Linganisha mbinu

	Uthabiti wa Kibayesiani wa Programu-shiriki za Nambari	Mixed-Integer Programming
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1990s–2000s	1958–1960
Mwanzilishi	Baptiste, Lassagne, Nuijten and others in Bayesian optimization community	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)
Aina	Probabilistic combinatorial optimization	Mathematical optimization
Chanzo asilia	Baptiste, P., Lassagne, I., & Nuijten, W. (2001). Bayesian reasoning in mixed integer programming. European Journal of Operational Research, 130(2), 293–313.	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432
Majina mbadala	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
Zinazohusiana	6	6
Muhtasari	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.	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.