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	Programmazione Lineare Intera Mista Multi-Obiettivo	Programmazione Dinamica Multi-Obiettivo
Campo	Simulazione	Simulazione
Famiglia	Process / pipeline	Process / pipeline
Anno di origine	1980s–2000s	1957-1975
Ideatore	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization	Extension of Bellman (1957); formalized by multiple authors from 1970s onward
Tipo	Mathematical optimization	Exact optimization — recursive multi-objective decomposition
Fonte seminale	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516
Alias	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming
Correlati	5	5
Sintesi	Multi-Objective Mixed-Integer Programming (MO-MIP) is an optimization framework that simultaneously optimizes two or more conflicting objective functions subject to linear or nonlinear constraints, where some decision variables are restricted to integer values and others are continuous. It is widely applied in engineering design, supply chain planning, resource allocation, and scheduling problems that require discrete choices alongside continuous quantities.	Multi-Objective Dynamic Programming (MODP) extends Bellman's classical dynamic programming to settings where a decision-maker must optimize several competing objectives simultaneously across a sequence of stages. Rather than a single optimal policy, it produces a Pareto-optimal set of policies — each representing a distinct trade-off profile — by propagating vector-valued value functions backward through the state space.