قارن الطرق

	نموذج حد القطع لـ لين	خوارزمية ليرش-غروسمان	خوارزمية التدفق الزائف
المجال	هندسة التعدين	هندسة التعدين	هندسة التعدين
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1988	1965	1992
صاحب الطريقة	K. F. Lane	Helmut Lerchs and Israel Grossmann	Dorit S. Hochbaum
النوع	Economic optimization framework for ore classification	Graph-theoretic algorithm for pit limit optimization	Efficient algorithm for maximum closure problem
المصدر التأسيسي	Lane, K. F. (1988). The economic definition of ore: cutoff grades in theory and practice. Mining Journal Books, London.	Lerchs, H., & Grossmann, I. F. (1965). Optimum design of open-pit mines. Canadian Mining and Metallurgical Bulletin, 58(633), 47-54.	Hochbaum, D. S. (1992). A new-old algorithm for minimum-cut and maximum-flow problems. Journal of the ACM, 1(1), 76-109.
الأسماء البديلة	Lane Model, Cut-off Grade Optimization, Lane's Optimization Model	Lerchs-Grossmann Method, LG Algorithm	Pseudoflow Algorithm, Hochbaum Algorithm
ذات صلة	3	4	3
الملخص	Lane's Cut-off Grade Model, developed by Kenneth F. Lane and formalized in his 1988 book, provides a rigorous economic framework for determining the minimum grade at which ore should be mined and processed. It accounts for variable mining costs, metallurgical recovery, and commodity prices to optimize profit per unit processed. The model is foundational in mining economics and underpins daily operational decisions at thousands of mines worldwide.	The Lerchs-Grossmann Algorithm is a graph-theoretic method for determining the ultimate pit limit in open-pit mining operations. Introduced by Helmut Lerchs and Israel Grossmann in 1965, it maximizes the net present value of extracted ore while respecting slope stability constraints. This algorithm forms the theoretical foundation for most modern pit optimization software.	The Pseudoflow Algorithm, developed by Dorit Hochbaum in 1992, is a polynomial-time algorithm for computing maximum weighted closures in directed acyclic graphs. In mining, it solves the ultimate pit limit problem more efficiently than earlier methods. By maintaining feasible pseudoflows and iteratively eliminating negative-cost nodes, it achieves near-optimal practical performance even on industrial-scale block models.