Performance evaluation of stochastic DES through analytical models and simulation: an open-pit mine study

Abstract

Although the increase of computing power over the last years have opened up the possibility of optimizing stochastic DES (Discrete Event System) problem, the development of efcient methodologies for this purpose is still a grand challenge. The main reason is the fact that numerical solutions for stochastic DES problem, generally, require considerable computational effort. This Thesis discusses a nonlinear project portfolio problem which we must estimate the effect of each project combination through stochastic DES methods. Particularity, the system studied represents an open-pit mine appropriate for estimating the iron production index. Once that the time taken to run each estimative is a crucial aspect in optimization context, the purpose of this work is presenting alternative methods which address such stochastic DES system. Hence, we explored Markovian properties to design a load-haulage cycle of an open-pit mine. The Thesis presents analytical approximation methods and a new hybrid methodology. Regarding the analytical methods, we considered a rst-moment and a second-moment approximation. Although we did not nd evidence of equivalence between the analytical models and a standard simulation model, the results suggest that analytical approximation methods consist of a quite attractive and competitive way to concern with project portfolio optimization once that the computational time taken to run each estimative is remarkably faster than the standard simulation tool. Regarding the new hybrid method, it consists of an alternative methodology also faster than the standard simulation tool, but not so fast as analytical approximation methods. Such methodology aggregates Max-Plus Algebra with Markov Chain for modeling the same system. The experimental analysis conducted showed evidence of equivalence between the results acquired by this hybrid methodology and by the standard simulation tool. Once that this Thesis addresses a nonlinear project portfolio problem, we also proposed an inductive linearization technique. Regarding this technique, it consists of a column generation mechanism, in which, the nonlinear terms are partiality converted into new decision variables. The columns are generated heuristically based on the system dynamic and evaluated by some stochastic DES method. As a result, we can state that this linearization strategy combined with an analytical approximation method consists of an efcient strategy address decision makers of a project portfolio problem with interrelationships between projects.