Stochastic Simulation of Open Pit Pushbacks with a Production Simulator
CIM Edmonton 2004
Kwame Awuah-Offei, Samuel Frimpong,
Material scheduling and sequencing planning and execution are the core tactical mine plan for achieving production targets that maximize the objective function of any mine production entity. This objective function is constrained by several exogenous and endogenous constraints including geological, operating, technological, marketing, financial, political, social and local field constraints. Linear and dynamic programming techniques have been used to formulate algorithms to solve the problems associated with scheduling and sequencing operations. These algorithms possess the mathematical rigor for dealing with the fundamental problems but they fail to provide adequate answers to random and dynamic process problems. Materials scheduling and sequencing are carried out within the bounds of random and dynamic fields. The functional relations between the output and dependent variables are random, and thus, current algorithms are limited in their abilities to address the problems arising from these random field processes. In this study a production simulator is developed to capture the random field process associated with materials scheduling and sequencing in an open pit environment. The algorithm incorporates a geometric pit evolution model, using solid geometry of an ellipsoidal frustum to capture material displacement dynamics. Taylor series expansion about the dimensions of the initial frustum is used to provide numerical solutions to the resulting partial differential equations governing the pushback dynamics. A production simulator, derived from the stochastic and dynamic models, is developed, validated and used to simulate the changes in the pit volume resulting from periodic incremental pushbacks and the random field process. The hybrid stochastic-optimization algorithm provides a powerful tool for addressing the random field and dynamic process problems. Combined with a hybrid stochastic-optimization dispatch system, tactical production planning and execution will be efficient and economic for achieving desired objectives.
Pushbacks, Stochastic simulation, Radom Field Process, Open pit mining, Scheduling