手法を比較

	ベイズ整数計画法	ベイズ線形計画法
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	1990s–2000s	1970s–1980s
提唱者	Baptiste, Lassagne, Nuijten and others in Bayesian optimization community	Integrated from Dantzig (LP) and Zellner/Bayesian econometrics traditions
種類	Probabilistic combinatorial optimization	Optimization under Bayesian uncertainty
原典	Baptiste, P., Lassagne, I., & Nuijten, W. (2001). Bayesian reasoning in mixed integer programming. European Journal of Operational Research, 130(2), 293–313.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press, Princeton, NJ. ISBN: 9780691059136
別名	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	BLP, Bayesian LP, Bayesian stochastic linear programming, prior-posterior LP
関連	6	6
概要	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.	Bayesian Linear Programming (BLP) integrates Bayesian statistical inference with classical linear programming to handle uncertainty in model parameters such as objective function coefficients, constraint coefficients, or right-hand-side values. Instead of treating parameters as fixed or governed by worst-case bounds, BLP uses prior beliefs updated by data to form posterior distributions, which then guide the LP formulation and solution, producing decisions that are optimal in a probabilistic, data-informed sense.