Mixed Integer Programming Models for Intermediate Open Pit Scheduling with Variable Slopes

Open pit mine plans define the complex strategy of displacement of ore and waste over the mine life. The objective of the mine plan is to maximize the future cash flows within the technical and physical constraints. Various mixed integer linear programming (MILP) formulations have been used for production scheduling of open pit mines. In the MILP formulation the slope constraints guarantee that all the overlying blocks are mined prior to mining a given block. Traditionally, the slope constraints have been modeled with cone templates representing the required wall slopes of the open pit mine. The overall pit slopes constructed by these templates are a function of the width and height of the geological block model. Therefore, the overall slopes are fixed in one bearing. This paper presents a general MILP model for open pit mine scheduling with variable slopes constraints. The methodology utilizes a directed graph to capture the precedence of extraction of blocks and pit slopes in different bearings. Depth-first-search algorithm was used to traverse the graph for constructing the slope constraints in the MILP problem. TOMLAB/CPLEX was used as the implementation platform to efficiently integrate the mathematical solver package CPLEX with MATLAB. A case study on intermediate scheduling of an iron ore mine over twelve periods was carried out to validate the models.