Planning for Mining Operations with Time and Resource Constraints

We study a daily mine planning problem where, given a set of blocks we wish to mine, our task is to generate a mining sequence for the excavators such that blending resource constraints are met at various stages of the sequence. Such time-oriented resource constraints are not traditionally handled well by automated planners. On the other hand, the remaining problem involves finding node-disjoint sequences with state-dependent travel times on the arcs, which are highly challenging for a Mixed-Integer Program (MIP). In this paper, we address the problem of finding feasible sequences using a combined MIP and planning based decomposition approach. The MIP takes care of the resource constraints, and the planner solves the remaining sequence problem. We extend the notion of finding feasible sequences to finding good feasible sequences, by devising a heuristic objective function in the MIP, which improves the resulting search space for the planner. We empirically analyse the scalability of our approach on a benchmark data set, before demonstrating its effectiveness on a real world case study provided by our industry partner. These results demonstrate that by using a heuristic MIP, it is possible to obtain better makespan results with a suboptimal planner than by using an optimal planner with an uninformed MIP. Introduction Daily open-pit mine planning is the problem of generating feasible sequences of blocks for excavating-equipment to mine, such that blending requirements are met at the product stockpiles. A feasible sequence is a series of actions for each excavator, including movements between blocks, and mining the blocks themselves. The task of generating a feasible sequence involves allocating excavating equipment to blocks. The scope of this paper is limited to excavators, rather than also considering truck/hauling equipment. In a surface mine, the blocks are pre-determined sections of ore that are marked for mining in this schedule. Naturally, there is a precedence ordering on the blocks for the case where some blocks must be mined to reach the blocks behind. A number of excavators have the task of mining this set of blocks. The excavators move from block to block, Copyright c 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. forming a mine sequence. The order of the blocks in these sequences will affect the makespan and the ability to achieve the required blend of the formed stockpiles. The excavators may not mine more than one block simultaneously, leading to a state-wise node-disjoint path sub-structure to the problem. Furthermore, the time required for an excavator to travel between two blocks is dependent on what has already been mined. That is, as blocks are removed, new pathways may be formed. Therefore, the travel time is dependent on the state of the mine. In this paper, we address the problem of finding parallel plans that yield good, but not necessarily optimal, makespans such that these criteria are met. The computational difficulty for this problem arises not in the size of the instances—these are actually quite small— but in the layering of several difficult sub-structures. The state-wise node-disjoint path sub-structure, which imposes that excavator movements are contiguous and do not intersect at blocks at any given moment, is analogous to the problem of finding optimal multi-commodity network flow, which is already NP-complete for the case of Euclidean traversal times between blocks (Even, Itai, and Shamir 1975). The precedence constraints alone can undesirably convert a polynomial-time solvable problem to NPcomplete (Lenstra and Rinnooykan 1978). On top of this, we have the resource constraints, which are known to convert polynomial-time solvable problems to NP-hard complexity (Blazewicz, Lenstra, and Rinnooykan 1983). This challenging problem is of great practical importance to mining operations. In this setting, long-term plans are used to guide the derivation of short-term plans which, in turn, are handed down to operational planners who must implement the final, weekly, fine-resolution plan. It is at this stage that undetected infeasibilities in the plans frequently become apparent. Infeasibilities arise due to inaccurate allocation of attributes of the ore in any given block, unavailability of some equipment due to maintenance and breakdowns, or, quite simply, the impossibility of achieving the plan due to the time required to move equipment. The latter can only be coarsely estimated in higher level planning, where the plan fidelity is not sufficiently detailed to account for this fine-grain information (Sandeman et al. 2010). The current approach in industry is to solve the problem using manual block picks. That is, a highly trained human planner utilises their experience of plan actualisation to de404 Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling