risk analysts who need quantitative tools beyond deterministic models.
  • Energy system planners dealing with renewable variability.
  • Decision scientists building robust, data-driven decision models.
  • Supply chain engineers designing resilient networks.
  • Quantitative analysts applying CVaR and robust methods to portfolios.
  • Engineering or science graduates aiming to move into the energy sector.
Standards & tools

What you'll work with

  • ISO 31000 (risk management guidelines)
  • IEC 31010 (risk assessment techniques)
  • JCGM 100:2008 (GUM) (Guide to the Expression of Uncertainty in Measurement)
  • JCGM 101:2008 (propagation of distributions using a Monte Carlo method)
  • ISO 2394 (general principles on reliability for structures)
  • ISO 22301 (business continuity management systems)
  • Gurobi
  • Pyomo
  • JuMP with SDDP.jl
  • RSOME
  • Python with SciPy
Syllabus

12 modules · 1900 h

  1. 1.1Sources of aleatory and epistemic uncertainty
  2. 1.2Probabilistic and set-based representation
  3. 1.3The value of information
  4. 1.4Risk and risk aversion
  5. 1.5VaR and CVaR risk measures
  6. 1.6Here-and-now versus wait-and-see decisions
  7. 1.7The value of the stochastic solution
  8. 1.8Robustness versus optimality
  9. 1.9Typology of approaches under uncertainty
  10. 1.10Case study: uncertainty in a capacity plan
  1. 2.1Distributions and parameter estimation
  2. 2.2Monte Carlo simulation
  3. 2.3Latin hypercube sampling
  4. 2.4Scenario generation
  5. 2.5Multi-stage scenario trees
  6. 2.6Scenario reduction
  7. 2.7Copulas and dependence
  8. 2.8Scenarios from probabilistic forecasts
  9. 2.9Scenario quality
  10. 2.10Lab: demand scenario tree
  1. 3.1Formulation with recourse
  2. 3.2The deterministic extensive form
  3. 3.3The L-shaped decomposition method
  4. 3.4Sample average approximation
  5. 3.5Problems with integer recourse
  6. 3.6Bounds and convergence
  7. 3.7Applications in capacity planning
  8. 3.8Applications in supply chains
  9. 3.9Interpreting solutions
  10. 3.10Practical: facility location with uncertain demand
  1. 4.1Sequential decisions and non-anticipativity
  2. 4.2Stochastic dynamic programming
  3. 4.3SDDP: stochastic dual dynamic programming
  4. 4.4Linear decision rules
  5. 4.5Rolling-horizon planning
  6. 4.6Hydroelectric reservoir management
  7. 4.7Investment planning
  8. 4.8Computational complexity of multi-stage models
  9. 4.9Policies versus plans
  10. 4.10Lab: hydrothermal scheduling with SDDP
  1. 5.1Individual and joint chance constraints
  2. 5.2Convex reformulations of chance constraints
  3. 5.3Scenario-based approximations
  4. 5.4Bernstein and CVaR approximations
  5. 5.5Confidence and reliability levels
  6. 5.6Applications in power grids
  7. 5.7Applications in chemical processes
  8. 5.8Reliability-based design
  9. 5.9Out-of-sample validation
  10. 5.10Workshop: dispatch with chance constraints
  1. 6.1Box, ellipsoidal and polyhedral uncertainty sets
  2. 6.2Tractable robust counterparts
  3. 6.3The Bertsimas-Sim budget of uncertainty
  4. 6.4Adjustable robust optimisation
  5. 6.5Affine decision rules
  6. 6.6Robustness versus conservatism
  7. 6.7Robustness in integer programming
  8. 6.8Data-driven uncertainty sets
  9. 6.9Robust modelling tools
  10. 6.10Practical: robust production plan
  1. 7.1Ambiguity in the distribution
  2. 7.2Moment-based sets
  3. 7.3Wasserstein balls
  4. 7.4Ambiguity sets with phi-divergences
  5. 7.5Tractable dual reformulations of the problem
  6. 7.6Out-of-sample performance guarantees
  7. 7.7Relationship with regularisation
  8. 7.8Applications in portfolios
  9. 7.9Applications in energy
  10. 7.10Lab: robust portfolio with Wasserstein ambiguity
  1. 8.1Coherent risk measures
  2. 8.2Mean-risk optimisation of technical portfolios
  3. 8.3CVaR in linear programming
  4. 8.4Risk in multi-stage problems
  5. 8.5Stochastic dominance constraints
  6. 8.6Risk management according to ISO 31000
  7. 8.7Risk in engineering projects
  8. 8.8Financial risk of investments
  9. 8.9Communicating risk
  10. 8.10Case study: project portfolio with CVaR
  1. 9.1Taguchi robust design
  2. 9.2Reliability-based optimisation
  3. 9.3Uncertainty propagation in models
  4. 9.4Polynomial chaos expansion
  5. 9.5Surrogate models with uncertainty
  6. 9.6Bayesian optimisation with noise
  7. 9.7Tolerance design
  8. 9.8Global sensitivity analysis
  9. 9.9Experimental validation of robust design
  10. 9.10Workshop: reliability-based design of a structure
  1. 10.1Predict-then-optimise
  2. 10.2Decision-focused optimisation
  3. 10.3Multi-armed bandits and exploration
  4. 10.4Robust reinforcement learning
  5. 10.5Optimisation with contextual data
  6. 10.6Uncertainty quantification in predictions
  7. 10.7Conformal prediction for decisions
  8. 10.8Online optimisation
  9. 10.9Assessing the value of models
  10. 10.10Practical: inventory with conformal forecasts
  1. 11.1Power system planning with renewables
  2. 11.2Resilient supply chains
  3. 11.3Water resource management
  4. 11.4Maintenance planning with random failures
  5. 11.5Logistics with uncertain times
  6. 11.6Infrastructure investments
  7. 11.7Chemical processes with uncertain parameters
  8. 11.8Emergency management
  9. 11.9Insurance and reinsurance of technical risks
  10. 11.10Case study: microgrid planning with wind uncertainty
  1. 12.1Selecting the problem with uncertainty
  2. 12.2Characterising the uncertainty
  3. 12.3Deterministic reference formulation
  4. 12.4Stochastic and robust models
  5. 12.5Implementation and solution
  6. 12.6Out-of-sample evaluation
  7. 12.7Risk and robustness analysis
  8. 12.8Conclusions on robustness and risk
  9. 12.9Thesis 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 materials, 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 Gurobi, Pyomo, JuMP with SDDP.jl, RSOME and Python with SciPy, in free, academic or evaluation versions. Real procedures are studied, such as energy planning with renewable scenarios, resilient supply chain design and portfolio optimisation with risk measures. Assessment is continuous by module, plus the final Master's Thesis.

Standards covered: ISO 31000, IEC 31010, JCGM 100:2008 (GUM), JCGM 101:2008, ISO 2394, ISO 22301.

Assigned technical tutor:every module ends with a deliverable that your tutor marks individually.
Standards-based learning:guided reading of ISO 31000, IEC 31010 and JCGM 100:2008 (GUM) applied to real cases, not as a theoretical annex.
Industry software:Gurobi, Pyomo, JuMP with SDDP.jl, RSOME and Python with SciPy, in free, academic or evaluation versions.
Master's Thesis with defence:an optimisation under uncertainty project, from characterising the uncertainty to stochastic and robust models, out-of-sample evaluation and risk analysis, 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.

Characterise the uncertainty
Select the problem and model its sources of uncertainty with scenarios.
Set the deterministic baseline
Formulate and solve the deterministic reference model.
Build stochastic and robust models
Formulate stochastic, robust and chance-constrained versions of the model.
Evaluate out of sample
Compare the solutions out of sample and analyse risk with CVaR.
Master's Thesis
Present the conclusions on robustness and risk, defended before a panel.
Career opportunities

Where this takes you

Stochastic optimisation engineerRisk analystEnergy systems plannerDecision scientistSupply chain engineerQuantitative analyst
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 Gurobi, Pyomo, JuMP with SDDP.jl, RSOME and Python with SciPy, 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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