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Diploma in Robust and Stochastic Optimization

Online postgraduate diploma of 800 hours in robust and stochastic optimisation. 8 modules covering uncertainty modelling, two-stage and multi-stage stochastic programming, chance constraints and CVaR, robust and distributionally robust optimisation and out-of-sample evaluation in line with ISO 31000:2018, IEC 31010:2019 and JCGM 101:2008, with an assigned technical tutor.

Duration6–8 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

Quantify the impact of uncertainty on decisions.

02

Formulate and solve two-stage stochastic problems.

03

Apply multi-stage methods such as SDDP and Progressive Hedging.

04

Incorporate chance constraints and risk measures.

05

Build robust counterparts with uncertainty sets.

06

Apply data-driven distributionally robust optimisation.

07

Evaluate and communicate solutions under uncertainty.

Profile

Who it's for

  • Operations research engineers.
  • Quantitative risk analysts.
  • Energy system planners facing uncertain demand, prices and inflows.
  • Decision scientists.
  • Supply chain engineers.
  • Optimisation researchers.
  • Engineering or science graduates seeking to enter the energy sector.
Standards & tools

What you'll work with

  • ISO 31000:2018 (Risk management)
  • IEC 31010:2019 (Risk assessment techniques)
  • JCGM 101:2008 (Propagation of distributions using a Monte Carlo method)
  • ISO 22301:2019 (Business continuity)
  • SMPS format (Stochastic MPS)
  • Pyomo with mpi-sppy
  • JuMP with SDDP.jl
  • RSOME
  • Gurobi
  • Python with SciPy
Syllabus

8 modules

  1. 1.1Sources of uncertainty in engineering
  2. 1.2The cost of ignoring uncertainty
  3. 1.3Value of the stochastic solution (VSS)
  4. 1.4Expected value of perfect information (EVPI)
  5. 1.5Representation with distributions and sets
  6. 1.6Here-and-now and recourse decisions
  7. 1.7Approaches: stochastic, robust and distributionally robust
  8. 1.8Risk measures: VaR and CVaR
  9. 1.9Choosing the approach
  10. 1.10Workshop: calculating VSS and EVPI in a simple problem
  1. 2.1Formulation with recourse
  2. 2.2Deterministic extensive form
  3. 2.3Complete and relatively complete recourse
  4. 2.4Van Slyke and Wets L-shaped decomposition
  5. 2.5Multi-cut Benders variant
  6. 2.6Sample average approximation (SAA)
  7. 2.7Statistical validation of solutions
  8. 2.8Modelling with Pyomo and mpi-sppy
  9. 2.9Applications in capacity and production
  10. 2.10Practical exercise: two-stage capacity sizing
  1. 3.1Scenario trees
  2. 3.2Non-anticipativity constraints
  3. 3.3Scenario generation and reduction
  4. 3.4Stochastic dual dynamic programming (SDDP)
  5. 3.5Rockafellar and Wets Progressive Hedging algorithm
  6. 3.6Policies versus plans
  7. 3.7Hydrothermal planning as a classic case
  8. 3.8Computational cost of trees
  9. 3.9Comparison with periodic reoptimisation
  10. 3.10Lab: SDDP for reservoir management
  1. 4.1Individual and joint chance constraints
  2. 4.2Conservative convex approximations
  3. 4.3CVaR formulation in linear programming
  4. 4.4Mean-risk optimisation with scenarios
  5. 4.5Stochastic dominance constraints
  6. 4.6Scenario approximation
  7. 4.7Calibrating the risk level
  8. 4.8Interpretation for management
  9. 4.9Applications in supply and energy
  10. 4.10Practical exercise: planning with a CVaR constraint
  1. 5.1Uncertainty sets: box, ellipsoid and polyhedron
  2. 5.2Tractable robust counterpart
  3. 5.3Bertsimas-Sim uncertainty budget
  4. 5.4Adjustable robustness and linear decision rules
  5. 5.5Two-stage robust optimisation
  6. 5.6The price of robustness
  7. 5.7Data-driven uncertainty sets
  8. 5.8Tools: RSOME and modelling in JuMP
  9. 5.9Comparison with the stochastic approach
  10. 5.10Lab: robust scheduling with an uncertainty budget
  1. 6.1Ambiguity sets
  2. 6.2Wasserstein balls
  3. 6.3Moment-based ambiguity
  4. 6.4Tractable reformulations as conic programs
  5. 6.5Out-of-sample guarantees
  6. 6.6Relationship with regularisation
  7. 6.7Data-driven optimisation
  8. 6.8Predict-then-optimise versus integrated approaches
  9. 6.9Industrial applications of distributional robustness
  10. 6.10Case study: inventory with Wasserstein ambiguity
  1. 7.1Out-of-sample simulation
  2. 7.2Performance and risk metrics
  3. 7.3Parameter sensitivity analysis
  4. 7.4Communicating robust solutions
  5. 7.5Integration into planning processes
  6. 7.6Computational scaling of large models
  7. 7.7Cases in energy, logistics and production
  8. 7.8Common modelling errors
  9. 7.9Final choice of approach
  10. 7.10Workshop: comparative evaluation of approaches
  1. 8.1Problem and sources of uncertainty
  2. 8.2Deterministic reference model
  3. 8.3Two-stage stochastic model
  4. 8.4Robust model with uncertainty budget
  5. 8.5Out-of-sample evaluation
  6. 8.6Risk analysis with CVaR
  7. 8.7Recommendation for management
  8. 8.8Technical conclusions and limitations
  9. 8.9Report and presentation
  10. 8.10Final project: final review with the tutor
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 is compatible with work.

Each module combines theory, guided reading of the original standard and applied exercises. The working software is Pyomo with mpi-sppy, JuMP with SDDP.jl, RSOME, Gurobi and Python with SciPy, in free, academic or evaluation versions. Practical work is based on real procedures for out-of-sample evaluation of robust and stochastic solutions, generation and reduction of scenario trees and analysis of the price of robustness. Assessment is continuous by module plus the final project.

Standards covered: ISO 31000:2018, IEC 31010:2019, JCGM 101:2008, ISO 22301:2019, SMPS format.

Assigned technical tutor:every module ends with a deliverable that your tutor marks individually.
Standards-based learning:guided reading of ISO 31000:2018, IEC 31010:2019 and JCGM 101:2008 applied to real cases, not as a theoretical annex.
Industry software:Pyomo with mpi-sppy, JuMP with SDDP.jl, RSOME, Gurobi and Python with SciPy, in free, academic or evaluation versions.
Final project:an optimisation under uncertainty study of a real problem, comparing deterministic, stochastic and robust models with CVaR risk analysis and a recommendation for management, reviewed by your tutor.
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.

Problem and uncertainty
Define the decision problem, its sources of uncertainty and a deterministic reference model.
Two-stage stochastic model
Formulate and solve the stochastic model with recourse using SAA and mpi-sppy.
Robust model
Build a robust counterpart with a Bertsimas-Sim uncertainty budget.
Out-of-sample and risk
Evaluate all models out of sample and analyse risk with CVaR.
Final project
Present a recommendation for management with technical conclusions and limitations, reviewed by your tutor.
Career opportunities

Where this takes you

Operations research engineerQuantitative risk analystEnergy system plannerDecision scientistSupply chain engineerOptimisation researcher
Admissions & scholarships

Requirements

  • Prior technical training or professional experience in the sector. No university degree is required.
  • 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 800 hours over 6–8 months. You set your own pace within each intake, and your tutor helps you plan the workload around your job.

You work with Pyomo with mpi-sppy, JuMP with SDDP.jl, RSOME, Gurobi 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 final project. 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 are recognised in a higher programme in the same area (postgraduate diploma or master's). Ask about the recognition policy when you enrol.

Prior technical training or professional experience in the sector (no university degree required), a computer able to run the programme 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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