Multi-stage mine production timetabling with optimising the sizes of mining operations: an application of parallel-machine flow shop scheduling with lot streaming

In open-pit mining, a trade-off between determination of appropriate sizes of mining jobs and optimisation of allocating and sequencing mining equipment units at each operational stage is one of critical decisions for mining practitioners. To simultaneously optimise the above data-driven interplay between planning and scheduling decisions in multi-stage mine production timetabling, we introduce a novel integrated-planning-scheduling problem for considering the disturbances and variability of jobs’ sizes based on the theory of parallel-machine flow shop scheduling with lot streaming. This new problem is called the “Multi-stage Mine Production Timetabling with Optimising the Sizes of Mining Operations” and abbreviated as the MMPT-OSMO, in which the sizes of mining jobs (i.e., the number of block units to be aggregated on different working benches) are considered as planning-type variables and integrated with scheduling-type variables in a parallel-machine flow shop scheduling system. Due to considerable complexity, an innovative math-heuristic approach embodied as a hybridisation of decomposed mixed integer programming models and heuristic algorithms under a three-level divide-&-conquer scheme is devised to efficiently solve the MMPT-OSMO. By integrating both planning and scheduling decision variables in such a solitary problem, the MMPT-OSMO intrinsically characterises the potential to significantly improve mining productivity, which is validated by theoretical analysis and extensive computational experiments. In real-world implementation, replacing the current labour-intensive manual way, the proposed MMPT-OSMO methodology provides an intelligent decision-making tool to mathematically optimise the interactive decisions between mine planning and scheduling engineers. The proposed MMPT-OSMO methodology would make a breakthrough in the field of mining optimisation, as it contributes to extend mathematical modelling boundary by applying continuous-time machine scheduling theory to operational-level mining optimisation in theory and to help mining practitioners improve the production throughput using lot-streaming techniques in practice.