مقایسهٔ روش‌ها

	برنامه‌ریزی عدد صحیح (IP) و برنامه‌ریزی عدد صحیح مختلط (MIP)	بهینه‌سازی استوار
حوزه	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1958	1970s theoretical roots; modern tractable form from late 1990s–2004
پدیدآور	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Ben-Tal, El Ghaoui & Nemirovski (seminal book, 2009); Bertsimas & Sim (tractable polyhedral formulation, 2004)
نوع	Mathematical optimisation — exact combinatorial method	Mathematical programming framework
منبع بنیادین	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009). Robust Optimization. Princeton University Press. ISBN: 9780691143682
نام‌های دیگر	IP, MIP, mixed-integer programming, mixed-integer linear programming	minimax optimization, worst-case optimization, Gürbüz Optimizasyon (Robust Optimization)
مرتبط	4	5
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.	Robust optimization is a mathematical programming framework, formalised by Ben-Tal and Nemirovski in the late 1990s and made broadly tractable by Bertsimas and Sim (2004), that finds decisions guaranteed to perform acceptably under every scenario within a predefined uncertainty set — rather than assuming parameter values are known exactly. Instead of optimising for a single expected outcome, it minimises the worst-case objective across all plausible realisations of uncertain data.