手法を比較

	決定版混合整数計画法	多目的混合整数計画法
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	1958–1960	1980s–2000s
提唱者	Gomory, R. E.; Dantzig, G. B.; Land, A. H.; Doig, A. G.	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization
種類	Mathematical programming / combinatorial optimization	Mathematical optimization
原典	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, New York. ISBN: 9780471359432	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987
別名	Deterministic MIP, Deterministic MILP/MIQP, Classical Mixed-Integer Programming, Deterministic MIP Optimization	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP
関連	6	5
概要	Deterministic Mixed-Integer Programming (MIP) is a mathematical optimization framework that finds the provably optimal solution to problems involving both continuous and integer decision variables under fully known, fixed coefficients and constraints. It is the foundational workhorse of operations research when all data are treated as certain.	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.