Lane’s Algorithm Revisited

Marcos Goycoolea (), Patricio Lamas (), Bernardo K. Pagnoncelli () and Adriana Piazza ()
Additional contact information
Marcos Goycoolea: Business School, Universidad Adolfo Ibáñez, Peñalólen 7941169, Chile
Patricio Lamas: Business School, Universidad Adolfo Ibáñez, Peñalólen 7941169, Chile
Bernardo K. Pagnoncelli: Business School, Universidad Adolfo Ibáñez, Peñalólen 7941169, Chile
Adriana Piazza: Department of Economics, Faculty of Economics and Business, University of Chile, Santiago 8330015, Chile

Management Science, 2021, vol. 67, issue 5, 3087-3103

Abstract: In 1964, Kenneth Lane proposed an algorithm to optimize the production schedule of a single-metal, single-processor open pit mine. For this, he proposed a policy based on varying, over time, the so-called “cutoff grade”—or grade threshold used to determine if extracted material should be ore (processed material) or waste (thrown away). Lane’s algorithm had a profound impact on the mining industry. However, though it has been used in multiple commercial software systems and has traditionally been taught to every aspiring mining engineer, it is widely considered a heuristic, and little is known regarding the quality of the solutions it produces. In this paper, we formally study Lane’s problem. We show that Lane’s algorithm can be viewed as an approximate dynamic programming scheme and that Lane’s optimality conditions can be formally derived in two different ways: by considering a variant of the problem where the future value function is linearly approximated or by deriving the optimality conditions of a continuous-time version of the problem. We further show that Lane’s algorithm can naturally be extended to this continuous-time version of the problem and that when this algorithm converges, it converges to an optimal solution. Finally, through a reformulation, we show that Lane’s original problem can be solved using convex mixed-integer programming. Though hypothetical counterexamples can be constructed, computational experiments prove that Lane’s algorithm can produce the optimal solution in every real-world data set tested, thereby lending solid support for its practical application.

Keywords: cutoff grade optimization; Lane’s algorithm; large-scale open-pit mining; limiting economic cutoff grades (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.2020.3685 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:67:y:2021:i:5:p:3087-3103

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().