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	Programmazione Intera Bayesiana	Programmazione Lineare Intera Robusta
Campo	Simulazione	Simulazione
Famiglia	Process / pipeline	Process / pipeline
Anno di origine	1990s–2000s	2003
Ideatore	Baptiste, Lassagne, Nuijten and others in Bayesian optimization community	Bertsimas, D. and Sim, M.
Tipo	Probabilistic combinatorial optimization	Deterministic robust optimization with integer variables
Fonte seminale	Baptiste, P., Lassagne, I., & Nuijten, W. (2001). Bayesian reasoning in mixed integer programming. European Journal of Operational Research, 130(2), 293–313.	Bertsimas, D., Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1-3), 49-71.
Alias	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	RIP, Robust IP, Robust Combinatorial Optimization, Integer Robust Optimization
Correlati	6	6
Sintesi	Bayesian Integer Programming (BIP) integrates Bayesian probabilistic reasoning with integer programming to solve combinatorial optimization problems under uncertainty. Instead of treating parameters as fixed, it encodes prior beliefs about uncertain coefficients and updates them with observed data, producing a posterior-guided search over integer-feasible solutions. The approach is widely used in scheduling, resource allocation, and supply-chain planning where data are incomplete or noisy.	Robust Integer Programming (RIP) finds integer or binary solutions that remain feasible and near-optimal across all scenarios in a prescribed uncertainty set. Rather than assuming exact knowledge of data, RIP hedges against the worst-case realization of uncertain costs or constraint coefficients, delivering decisions that are guaranteed to perform well even when inputs deviate from their nominal values.