Optimization of the Long-Term Production Scheduling Model by Considering the Grade Uncertainty by the Lagrangian Relaxation Method - Bat Algorithm

Summary:

One of the main problems of mine planning is long-term production scheduling, which is very important in the theoretical research of open-pit mining and determines the distribution of cash flow throughout the life of the mine. In fact, the purpose is to maximize the net present value of the future profits generated. Among the uncertainties, grade uncertainty will play a major role in the accuracy of long-term production scheduling. In this paper, a hybrid model is presented by the Lagrangian relaxation method and bat algorithm to solve the problem of long-term production of open-pit mines, in which the uncertainty of the grade is also considered. The new approaches proposed are based on optimizing Lagrange coefficients and comparing them with the traditional method. The bat algorithm is used to update the Lagrange coefficients. The results of the case study show that the hybrid strategy can provide an acceptable solution compared to the traditional approximation method so that over a given period the net present value using the proposed hybrid method is 6.69% higher than the traditional one.

In recent years, a new approach to cheaper computational algorithms, such as meta-heuristic techniques, has attracted more attention from researchers to solve production scheduling problems. Although these techniques do not guarantee optimization as a final solution for production, they can provide suitable solutions for production at a lower computational cost.

Methodology and Approaches:

In this paper, an optimal hybrid model by the Lagrangian relaxation method and bat algorithm is presented to solve the problem of long-term production of open-pit mines, where the uncertainty of the grade is also considered. The newly proposed approach is based on optimizing Lagrange coefficients and comparing it with the traditional method. The results of the proposed approach are also compared with the combined approach based on the Lagrangian relaxation method and genetic algorithm. The bat algorithm is used to update the Lagrange coefficients.

The results of a case study show that the Lagrangian relaxation method can provide a suitable solution to the main problem and the combined strategy can produce a more effective solution than the traditional approximation method. It was also found that the proposed method has advantages, such as stable convergence property and prevention of early convergence. Over a given period, the net present value using the LR-BA hybrid method is 6.69% higher than the traditional method and also 5.58% higher than the LR-GA method.