Linganisha mbinu

	Utekelezaji wa Namba Kamili	Programu Sanifu	Mpangilio wa Malengo
Nyanja	Uboreshaji	Uboreshaji	Ufanyaji Maamuzi
Familia	Process / pipeline	Process / pipeline	MCDM
Mwaka wa asili	1958	1957	1955
Mwanzilishi	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Richard Bellman	Charnes, A., Cooper, W. W.
Aina	Mathematical optimisation — exact combinatorial method	Exact combinatorial optimization via recursive decomposition	Multi-objective optimisation — weighted/lexicographic goal deviation minimisation
Chanzo asilia	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Charnes, A., Cooper, W. W. (1955). Optimal estimation of executive compensation by linear programming. Management Science
Majina mbadala	IP, MIP, mixed-integer programming, mixed-integer linear programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	—
Zinazohusiana	4	3	8
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.	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.	GOAL-PROGRAMMING (Goal Programming — Minimise deviations from multiple aspiration levels) is a ranking multi-criteria decision-making (MCDM) method introduced by Charnes, A., Cooper, W. W. in 1955. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.