Linganisha mbinu

	Multi-objective mixed-integer programming	Upangaji Laini wa Malengo Mengi (MOLP)
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1980s–2000s	1955–1986
Mwanzilishi	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization	Steuer, R. E.; Charnes, A.; Cooper, W. W.
Aina	Mathematical optimization	Mathematical optimization / vector optimization
Chanzo asilia	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987	Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. John Wiley & Sons, New York. ISBN: 9780471888468
Majina mbadala	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP	MOLP, Vector Linear Programming, Multi-criteria LP, Linear Vector Optimization
Zinazohusiana	5	3
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 Linear Programming (MOLP) extends classical linear programming to handle several conflicting linear objective functions simultaneously over a feasible region defined by linear constraints. Instead of a single optimal solution, MOLP produces a Pareto-efficient frontier from which a decision-maker selects a preferred trade-off. It is foundational to operations research and management science for resource allocation, planning, and design problems with competing goals.