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	Lerchs-Grossmann アルゴリズム	レーンのカットオフグレードモデル	鉱山換気	擬似フローアルゴリズム
分野	鉱山工学	鉱山工学	鉱山工学	鉱山工学
系統	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1965	1988	1880	1992
提唱者	Helmut Lerchs and Israel Grossmann	K. F. Lane	Mining Engineering Practice	Dorit S. Hochbaum
種類	Graph-theoretic algorithm for pit limit optimization	Economic optimization framework for ore classification	System design for safe air quality and worker cooling in underground mines	Efficient algorithm for maximum closure problem
原典	Lerchs, H., & Grossmann, I. F. (1965). Optimum design of open-pit mines. Canadian Mining and Metallurgical Bulletin, 58(633), 47-54.	Lane, K. F. (1988). The economic definition of ore: cutoff grades in theory and practice. Mining Journal Books, London.	Hartman, H. L., Mutmansky, J. M., Ramani, R. V., & Wang, Y. J. (2012). Mine ventilation and ambient air quality. Society for Mining, Metallurgy & Exploration, Inc.	Hochbaum, D. S. (1992). A new-old algorithm for minimum-cut and maximum-flow problems. Journal of the ACM, 1(1), 76-109.
別名	Lerchs-Grossmann Method, LG Algorithm	Lane Model, Cut-off Grade Optimization, Lane's Optimization Model	Underground Mine Ventilation, Air Flow Design, Mine Haulage Ventilation	Pseudoflow Algorithm, Hochbaum Algorithm
関連	4	3	3	3
概要	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.	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.	Mine ventilation is the design and operation of systems that deliver fresh air to underground mining areas and remove contaminated air, heat, and hazardous gases. It is critical for worker safety and productivity, maintaining breathable air (sufficient oxygen, low dust and gas concentrations) and acceptable temperatures. Proper ventilation design requires calculating heat loads from mining operations, determining required air volumes, and designing shaft/drift geometry to deliver adequate flow.	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.