قارن الطرق

	نموذج ماركوف	البرمجة الديناميكية
المجال	المحاكاة	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1906	1957
صاحب الطريقة	Andrei Markov	Richard Bellman
النوع	Probabilistic state-transition model	Exact combinatorial optimization via recursive decomposition
المصدر التأسيسي	Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6
الأسماء البديلة	Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
ذات صلة	5	3
الملخص	A Markov Model represents a system as a finite set of states and specifies the probability of moving from one state to another at each time step. By capturing only the current state — not the full history — it enables tractable analysis of complex dynamic processes across health economics, engineering reliability, operations research, and social-science modeling.	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.