Linganisha mbinu

	Upangaji wa Mchanganyiko wa Stochastiki	Mixed-Integer Programming
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1990s–2000s	1958–1960
Mwanzilishi	Birge, J. R.; Louveaux, F.; Sen, S.	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)
Aina	Stochastic optimization model	Mathematical optimization
Chanzo asilia	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432
Majina mbadala	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
Zinazohusiana	5	6
Muhtasari	Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.