Scheduling Tools for Open-Pit Mining Operations

In open-pit mining operations, there are several levels of planning, each of which passes down restrictions to the level below. Each planning task is to determine the order in which material should be mined and how it should be processed, such that blending and utilisation targets are met. The mining operations are subject to various constraints on equipment use, maintenance and other resources. In this paper, we present a demo for two levels of planning: short-term scheduling and operations planning. The short-term schedule determines the blocks which should be mined, and when. The operational planners have the task of enacting the plans at a finer time horizon. Our system computes a set of schedules that can then be visualised in the form of tables, charts, and maps to support human expert planners. Open-pit Mining Operation Problem In open-pit mining operations, there are several levels of planning, each of which pass down restrictions to the level below. In this paper, we present scheduling tools for two levels of planning in this application: short-term scheduling (13 week horizon) and operations planning (3 week horizon). Our tools are designed to aid decision making in the context of a single open-pit mine that produces a single product with desired bounds on its grade (percentage of metal) and quality (levels of a range of contaminants). The orebody of the mine is divided into a set of blocks, each associated with an estimated grade, quality, and tonnage. The scheduling problem can be heavily constrained. For example, truck and dig unit capacities must not be exceeded, all processing facilities must be utilised to their available capacity, in each week, and mining precedences have to be respected, constraining the order in which blocks of material can be extracted. The short-term scheduling task is to (a) select a set of blocks to be mined in each week of a (typically) 13 week horizon, and (b) allocate routes from the mining source to a destination. The destinations may include processing facilities (crusher), stockpiles or ROM (run of mine stockpile), or waste dumps. The goals are (a) the correct blending of material to produce ore to a specification on average each Copyright c © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. week, and (b) the appropriate utilisation of equipment using coarse estimates. The output of a short-term schedule is a set of blocks to be mined within that period, and an allocation of these blocks to weekly mining periods, such that each weekly period conforms with blending and utilisation constraints. Given a weekly short-term schedule, operational planners have the task of enacting the plans—physically, with trucks and dig units—such that all mine performance goals are met. At the core of operational planning is a nonlinear scheduling problem with shared resources, blending, and maintenance constraints. The goals are to refine the blending and equipment utilisation estimates from the short-term schedule, and ensure that resulting plans are realisable. The output of an operational mine plan is a sequence of builds (i.e., small, short-term stockpiles) with an allocation of partial movements of material to builds such that the builds have the correct blend and crushers are maximally utilised. The key differences between the two levels of planning are that time units in the short-term schedule is a week, whereas in the operational plan the time unit is a minute—the latter permits a finer analysis of equipment utilisation. We present, in this paper, a tool for the generation of multiple candidate solutions to the short-term scheduling task, given a priority ordering over a set of supported objectives, and a tool to enact these schedules, in the form of operational plans, taking into account the more complex constraints of daily operations. Short-term Scheduler For the short-term scheduling problem, our system extends prior work, in which a rolling horizon based heuristic was presented for the generation of short-term schedules at single mine sites [(Blom et al. 2014), (Blom, Pearce, and Stuckey 2015)]. This heuristic splits a horizon of T periods into two periods of size 1 and T − 1. A mixed integer program (MIP) models the short-term scheduling problem across this two period horizon. Decision variables define which blocks are to be extracted in each period, and the destination of this material. Constraints place restrictions on the use of truck, dig unit, and processing resources. Given a solution to this two-period MIP, the activities of the first period are fixed, and we roll forward one period to consider the remaining horizon. A second two-time period MIP, covering periods 2 and 3 to T , is solved, and the activities of period 2 fixed. This process continues until all T periods are scheduled. An optimise-and-prune approach, is used to find a solution to our short-term scheduling problem, given a sequence of objectives ~ O, ordered from highest to lowest priority, to be optimised. Each MIP formed by our rolling horizon method is solved, with respect to each objective o in ~ O, in turn, to obtain a solution ~x with objective value o(~x). Constraints are added to the MIP to prune from the space of feasible solutions all ~x′ for which o(~x′) < o(~x) − o for a maximisation objective, and o(~x′) > o(~x) + o otherwise, where o 1. The final solution obtained to the MIP covering periods t′ to T , after consideration of each objective, is used to fix the activities of period t′. We have found that this staged method of optimising with respect to a sequence of objectives ~ O is preferable to solving a single MIP whose objective is a weighted sum over ~ O. A split-and-branch method is designed for the concurrent generation of multiple candidate schedules, each of which extracts blocks in a different sequence across the scheduling horizon. A split and branch factor, αs ≥ 1 and αb ≥ 1, characterise the number of schedules generated by our solver and the manner in which they differ. Our approach maintains an initially empty set of schedules in progress, X . We mark αs periods in our horizon, starting with t = 1, as split points, evenly distributing these points across the horizon. Starting with the first N -period MIP solved, covering split point t = 1 and periods t = 2 to T , distributed across N − 1 period aggregates, we find αb distinct solutions. For each of these solutions, we add a new partial schedule to X in which the activities of t = 1 haven been fixed. For each schedule ~x in X , we fix the activities of each remaining period until we reach the next split point t′. At t′, for each ~x ∈ X , we find αb distinct solutions to the relevant MIP, generating and adding αb − 1 new schedules to X , each of which contain the same activities for periods t < t′, but varying activities in period t′. This process is repeated until all T periods, in all ~x ∈ X , have been scheduled, resulting in αs b distinct solutions to our scheduling problem.