A Stochastic Mixed Integer Programming Framework for Underground Mining Production Scheduling Optimization Considering Grade Uncertainty

Abstract

Conventional mine planning approaches use an estimated orebody model as input to generate optimal production schedules. The smoothing effect of some geostatistical estimation methods cause most of the mine plans and production forecasts to be unrealistic and incomplete. With the development of simulation methods, the risks from grade uncertainty in ore reserves can be measured and managed through a set of equally probable orebody realizations. In order to incorporate grade uncertainty into the strategic mine plan, a stochastic mixed integer programming (SMIP) formulation is presented to optimize an underground cut-and-fill mining production schedule. The objective function of the SMIP model is to maximize the net present value (NPV) of the mining project and minimize the risk of deviation from the production targets. To demonstrate the applicability of the SMIP model, a case study on a cut-and-fill underground gold mining operation is implemented.

A Review of Models and Algorithms for Surface-Underground Mining Options and Transitions Optimization: Some Lessons Learnt and the Way Forward

“…The OP-UG mining options and transitions planning problem becomes complex when critical indicators such as crown pillar positioning and other essential underground mining constraints including primary and secondary access development, ventilation development, and geotechnical requirements for the development openings and stopes are integrated into the optimization framework. These essential UG mining developments were previously not considered in the optimization process because of computational complexities and the difficulty of integrating them with open pit mining operations [32]. The importance of incorporating crown pillar positioning, geotechnical support activity sequencing, underground infrastructure development, and mine management strategy in OP-UG mining options optimization studies are essential to attaining realistic mine plans [9,30].…”

“…They focused on determination of the transition depth in 2D environment, and do not incorporate other essential underground mining constraints such as primary and secondary development, ventilation shaft development, and geotechnical requirements for the development openings and stopes in the optimization framework [7,20,30,31]. This is because the optimization of underground mines is computationally complex [32] and integrating it with open pit mining makes it more challenging [33].…”

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

“…C HALLENGES, restrictions, and affects such as uncertainty [1]- [3], integrality [4]- [7], and conicity [8]- [11] arise naturally in real-world applications. For example, the (deterministic) mixed-integer secondorder cone programming (DMISOCP) models pre-sented in [12] (see also [13]- [15]) have proved to be useful in dealing with a variety of applications that involve integrality and conicity.…”

Stochastic stope design optimisation under grade uncertainty and dynamic development costs

“…Two-stage stochastic integer programming (SIP) formulations [35] were initially introduced in mine planning for long-term production scheduling of a single open-pit mine [37,38] and have since been successfully extended to the simultaneous optimisation of mining complexes [39,[40][41][42] . Although fewer applications have been applied to underground settings, recent promising SIP formulations have been developed for long-term underground mine production scheduling employing different mining methods, such as a hybrid cut-and-fill with longhole [43], purely cut-and-fill [41], and block caving [42].…”

“…Two-stage stochastic integer programming (SIP) formulations [35] were initially introduced in mine planning for long-term production scheduling of a single open-pit mine [37,38] and have since been successfully extended to the simultaneous optimisation of mining complexes [39,[40][41][42] . Although fewer applications have been applied to underground settings, recent promising SIP formulations have been developed for long-term underground mine production scheduling employing different mining methods, such as a hybrid cut-and-fill with longhole [43], purely cut-and-fill [41], and block caving [42]. The applications demonstrate that the stochastic frameworks capitalise on the grade and operational uncertainties to provide physically different schedules with a higher expected net present value, while managing the risk of not achieving production targets when compared to the deterministic approaches.…”