Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Devendra Joshi,Snehamoy Chatterjee,Amol Paithankar,Sk Md Equeenuddin

doi:10.3390/mining2010003

Abstract

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model.

Highlights

IntroductionOpen pit mine production scheduling is a multicycle priority constraint knapsack problem, usually suitable for mixed-integer linear programming (MILP) frameworks [1,2]
Open pit mine production scheduling is a multicycle priority constraint knapsack problem, usually suitable for mixed-integer linear programming (MILP) frameworks [1,2].The production schedule begins with the geological block model, which is represented as a three-dimensional array of blocks
If the solution from the parametric minimum cut algorithm violates the upper limits of the resource constraints, a repair algorithm is used as the branch-and-cut algorithm to respect those constraints

Summary

Introduction

Open pit mine production scheduling is a multicycle priority constraint knapsack problem, usually suitable for mixed-integer linear programming (MILP) frameworks [1,2]. The production schedule begins with the geological block model, which is represented as a three-dimensional array of blocks. Each block represents the volume of material that can be mined. The size of the blocks in the block model is determined considering the exploration drilling patterns, geological conditions, and the size of the mining equipment to be used. The information obtained from the exploration drilling is used to interpolate weight and metal content for each block [3]. The mining blocks are represented by their weights, economic values (net profit from the block), ore contents (weight of the block with positive economic value), and metal contents (amount of metal released after processing ore block)

Methods

Results

Discussion

Conclusion