Linganisha mbinu

	Upangaji wa Mchanganyiko wa Stochastiki	Utekelezaji Sanifu wa Kielelezo
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1990s–2000s	1957
Mwanzilishi	Birge, J. R.; Louveaux, F.; Sen, S.	Bellman, R.; formalized for stochastic settings by Puterman, M. L.
Aina	Stochastic optimization model	Sequential optimization under uncertainty
Chanzo asilia	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093
Majina mbadala	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP	SDP, Markov Decision Process, MDP, Stochastic DP
Zinazohusiana	5	6
Muhtasari	Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.	Stochastic Dynamic Programming (SDP) is a mathematical optimization framework for sequential decision problems where outcomes are partly random. It extends Bellman's principle of optimality to stochastic environments, representing problems as Markov Decision Processes (MDPs) and computing optimal policies by solving recursive value equations over states and time periods.