Σύγκριση μεθόδων

	Προγραμματισμός Μικτών Ακέραιων Τιμών	Δυναμικός Προγραμματισμός
Πεδίο	Προσομοίωση	Βελτιστοποίηση
Οικογένεια	Process / pipeline	Process / pipeline
Έτος προέλευσης	1958–1960	1957
Δημιουργός	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)	Richard Bellman
Τύπος	Mathematical optimization	Exact combinatorial optimization via recursive decomposition
Θεμελιώδης πηγή	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6
Εναλλακτικές ονομασίες	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
Συναφείς	6	3
Σύνοψη	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.	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.