Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
412
Mine schedule optimization and mine operational realities:
Bridging the gap
A. Chowdu
South Dakota School of Mines and Technology, Rapid City, SD, USA
M. Goycoolea
Universidad Adolfo Ibanez, Peñalohén, Santiago, Chile
A. Brickey
South Dakota School of Mines and Technology, Rapid City, SD, USA
ABSTRACT: Advancement in solution algorithms and computing power continues
to drive the adoption of optimization techniques within the underground mining sector. However, limitations in the available data and the choices made during the model
setup can create a gap between optimal solutions and operational reality. This paper
presents a mining practitioner’s guide on effectively utilizing Multi-time Period Knapsack Constraints (MPKC) in scheduling underground mine production, which can close
part of that gap. Models with MPKC implemented at different time fidelities, i.e., weekly,
monthly and annual, are compared by evaluating solution quality and solver performance.
We provide recommendations that can assist in developing both optimal and operationally representative schedules.
Keywords: Underground mining, Production scheduling, Optimization
1 INTRODUCTION
Optimization models are approximate representations of real-world systems. Practitioners
often must make simplifying assumptions to ensure feasibility or relax constraints to improve
tractability. Any such model’s purpose is to provide useful information and improve decisionmaking abilities. With any model formulation, it is important that the assumptions made do
not detract from the model’s applicability to the operation. Advances in computation power
and solution algorithms have enabled researchers to create and solve model formulations
more complex and operationally representative than previously possible. In this paper, we
explore some of the recent advances in constructing models with a particular focus on underground mine production schedules.
Williams et al. (1973) were the first to make use of operations research principles to
develop an underground production schedule that maximized ore production at a copper
operation. The original intent of the project was to formulate a linear program to produce
“good” schedules; however, the group was unable to define the qualities that comprised a
“good” schedule. Revising their approach, they instead set out to produce a tool to that
would help planners evaluate several schedules and then choose the “best” option; while
not necessarily achieving optimality, they expected to realize a significant improvement over
manual scheduling. As computational power increased with time, researchers began developing integer programs, incorporating binary variables and allowing for ‘yes-no’ decisions
(Trout, 1995; Winkler, 1996). Trout utilized an integer programming model to schedule the
operational sequence, i.e., extraction and backfilling, of 55 stopes at the Mt. Isa copper mine
in Australia. With over 3500 variables and 6900 constraints, it was substantially larger than
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
412
Mine schedule optimization and mine operational realities:
Bridging the gap
A. Chowdu
South Dakota School of Mines and Technology, Rapid City, SD, USA
M. Goycoolea
Universidad Adolfo Ibanez, Peñalohén, Santiago, Chile
A. Brickey
South Dakota School of Mines and Technology, Rapid City, SD, USA
ABSTRACT: Advancement in solution algorithms and computing power continues
to drive the adoption of optimization techniques within the underground mining sector. However, limitations in the available data and the choices made during the model
setup can create a gap between optimal solutions and operational reality. This paper
presents a mining practitioner’s guide on effectively utilizing Multi-time Period Knapsack Constraints (MPKC) in scheduling underground mine production, which can close
part of that gap. Models with MPKC implemented at different time fidelities, i.e., weekly,
monthly and annual, are compared by evaluating solution quality and solver performance.
We provide recommendations that can assist in developing both optimal and operationally representative schedules.
Keywords: Underground mining, Production scheduling, Optimization
1 INTRODUCTION
Optimization models are approximate representations of real-world systems. Practitioners
often must make simplifying assumptions to ensure feasibility or relax constraints to improve
tractability. Any such model’s purpose is to provide useful information and improve decisionmaking abilities. With any model formulation, it is important that the assumptions made do
not detract from the model’s applicability to the operation. Advances in computation power
and solution algorithms have enabled researchers to create and solve model formulations
more complex and operationally representative than previously possible. In this paper, we
explore some of the recent advances in constructing models with a particular focus on underground mine production schedules.
Williams et al. (1973) were the first to make use of operations research principles to
develop an underground production schedule that maximized ore production at a copper
operation. The original intent of the project was to formulate a linear program to produce
“good” schedules; however, the group was unable to define the qualities that comprised a
“good” schedule. Revising their approach, they instead set out to produce a tool to that
would help planners evaluate several schedules and then choose the “best” option; while
not necessarily achieving optimality, they expected to realize a significant improvement over
manual scheduling. As computational power increased with time, researchers began developing integer programs, incorporating binary variables and allowing for ‘yes-no’ decisions
(Trout, 1995; Winkler, 1996). Trout utilized an integer programming model to schedule the
operational sequence, i.e., extraction and backfilling, of 55 stopes at the Mt. Isa copper mine
in Australia. With over 3500 variables and 6900 constraints, it was substantially larger than