قارن الطرق

	البرمجة الديناميكية الحتمية	البرمجة الديناميكية العشوائية
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1957	1957
صاحب الطريقة	Richard E. Bellman	Bellman, R.; formalized for stochastic settings by Puterman, M. L.
النوع	Exact sequential optimization algorithm	Sequential optimization under uncertainty
المصدر التأسيسي	Bellman, R. E. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093
الأسماء البديلة	DDP, Deterministic DP, Classical Dynamic Programming, Bellman Dynamic Programming	SDP, Markov Decision Process, MDP, Stochastic DP
ذات صلة	6	6
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.	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.