New integer programming models for tactical and strategic underground production scheduling

"In this paper, we consider an underground production scheduling problem consisting of determining the proper time interval or intervals in which to complete each mining activity so as to maximize a mine’s discounted value while adhering to precedence, activity durations, and production and processing limits. We present two different integer programming formulations for modeling this optimization problem. Both formulations possess a resource-constrained project scheduling problem structure. The first formulation uses a fine time discretization and is better suited for tactical mine scheduling applications. The second formulation, which uses a coarser time discretization, is better suited for strategic scheduling applications. We illustrate the strengths and weaknesses of each formulation with examples.IntroductionProject scheduling is an important aspect of underground mine planning that consists of determining the start dates for a given set of activities so as to maximize the value of a project while adhering to operational and re-source-availability constraints. Important activities that require scheduling include development, drilling, stoping and other ore-extraction techniques, and backfilling. Precedence relation-ships impose an order in which activities can be carried out based on their location in the mine: for example, the activity a associated with development of an area must be completed before the activity a´ associated with extraction of that same area can begin. Re-sources include attributes of the mining operation, such as the amount of extraction and mill capacity available per time period, and are determined by capital and equipment availability and other factors. In this paper, for our set-ting, resource-availability constraints consider the amounts of material that can be extracted and sent to the mill — that is, processed — per time period."