Linganisha mbinu

	Multi-objective mixed-integer programming	Mpango wa Malengo Mengi (MOGP)
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1980s–2000s	1961
Mwanzilishi	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization	Charnes, A. and Cooper, W. W.
Aina	Mathematical optimization	Mathematical programming / multi-criteria optimization
Chanzo asilia	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987	Charnes, A., Cooper, W. W. (1961). Management Models and Industrial Applications of Linear Programming. Wiley, New York. ISBN: 978-0471148258
Majina mbadala	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP	MOGP, Multi-goal programming, Vector goal programming, Multi-criteria goal programming
Zinazohusiana	5	4
Muhtasari	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 Goal Programming (MOGP) is a mathematical programming technique that simultaneously pursues several aspirational targets by minimizing weighted deviations from each goal. Rooted in Charnes and Cooper's original goal programming framework (1961), MOGP extends it to handle multiple competing objectives, making it indispensable in operations research, supply chain design, resource allocation, and policy analysis where decision-makers must satisfy — or come close to — multiple conflicting requirements at once.