Block/Panel caving scheduling under precedence constraints
Milivoj Smoljanovic, Enrique Rubio and Nelson Morales Delphos Mine Planning Laboratory, Mining Engineering Department, Universidad de Chile
Currently, mine plans are optimised by using many criteria, like profit, life‐of‐mine, concentration of some pollutants, mining costs, confidence level or ore resources, while attending to constraints related to production rates, plant capacities and grades. While this approach is successful in terms of producing high value production schedules, it uses a static opening sequence of production units and, consequently, the optimisation is performed within the level of freedom left by the original opening schedule, it is therefore far from the true optimal value of the project. Often in the industry this approach is used and as a result the value addition that is involved when optimising the mining sequence is disregarded. This paper summarises an investigation that aims to construct a model to optimise the draw point opening sequence over a given time horizon for a panel cave mine. The emphasis is on the precedence constraints that are required to produce meaningful operational sequences considering the exploitation method (panel or block caving), physics considerations and logical rules. Furthermore, it applies the standard approach of maximising NPV and considers other targets for optimisation, like the robustness and constructability of the plans and the mining system. The results indicate that sequence is important if it compares the results of the objective function or the grade. The changes can be up to 46% in the best case scenario. Changes in the production rate per cross‐cut can change the result of the objective function by up to 3%.
As the industry is faced with more and more marginal reserves, it is becoming imperative to generate mine plans that will provide optimal operating strategies and make the industry more competitive . To obtain these strategies (objective functions), it is important to consider many constraints, like mining and processing capacity and geomechanical constraints, among others. The construction of the optimisation problems has required rational studies of which mining constraints are applicable in each case .These constraints are important because they limit the objective function and define the set of feasible solutions. This paper reviews the importance of other variables within underground planning, specifically for the panel caving method. Thus, this paper shows a mathematical model that represents this fact. The model incorporates the majority of relevant constraints and adding the sequencing (viewed as a set of constraints), among other factors. As motivation, an example is presented that shows what happens if a sequence changes in a fixed 2D model showing value in USD.
Case 1 Case 2 Case 3
1 6 1 12 99
3 3 5 3 90
2 4 9 6 98
3 1 9 4 8 21 4 1 15 3 19 29 6 8 187 261 320 345
1 3 2 3 1 1 3 2 6 3 4 4 8 6 3 4 1 5 9 4 1 1 5 9 12 3 6 3 19 12 3 6 99 90 98 6 8 99 90 98 ## 86 89 14 23 ## 21 18 N N N N N
3 4 4 3 6 23
1 8 1 19 8 9
NPV 10% c. 1 NPV 10% c. 2 NPV 10% c. 3
Period 5 Period 4 Period 3 Period 2 Period 1
Figure 1 Alternative sequences for a given 2D fixed value block model Figure 1 shows a set of blocks (each block could be a drawpoint). Each block has a value representing its profit. For every period the profit is calculated by adding the block values at the period. Then, NPV is calculated for each case, and it can be concluded that the third sequence is the best one. This demonstrates ...