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Robust Optimization is an uncertainty modeling approach suitable for a situation where the range of the uncertainty is known and not necessarily the distribution (depending on the industry, this could be price, temperature, demand, etc). Typically some inputs take an uncertain value anywhere between a fixed minimum and a maximum. Solutions will be feasible for all the constraints when the inputs drift within the uncertainty ranges. If this is too strict, one can even provide a probability for which the solution is required to satisfy specific constraints (e.g. the chance that the demand for electricity will be met is at least 95%).The robustness of your decisions is measured in terms of the best performance against all possible realizations of the parameters values.
Robust Optimization is very suitable for many problems as only simple inputs are required from the user about the data uncertainty (no scenarios or distribution functions need to be defined). Where Stochastic Programming can result in large models when considering many scenarios (making it important to limit the number of considered scenarios, but therefore also making the results less robust), Robust Optimization models grow only slightly when uncertainty is added, and therefore can be solved efficiently.
Robust Optimization in AIMMS
AIMMS offers support for generating a robust optimization model from any given deterministic LP/MIP model, without the need to reformulate any of the constraint definitions. By only supplying additional attributes for selected parameters, variables and constraints, AIMMS can generate both a deterministic and a robust model from the same formulation. A deterministic model, a stochastic model and a robust optimization model can again co-exist within the same master model and their respective solutions can be compared.
AIMMS has a partnership with Technion and is working with 
Professor A. Ben-Tal, who developed the Robust Optimization Methodology with Professor A. Nemirovski, to assure AIMMS users can apply Robust Optimization to their models successfully.
Additional Information:
- “Robust Optimization” - AIMMS Language Reference (3.11 FR1, Chapter 20).
- Example “Power System Expansion RO”, “Chance Constraints” - AIMMS Installation.
- Section operations-research/mathematical-programming/robust-optimization.
- http://en.wikipedia.org/wiki/Robust_optimization.
- "Robust Convex Optimization", Aharon Ben-Tal and Arkadi Nemirovski, Mathematics of Operations Research, 23, (1998),769-805.
- “Supplier-Retailer Flexible Commitments Contracts: A Robust Optimization Approach”, Aharon Ben Tal, Boaz Golany, Arkadi Nemirovski, Jean-Philippe Vial, Manufacturing & Service Operations Management, 7. (2003),248-271.
- "Robust Multi Echelon Multi Period Inventory Control”, Aharon Ben-Tal, Boaz Golany, Shimrit Shtern European J. on operations Research,199. (2009), 922-935.).
- “Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty”, Dimtris Bertsimas, Aurelie Thiele Tutorials on Operations Research. INFORMS,Chapter 4, (2006), 122-195.
- “Robust Optimization”, Aharon Ben-Tal, Laurent El Ghaoui & Arkadi Nemirovski (Princeton Series in Applied Mathematics, 2009), Princeton University Press, Princeton and Oxford, (2009).
Examples
Other ways of modeling uncertainty:
- Uncertainty modeling (overview)
- Scenario Analysis
- Stochastic Programming
- Robust Optimization
