Abstract

Underground mining is a highly uncertain environment where durations of activities and resources (equipment) may be affected by multiple uncertainty sources. Thus, the short-term plan is sensitive to variations in the duration of activities and resource breakdowns. Short-term planning, which aims to schedule activities allocating resources to tasks on a given time horizon (a work shift to three months), becomes necessary to manage complex operations. Plus, the implementation of data collection systems enable to optimize underground operations having access to more information.

We present a robust short-term scheduling model using constraint programming to build good robust feasible solutions for both mining development and production. Development operations are often neglected in optimization model while it is a critical step in mining extraction to quickly have access to the ore body. The robust stochastic short-term model is based on multiple scenarios to produce a set of ordered robust sequences of activities for each available disjunctive resource, minimizing the expected makespan (or the expected duration of activities). It enables to minimize the impact of disturbances happening during the execution of considered operations. Indeed, various disturbances may lead to sub-optimal makespan.

Then, the produced set of ordered sequences of activities for each resource is provided to a simulation model to evaluate performances of the set of robust sequences on new simulated data. Both models take into account uncertainties about the duration of activities and resource breakdowns to produce more relevant solutions while taking into account various operational constraints: backfilling, transition times, equipment-capacity, precedence between operations, etc...

Implemented models are tested on real data sets from a sub-level long-hole stoping gold mine located in Canada. Indeed, tasks durations are sampled into statistical distributions built regarding historical data from the studied site. Deterministic models (for both development and production) have also been implemented to compare performances with the developed robust model. These models are often too optimistic as they don’t take into account the variability sources affecting the duration of activities. The constraint programming paradigm has been proven to be efficient to solve scheduling problems with scarce disjunctive resources. Obtained results show a significant improvement of the objective in comparison to the real-world execution and a good stability of the makespan using generated robust sequences.