مقایسهٔ روش‌ها

	برنامه‌ریزی عدد صحیح (IP) و برنامه‌ریزی عدد صحیح مختلط (MIP)	برنامه‌ریزی محدودیت (Constraint Programming)	برنامه‌ریزی خطی
حوزه	بهینه‌سازی	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1958	2006	1947
پدیدآور	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Rossi, van Beek & Walsh	George B. Dantzig
نوع	Mathematical optimisation — exact combinatorial method	Declarative combinatorial optimization	Mathematical programming / continuous optimization
منبع بنیادین	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	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
نام‌های دیگر	IP, MIP, mixed-integer programming, mixed-integer linear programming	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	LP, linear optimization, Doğrusal Programlama (LP)
مرتبط	4	3	4
خلاصه	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.	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.