{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T05:39:22Z","timestamp":1736573962044,"version":"3.32.0"},"reference-count":24,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,2]],"date-time":"2006-10-02T00:00:00Z","timestamp":1159747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[2007,1]]},"abstract":"Abstract<\/jats:title>Efficient methods to model and optimize the design of open\u2010cut mines have been known for many years. The design of the infrastructure of underground mines has a similar potential for optimization and strategic planning. In this article we discuss the use of network optimization to tackle this problem. The idea is to design a connected system of declines, ramps, drives, and possibly shafts, to minimize capital development and haulage costs over the lifetime of a mine. This can be modeled as a variation on the Steiner problem, with suitable metric and constraints. These constraints include: an upper bound on the absolute gradient of arcs in the embedded network (typically 1\/7), turning circle restrictions for navigability, and obstacle avoidance. Here we give an overview of the literature, focussing on our published work. We investigate the way in which this design problem can be modeled as a network optimization problem that accurately reflects the real costs involved while remaining mathematically tractable. Our approach is to first establish a fundamental model, which principally captures the development costs of the mine, and to study its geometric properties. We then outline more complicated generalized models, which add extra costs and constraints to the fundamental model but are still solvable. \u00a9 2006\u00a0Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 40\u201350 2007<\/jats:p>","DOI":"10.1002\/net.20140","type":"journal-article","created":{"date-parts":[[2006,10,2]],"date-time":"2006-10-02T20:28:09Z","timestamp":1159820889000},"page":"40-50","source":"Crossref","is-referenced-by-count":37,"title":["Network optimization for the design of underground mines"],"prefix":"10.1002","volume":"49","author":[{"given":"M.","family":"Brazil","sequence":"first","affiliation":[]},{"given":"D.A.","family":"Thomas","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,2]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1179\/037178403225003546"},{"key":"e_1_2_1_3_2","first-page":"97","article-title":"A network model to optimise cost in underground mine design","volume":"93","author":"Brazil M.","year":"2002","journal-title":"Trans South Afr Inst Electr Eng"},{"key":"e_1_2_1_4_2","unstructured":"M.Brazil J.H.Rubinstein D.A.Thomas D.Lee J.F.Weng N.C.Wormald Network optimization of underground mine design The Australasian Institute for Mining and Metallurgy Proc 305 No.1 2000 pp.57\u201365."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011903210297"},{"key":"e_1_2_1_6_2","unstructured":"M.Brazil J.H.Rubinstein D.A.Thomas J.F.Weng N.C.Wormald Gradient\u2010constrained minimal Steiner trees (III). Minimizing Perturbations preprint 2004."},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1090\/dimacs\/040\/03","volume-title":"Network Design: Connectivity and Facilities Location (DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 40)","author":"Brazil M.","year":"1998"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11081-005-6797-x"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.50.6.1050.354"},{"key":"e_1_2_1_10_2","unstructured":"P.G.Carter D.H.Lee H.Baarsma \u201cOptimization methods for the selection of an underground mining method \u201dProceedings Orebody Modelling and Strategic Mine Planning 2004 pp.7\u201312."},{"key":"e_1_2_1_11_2","first-page":"55","article-title":"Computer\u2010aided mine design and planning for underground mines","volume":"79","author":"Chatterjee P.K.","year":"1986","journal-title":"Can Inst Mining Metallurgy Bull"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.2307\/2372560"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0950-6098(00)00027-5"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0116001"},{"volume-title":"New developments in underground mining technology","year":"1997","author":"Hall B.E.","key":"e_1_2_1_15_2"},{"key":"e_1_2_1_16_2","first-page":"183","article-title":"Mining software and computing into the next Millennium","volume":"1","author":"Henley S.","year":"1998","journal-title":"Int Mining Minerals"},{"volume-title":"The Steiner tree problem (Annals of Discrete Mathematics 53)","year":"1992","author":"Hwang F.K.","key":"e_1_2_1_17_2"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0950609802000835"},{"key":"e_1_2_1_19_2","first-page":"17","article-title":"Optimum design of open\u2010pit mines","author":"Lerchs H.","year":"1965","journal-title":"Trans Canadian Institute of Mining and Metallurgy"},{"key":"e_1_2_1_20_2","first-page":"41","article-title":"Optimal layout of underground mining levels","volume":"78","author":"Lizotte Y.","year":"1985","journal-title":"Can Inst Mining Metallurgy Bull"},{"key":"e_1_2_1_21_2","first-page":"45","article-title":"Shaft or decline? An economic comparison","volume":"14","author":"McCarthy P.L.","year":"1993","journal-title":"Austr Inst Geosci Bull"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0950609802000914"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02071984"},{"key":"e_1_2_1_24_2","doi-asserted-by":"crossref","unstructured":"H.J.Sussman Shortest 3\u2010dimensional paths with prescribed curvature bound Proc. 34th Conf. on Decision and Control IEEE 1995 pp.3306\u20133312.","DOI":"10.1109\/CDC.1995.478997"},{"key":"e_1_2_1_25_2","unstructured":"D. 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