Modeling uncertainty of expert-elicited data for use in risk-based, capital budgeting and underground mine production scheduling optimization models

Abstract

This dissertation consists of three papers in various stages of publication. The first paper, "Consistent Notation for Presenting Complex Optimization Models in Technical Writing,'' is published in Surveys in Operations Research and Management Science. The topics we discuss are: (i) conventions for defining sets, parameters, and variables, (ii) ways of presenting the objective and constraints, and (iii) means by which to organize formulations as they pertain to mathematical programming. A second paper, "Modeling uncertainty of expert elicitation for use in risk-based optimization,'' is under review, at the time of this submission, in Annals of Operation Research. We derive, for the first time, a three-dimensional density estimate with epi-splines from which we generate scenarios to implement in a superquantile risk-based, capital budgeting optimization model. The last paper, "Optimizing underground mine scheduling under production rate uncertainty,'' is awaiting the company's letter of endorsement necessary for submission to Interfaces. We employ a risk-based optimization model, with uncertain ground conditions, to demonstrate the effects geotechnical risk has on an underground mine production schedule.