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| Model Markowa× | Programowanie dynamiczne× | |
|---|---|---|
| Dziedzina≠ | Symulacja | Optymalizacja |
| Rodzina | Process / pipeline | Process / pipeline |
| Rok powstania≠ | 1906 | 1957 |
| Twórca≠ | Andrei Markov | Richard Bellman |
| Typ≠ | Probabilistic state-transition model | Exact combinatorial optimization via recursive decomposition |
| Źródło pierwotne≠ | 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 |
| Inne nazwy | Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| Pokrewne≠ | 5 | 3 |
| Podsumowanie≠ | 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. |
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