قارن الطرق

	البرمجة الديناميكية الحتمية	نموذج ماركوف
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1957	1906
صاحب الطريقة	Richard E. Bellman	Andrei Markov
النوع	Exact sequential optimization algorithm	Probabilistic state-transition model
المصدر التأسيسي	Bellman, R. E. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516	Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963
الأسماء البديلة	DDP, Deterministic DP, Classical Dynamic Programming, Bellman Dynamic Programming	Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process
ذات صلة	6	5
الملخص	Deterministic Dynamic Programming (DDP) is a mathematical optimization technique that decomposes a multi-stage decision problem into a sequence of simpler subproblems, solving them exactly when all system parameters — transition functions, costs, and rewards — are known with certainty. It guarantees a globally optimal policy via Bellman's principle of optimality.	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.