Linganisha mbinu

	Utekelezaji Sanifu wa Kielelezo	Upangaji wa Mchanganyiko wa Stochastiki
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1957	1990s–2000s
Mwanzilishi	Bellman, R.; formalized for stochastic settings by Puterman, M. L.	Birge, J. R.; Louveaux, F.; Sen, S.
Aina	Sequential optimization under uncertainty	Stochastic optimization model
Chanzo asilia	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
Majina mbadala	SDP, Markov Decision Process, MDP, Stochastic DP	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
Zinazohusiana	6	5
Muhtasari	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.	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.