পদ্ধতির তুলনা করুন

	মিশ্র-পূর্ণসংখ্যা প্রোগ্রামিং	ডায়নামিক প্রোগ্রামিং
ক্ষেত্র	অনুকরণ	অনুকূলকরণ
পরিবার	Process / pipeline	Process / pipeline
উদ্ভবের বছর	1958–1960	1957
প্রবর্তক	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)	Richard Bellman
ধরন	Mathematical optimization	Exact combinatorial optimization via recursive decomposition
মৌলিক উৎস	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
অপর নাম	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
সম্পর্কিত	6	3
সারসংক্ষেপ	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.