Jorge Amaya

Jorge Amaya
University of Chile · Centro de Modelamiento Matemático (CMM)

PhD

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33
Publications
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250
Citations

Publications

Publications (33)
Article
Full-text available
Determining a set of nested pits to support the design of an open pit mine that leads to high economic value is crucial for the strategic planning of these operations; thus, practitioners rely on optimization methods for finding high value solutions. However, current approaches are not sufficient as they lack at least one of the following features:...
Article
Full-text available
Los cambios en la institucionalidad educacional que están en marcha desde hace algunos años implican diversos desafíos de planificación, entre los cuales está la existencia de sectores geográficos sin provisión de oferta pública de calidad. Actualmente miles de estudiantes recorren largas distancias en zonas urbanas de alta densidad para asistir a...
Article
Full-text available
In this work we address the Final Open Pit problem in a continuous framework, that is, the problem of finding the optimal profile for an open pit that satisfies an additional slope and maximum capacity conditions on extraction. Using optimal control theory and calculus of variations tools, we provide optimality conditions for that problem. In parti...
Article
This paper presents a method for thermal comfort control for trams which achieves the desired thermal comfort and minimises the power consumption of heating, ventilation and air conditioning (HVAC). Mathematical models of all relevant parts are stated (these parts being the tram and the HVAC considering both comfort and energy consumption) and thes...
Article
This work introduces a model of the crew scheduling problem for the operation of trains in the mining industry in the North of Chile. The model possesses particular features due to specific regulations with which train operators in mine material transportation are required to comply: every week, a fixed set of trips must be made according to curren...
Article
Full-text available
This article presents predictive statistical models for fragmentation in open pit mines using drill-And-blast data. The main contribution of this work is the proposing of statistical models to determine the correlations between operational data and fragmentation. The practical use of these models allows the drill-And-blast parameters, ie. burden, s...
Conference Paper
Full-text available
In open pit mine planning, there are three well known models concerning how to find a region of maximal economic value under geotechnical stability constraints. These models belong to the area of integer programming and we respectively call them as Final Open Pit (FOP), Capacitated Open Pit (COP) and Capacitated Dynamic Open Pit (CDOP). In this wor...
Article
Full-text available
A crucial problem in the open pit mining industry is to determine the optimal block scheduling, defining how the orebody will be sequenced for exploitation. An orebody is often comprised of several thousand or million blocks and the scheduling models for this structure are very complex, giving rise to very large combinatorial linear problems. Opera...
Article
Full-text available
This article presents an economic decision model for planning in public education, considering the satisfaction of the total demand for education in a municipality and the annual cost involved in the system. Given a set of established schools in a municipality and possible new locations, the aim of the model is to find the optimal supply in terms o...
Article
Open-pit mining production planning is a risky problem: operation costs are considerable, many parameters are inherently subject to uncertainty and, moreover, the mining operation can only be done once. In this work we address uncertainty in the ore-grade, where we only assume the availability of an i.i.d. sample of the joint distribution of ore-gr...
Article
Full-text available
This paper proposes a new mathematical framework for the open pit mine planning problem, based on continuous functional analysis. The main challenge for engineers is to determine a sequence of nested profiles maximizing the net present value of the mining operation. The traditional models for this problem have been constructed by using binary decis...
Conference Paper
Full-text available
This paper reports on our experience in using OMNeT++ to develop a network simulator focused on railway environments. Common design problems are analyzed, making emphasis on radio communication models. Scalability issues are raised when modeling the large topologies that are associated with railway communications. Our conclusions point out that mod...
Article
Full-text available
This paper proposes a new mathematical model for the open pit mine planning problem, based on continuous functional analysis. The traditional models for this problem have been constructed by using discrete 0 − 1 decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming (MIP) problems. Instead, we use a continuous ap...
Article
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A critical aspect of long-term open-pit mine planning consists in computing a production schedule based upon a block sequencing strategy. Such a schedule should specify when and if blocks should be extracted in such a way as to maximize NPV, while satisfying wall-slope and production capacity constraints. It is well known that this problem can be m...
Article
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This paper deals with the stability of the feasible set mapping of linear systems of an arbitrary number (possibly infinite) of equations and inequalities such that the variable x ranges on a certain fixed constraint set X⊂ℝn (X could represent the solution set of a given constraint system, e.g., the positive cone of ℝn in the case of sign constrai...
Article
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This paper deals with the stability of the intersection of a given set \( X\subset \mathbb{R}^{n}\)with the solution, \(F\subset \mathbb{R}^{n}\), of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the solution set of the (possibly nonlinear) system formed by all...
Article
The aim of this work is to generalize strong duality theorems for inexact linear programming and to derive duality results for inexact semi-infinite programming problems. We give a detailed proof of the general result, using the Dubovitskii–Milyutin approach. The last section contains applications to inexact problems and a few comments for further...
Conference Paper
Full-text available
Visualization is a key issue for multivariate data analysis. Multivariate visualization is an active research topic and many efforts have been made in order to find suitable and meaningful visual representations. In this paper we present a technique for data projection in multivariate datasets, named Target Data Projection (TDP). Through this techn...
Article
Full-text available
In this paper, we apply the Dubovitskii-Milyutin approach to derive strong duality theorems for inexact linear programming problems. Inexact linear programming deals with the standard linear problem in which the data is not well known and it is supposed to lie in certain given convex sets. The case of parametric dependence of the data is particular...
Article
We propose a notion of dual problem for the inexact linear programming problem in general form. Weak and strong duality relations are discussed
Article
We propose a central trajectory motivation to derive the symmetric (primal-dual) interior point algorithm for linear programming. The central trajectory is chosen in such manner as the current solution lies on it. That is to say, the current point is the center of the polyhedron defined by the feasible region and a bound on the objective function....
Article
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In this paper we report numerical results on the symmetric afline scaling algorithm applied to degenerate linear programming problems. The performance is measured in terms of the number of iterations needed to reach a prefixed level of tolerance. We have found that the number of iterations increases with the number of primal variables and, for most...
Article
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In a previous work of the author, the convergence of the algorithm $$x_{k + 1} = x^k (t_k ) = {\text{x}}_{\text{k}} - s_k (t_k )\nabla f({\text{x}}_{\text{k}} )k = 0,1,2...$$ for the minimization of f: IRn → IR, was analyzed. Due to the nonlinearity of the matrix Sk the cost of evaluation of xk(t) for several values of t can be expensive, hence the...
Article
The purpose of this paper is to unify the conditions under which curvilinear algorithms for unconstrained optimization converge. Particularly, two gradient path approximation algorithms and a trust region curvilinear algorithm are examined in this context.
Chapter
Full-text available
In the capacitated open pit mining problem, we consider the sequential extraction of blocks in order to maximize the total discounted profit under an extraction capacity during each period of the horizon. We propose a formulation closely related to the resource-constrained project scheduling problem(RCPSP) where the genotype representation of the s...
Article
Full-text available
In the Capacitated Open Pit Mining Problem, we consider the sequential extraction of blocks in order to maximize the total discounted profit under an extraction capacity during each period of the horizon. We propose a formulation closely related to the Resource-Constrained Project Scheduling Problem (RCPSP) where the genotype representation of the...
Article
Full-text available
Resumen El desarrollo de sistemas de visualización en diversos dominios de aplicación, favorece el avance tanto en las aplicaciones como en la propia disciplina de visualización. En el presente trabajo se muestra la implementación de un sistema de visualización para planificación minera, analizándolo en el contexto de un modelo de referencia. El so...

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