Revenue Management (yield management) optimizes pricing and capacity allocation to maximize revenue from perishable inventory. Core problem: dynamically set prices or allocate capacity to different customer segments with varying willingness-to-pay and booking patterns. Techniques: (1) nested protection levels - reserve capacity for high-value segments; (2) bid-price control - accept bookings exceeding opportunity cost; (3) dynamic pricing - adjust prices based on remaining capacity and time. OR models: stochastic dynamic programming, network revenue management (multiple legs), and forecasting integration. Applications pioneered in airlines, now ubiquitous in: hotels, car rentals, theaters, and advertising. Success requires: demand forecasting, optimization, and operational execution.

Robust Optimization addresses optimization problems with uncertain parameters by seeking solutions that perform well across all possible parameter realizations within an uncertainty set. Unlike stochastic programming which assumes probability distributions, robust optimization uses deterministic uncertainty sets (boxes, ellipsoids, polyhedra). For uncertain constraints a(ξ)ᵀx ≤ b(ξ), the robust counterpart ensures feasibility for all ξ in the uncertainty set. Adjustable robust optimization allows some variables to adapt to uncertainty realizations (here-and-now vs. wait-and-see decisions). Advantages: distribution-free, computationally tractable (often reformulated as deterministic problems), and provides worst-case guarantees. Applications: portfolio optimization, supply chain design, and energy systems planning.