KAYA - Robust & Stochastic Optimization

Question 1

What makes Robust Optimization unique?

Answer 1

1. Worst-Case Feasibility: Uniquely ensures feasibility of constraints under the worst possible scenario (all scenarios) of uncertainty in a defined uncertainty set .
2. Static Solution: Produces a single, non-adaptive solution, meaning decisions don’t change based on how uncertainty actually unfolds.

Question 2

What makes Chance Constrained Programming unique?

Answer 2

1. Probabilistic Constraints: Uniquely incorporates constraints that must hold with a specified minimum probability, allowing for controlled violations.
2. Risk Tolerance: Explicitly includes a decision-maker’s risk tolerance (the acceptable violation probability) within the model, enabling flexible trade-offs between performance and reliability.

Question 3

What makes Stochastic Optimization with Recourse unique?

Answer 3

1. Multi-Stage Decisions: Uniquely models decisions in sequential stages, with the ability to adjust decisions as uncertainty is revealed.
2. Recourse Actions: Uniquely features recourse actions (adaptive responses) – corrective measures that mitigate the impact of specific outcomes of uncertainty – providing flexibility and robustness over time.

Question 4

What type of modeling method for MIN-Problem? min -2x1+2x2

Answer 4

• CCM directly addresses the requirement to allow violations with probability by reformulating the constraint. It leverages the discrete distribution convert this into a deterministic constraint based, making the problem tractable.
• Why Not RO: Too conservative, enforcing the constraint for the worst-case, which doesn’t align with allowing violations with probability.
• Why Not SOR: SOR focuses on handling violations via penalties in a two-stage framework, but this problem specifies a violation probability, not a penalty, making CCM a better fit.

Question 5

What type of modeling method for MAX-Problem: max -2x1+2x2

Answer 5

• SOR: allows to model the uncertainty using its discrete distribution, make first-stage decisions and handle violations in the second stage with a penalty. It aligns with the problem’s structure of allowing violations at a cost.
• Why Not RO: RO is too conservative, enforcing strict feasibility for the worst case and ignoring the penalty mechanism and distribution.
• Why Not CCM: CCM focuses on probabilistic constraint satisfaction, not on incorporating a penalty for violations, making it less suitable for optimizing with a loss function.

Question 6

Calculate EV

Answer 6

SUM(outcome*probablity)

Question 7

Calculate EVPI

Answer 7

WS = probablity * z-value of scenario
RP = read z*5
max-Problem EVPI = WS - RP
min-Problem EVPI = RP - WS