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	Programowanie całkowitoliczbowe bayesowskie	Programowanie stochastyczne z ograniczeniami całkowitoliczbowymi
Dziedzina	Symulacja	Symulacja
Rodzina	Process / pipeline	Process / pipeline
Rok powstania	1990s–2000s	1955
Twórca	Baptiste, Lassagne, Nuijten and others in Bayesian optimization community	Dantzig, G. B.; Beale, E. M. L.
Typ	Probabilistic combinatorial optimization	Optimization under uncertainty with discrete decisions
Źródło pierwotne	Baptiste, P., Lassagne, I., & Nuijten, W. (2001). Bayesian reasoning in mixed integer programming. European Journal of Operational Research, 130(2), 293–313.	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer, New York. ISBN: 978-1-4614-0237-4
Inne nazwy	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	SIP, Stochastic IP, Integer Stochastic Programming, Mixed-Integer Stochastic Programming
Pokrewne	6	6
Podsumowanie	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.	Stochastic Integer Programming (SIP) is an optimization framework that combines integer (discrete) decision variables with explicit probabilistic modeling of uncertainty. It seeks the best here-and-now decision that minimizes expected cost (or maximizes expected benefit) across a distribution of future scenarios, accounting for the fact that some decisions must be made before uncertainty is resolved.