Linganisha mbinu

	Utekelezaji wa Namba Kamili	Upangaji wa Vizuizi	Programu Sanifu	Usanifu wa Mipango
Nyanja	Uboreshaji	Uboreshaji	Uboreshaji	Uboreshaji
Familia	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	1958	2006	1957	1947
Mwanzilishi	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Rossi, van Beek & Walsh	Richard Bellman	George B. Dantzig
Aina	Mathematical optimisation — exact combinatorial method	Declarative combinatorial optimization	Exact combinatorial optimization via recursive decomposition	Mathematical programming / continuous optimization
Chanzo asilia	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
Majina mbadala	IP, MIP, mixed-integer programming, mixed-integer linear programming	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	LP, linear optimization, Doğrusal Programlama (LP)
Zinazohusiana	4	3	3	4
Muhtasari	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.	Constraint Programming (CP) is a declarative optimization paradigm in which a problem is formulated as a set of variables, finite domains, and constraints, and a solver systematically searches for assignments that satisfy all constraints. Formalized comprehensively by Rossi, van Beek, and Walsh in their 2006 Handbook of Constraint Programming, CP unifies propagation-based pruning with intelligent backtracking search to tackle combinatorial problems across scheduling, planning, and configuration domains.	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.	Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences.