| We introduce a new integer programming formulation to solve the underground project scheduling problem, which we define as determining the time period in which to complete each mining activity so as to maximize the value. We introduce a new formulation for the underground project scheduling problem that utilizes a coarse time fidelity and relies on a set of constraints that forces specific pairs of mining activities to be completed in different time periods. By pairing this novel formulation with recently developed linear programming algorithms and heuristics, we show a dramatic decrease in solution time. We use our formulation in combination with an ad hoc branching strategy, i.e., enumeration, to fix the binary variables that determine if material is to be classified as ore or waste in an underground mine. Finally, in conjunction with our underground model, we use an open pit formulation to determine the timing and location at which to transition from open pit to underground mining. We present multiple constraint reformulations that transform non-precedence constraints into precedence constraints to create a desirable math structure for this combined open-pit-to-underground-transition model. Our research allows mining companies to make more informed decisions regarding design aspects of a mine that can affect the net present value of a project by a significant amount. |
