Σύγκριση μεθόδων

	Προγραμματισμός Μικτών Ακέραιων Τιμών	Στοχαστικός Μικτός Ακέραιος Προγραμματισμός
Πεδίο	Προσομοίωση	Προσομοίωση
Οικογένεια	Process / pipeline	Process / pipeline
Έτος προέλευσης	1958–1960	1990s–2000s
Δημιουργός	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)	Birge, J. R.; Louveaux, F.; Sen, S.
Τύπος	Mathematical optimization	Stochastic optimization model
Θεμελιώδης πηγή	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
Εναλλακτικές ονομασίες	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
Συναφείς	6	5
Σύνοψη	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.	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.