tag:www.gerad.ca,2005:/fr/papersCahiers du GERAD2021-11-29T13:45:44-05:0020tag:www.gerad.ca,2005:Paper/29012021-11-29T13:45:44-05:002021-11-29T13:45:44-05:00G-2021-64 : Large satellite constellations and space debris: Exploratory analysis of strategic management of the space commonsPierre Bernhard, Marc Deschamps, Georges Zaccour
<p>L'utilisation de l'espace par les satellites est de plus en plus importante pour les nations, les entreprises et les particuliers. Cependant, depuis l'envoi du premier satellite en 1957, l'humanité pollue l'espace avec des débris (c'est-à-dire des objets artificiels sans fonction), en particulier sur les orbites basses (entre 100 et 2000 km). La situation actuelle est telle que : 1) les agences spatiales envoient en moyenne chaque jour plusieurs alertes de risque de collision, et 2) les satellites ainsi que la Station Spatiale Internationale effectuent régulièrement des manœuvres d’évitement pour ne pas être endommagés ou simplement détruits. De plus, ces dernières années, ces problèmes sont devenus plus préoccupants et peuvent changer définitivement de dimension avec l'avènement des méga-constellations de satellites. En effet, afin de développer les télécommunications et l'Internet haut débit, plusieurs sociétés (ex. Starlink, Kuiper, OneWeb, Hongyan, Hongyun, Leosat, Athena) envisagent d'envoyer plusieurs dizaines de milliers de satellites sur des orbites basses, qui sont déjà les plus polluées. Le but de cet article est de fournir une analyse économique en termes de jeux dynamiques de l’arbitrage entre la taille de la constellation et le coût de la préservation de l'environnement spatial. Notre objectif est de contribuer à fournir un cadre pour un développement durable d'une économie spatiale.</p>
2021-11-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/29002021-11-29T13:36:48-05:002021-11-29T13:39:37-05:00G-2021-62 : GPMR: An iterative method for unsymmetric partitioned linear systemsAlexis Montoison, Dominique Orban
<p>We introduce an iterative method named GPMR for solving 2X2 block unsymmetric linear systems.
GPMR is based on a new process that reduces simultaneously two rectangular matrices to upper Hessenberg form and that is closely related to the block-Arnoldi process.
GPMR is tantamount to BLOCK-GMRES with two right-hand sides in which the two approximate solutions are summed at each iteration, but requires less storage and work per iteration.
We compare the performance of GPMR with GMRES and BLOCK-GMRES on linear systems from the SuiteSparse Matrix Collection. In our experiments, GPMR terminates significantly earlier than GMRES on a residual-based stopping condition with an improvement ranging from around 10% up to 50% in terms of number of iterations.
We also illustrate by experiment that GPMR appears more resilient to loss of orthogonality than BLOCK-GMRES.</p>
2021-11-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28982021-11-19T13:24:11-05:002021-11-19T13:24:11-05:00G-2021-59 : Robust optimization for lot-sizing problems under yield uncertaintyPaula Metzker Soares, Simon Thevenin, Yossiri Adulyasak, Alexandre Dolgui
<p>Production yield can be highly volatile and uncertain, especially in industries where exogenous and environmental factors such as the climate or raw material quality can impact the manufacturing process. To address this issue, we propose a multiperiod single-item lot-sizing problem with backorder under yield uncertainty via a robust optimization methodology. First, we formulate the robust model based on the budgeted uncertainty set. The resulting model optimizes under the worst-case perspective to ensure the feasibility of the proposed plan for any realization of the uncertain yield. Second, we derive the properties of the optimal robust policies for the special cases under a box uncertainty, which helps us obtain a dynamic program with polynomial complexity. Finally, extensive computational experiments show the robustness and effectiveness of the proposed model through an average and worst-case analysis. The results demonstrate that the robust approach immunizes the system against uncertainty. In addition, a comparison with the stochastic models shows that the robust model balances the costs to reduce the backorders at the expense of more often producing a larger amount of goods.</p>
2021-10-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28942021-10-26T15:02:13-04:002021-10-26T15:02:13-04:00G-2021-58 : Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygonsChristian Bingane
<p>A small polygon is a polygon of unit diameter. The maximal area of a small polygon with <code>\(n=2m\)</code> vertices is not known when <code>\(m \ge 7\)</code>. In this paper, we construct, for each <code>\(n=2m\)</code> and <code>\(m\ge 3\)</code>, a small <code>\(n\)</code>-gon whose area is the maximal value of a one-variable function. We show that, for all even <code>\(n\ge 6\)</code>, the area obtained improves by <code>\(O(1/n^5)\)</code> that of the best prior small <code>\(n\)</code>-gon constructed by Mossinghoff. In particular, for <code>\(n=6\)</code>, the small <code>\(6\)</code>-gon constructed has maximal area.</p>
2021-10-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28972021-11-19T10:57:47-05:002021-11-19T10:58:24-05:00G-2021-57 : On the Geršgorin discs of distance matrices of graphsMustapha Aouchiche, Bilal A. Rather, Issmail El Hallaoui
<p>Pour un graphe simple et connexe <code>\(G\)</code>, soient <code>\(D(G), ~Tr(G)\)</code>, <code>\(D^{L}(G)=Tr(G)-D(G)\)</code>, et <code>\(D^{Q}(G)=Tr(G)+D(G)\)</code> la matrice des distances, la matrice diagonale des transmissions des sommets, le laplacien des distances et le laplacien sans signe des distances de <code>\(G\)</code>, respectivement. Atik et Panigrahi (2018) ont suggéré l'étude du problème: <em>Est-ce que toutes les valeurs propres de <code>\(D(G)\)</code> et de <code>\(D^{Q}(G)\)</code> appartiennent plus petit disque de Ger\v{s}gorin?</em> Dans cet article npus apportons une réponse négative en construisant une famille infinie de contre-exemples. </p>
2021-10-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28932021-10-26T14:55:16-04:002021-10-26T14:55:16-04:00G-2021-55 : Batch reinforcement learning for network-safe demand response in unknown electric gridsAntoine Lesage-Landry, Duncan Callaway
<p>We formulate a batch reinforcement learning-based demand response approach to prevent distribution network constraint violations in unknown grids. We use the fitted Q-iteration to compute a network-safe policy from historical measurements for thermostatically controlled load aggregations providing frequency regulation. We test our approach in a numerical case study based on real load profiles from Austin, TX. We compare our approach's performance to a greedy, grid-aware approach and a standard, grid-agnostic approach. The average tracking root mean square error is 0.0932 for our approach, and 0.0600 and 0.0614 for, respectively, the grid-aware and grid-agnostic implementations. Our numerical case study shows that our approach leads to a 95% reduction, on average, in the total number of rounds with at least a constraint violation when compared to the grid-agnostic approach.
Working under limited information, our approach thus offers lower but acceptable setpoint tracking performance while ensuring safer distribution network operations.</p>
2021-10-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28952021-11-18T16:32:18-05:002021-11-19T11:02:57-05:00G-2021-54 : Minimum values of the second largest `\(Q\)` eigenvalueMustapha Aouchiche, Issmail El Hallaoui
<p>Pour un graphe <code>\(G\)</code>, la matrice du laplacien sans signe <code>\(Q(G)\)</code> esf définie comme <code>\(Q(G) = D(G) + A(G)\)</code>, o`u <code>\(A(G)\)</code> est la matrice d'adjacence de <code>\(G\)</code> et <code>\(D(G)\)</code> est la matrice diagonale des degrés des sommets de <code>\(G\)</code>. Le <code>\(Q\)</code>-spectre de <code>\(G\)</code> est celui de <code>\(Q(G)\)</code>. Dans le présent article, on s'intéresse aux valeurs minimales de la deuxième plus grande valeur propre <code>\(q_2(G)\)</code> du laplacien sans signe d'un graphe connexe <code>\(G\)</code>. On evalue les cinq plus petites valeurs de <code>\(q_2(G)\)</code> sur l'ensemble des graphes connexes <code>\(G\)</code> d'ordre <code>\(n\)</code> fixé. Nous caractérisons les graphes réalisant ces valeurs.</p>
2021-09-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28922021-10-26T14:48:01-04:002021-10-26T14:48:01-04:00G-2021-53 : Off-line approximate dynamic programming for the vehicle routing problem with stochastic customers and demands via decentralized decision-makingMohsen Dastpak, Fausto Errico
<p>This paper studies a stochastic variant of the vehicle routing problem (VRP) where both customer locations and demands are uncertain. In particular, potential customers are not restricted to a predefined customer set but are continuously spatially distributed in a given service area. The objective is to maximize the served demands while fulfilling vehicle capacities and time restrictions. We call this problem the VRP with stochastic customers and demands (VRPSCD). For this problem, we first propose a Markov Decision Process (MDP) formulation representing the classical <em>centralized</em> decision-making perspective where one decision-maker establishes the routes of all vehicles. While the resulting formulation turns out to be intractable, it provides us with the ground to develop a new MDP formulation of the VRPSCD representing a <em>decentralized</em> decision-making framework, where vehicles autonomously establish their own routes. This new formulation allows us to develop several strategies to reduce the dimension of the state and action spaces, resulting in a considerably more tractable problem. We solve the decentralized problem via Reinforcement Learning, and in particular, we develop a Q-learning algorithm featuring state-of-the-art acceleration techniques such as Replay Memory and Double Q Network. Computational results show that our method considerably outperforms two commonly adopted benchmark policies (random and heuristic). Moreover, when comparing with existing literature, we show that our approach can compete with specialized methods developed for the particular case of the VRPSCD where customer locations and expected demands are known in advance. Finally, we show that the value functions and policies obtained by our algorithm can be easily embedded in Rollout algorithms, thus further improving their performances.</p>
2021-09-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28902021-10-12T15:42:48-04:002021-10-15T14:35:51-04:00G-2021-52 : The consistent production routing problemAldair Alvarez, Jean-François Cordeau, Raf Jans
<p>This paper introduces the consistent production routing problem in a setting with multiple plants and products. The problem consists in finding minimum-cost production-routing plans that also meet specific consistency requirements. In our context, consistency is defined as the degree to which some specified features of the solution remain invariant over time. We consider four forms of consistency, namely: driver, source, product and plant consistency. For each of these consistency requirements, there is a target maximum value defining the decision-maker's tolerance to deviations from a perfectly consistent solution. These targets are enforced as soft constraints whose violations need to be minimized when optimizing the integrated production and routing plan. We present a mathematical formulation for the problem and an exact branch-and-cut algorithm, enhanced with valid inequalities and specific branching priorities. We also propose a heuristic solution method based on iterated local search and several mathematical programming components. Experiments on a large benchmark set of newly introduced instances show that the enhancements substantially improve the performance of the exact algorithm and that the heuristic method performs robustly for production routing problems with different consistency requirements as well as for standard versions of the problem. We also analyze the cost-consistency trade-off of the solutions, confirming that it is possible to impose consistency without excessively increasing the cost. The results also reveal the impact of the first time period when optimizing and measuring the consistency features we study.</p>
2021-09-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28892021-10-12T15:35:39-04:002021-10-14T15:54:18-04:00G-2021-50 : Media abnormal tone, earnings announcements, and the stock marketDavid Ardia, Keven Bluteau, Kris Boudt
<p>We propose a tone-based event study to reveal the aggregate abnormal tone dynamics in
media articles around earnings announcements. We test whether
they convey incremental information that is useful for price discovery for non-financial S&P 500 firms. The positive relationship found between the abnormal tone and abnormal returns suggests that media provide incremental information relative to the information contained in earnings press releases and earnings calls. </p>
2021-09-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28882021-10-12T15:20:11-04:002021-10-12T15:20:11-04:00G-2021-49 : Formulations and exact solution approaches for a coupled bin-packing and lot-sizing problem with sequence-dependent setupsGislaine Mara Melega, Silvio Alexandre de Araujo, Raf Jans, Reinaldo Morabito
<p>We study bin-packing and lot-sizing decisions in an integrated way. Such a problem appears in several manufacturing settings where items first
need to be cut and next assembled into final products. One of the main novelties of this research is the modeling of the complex setup operations
for the cutting process. More specifically, we consider the operation regarding the insertion or removal of the knives in the cutting process.
Since this operation depends on the number of items cut in the current cutting process and in the previous one, the number of insertions and
removals is sequence-dependent. The setups in the lot-sizing problem related to the production of the final products are also sequence-dependent.
To deal with such a problem, two compact formulations are proposed, which are based on the assignment variables to model the bin-packing decisions.
The sequence-dependent setups in the bin-packing problem are modeled in two different ways. The first one is based on known constraints from the literature and the second one is based on the idea of micro-periods and a phantom cutting process. Due to the dependency of the setup decisions in the bin-packing problem with sequence-dependent setups, the resulting formulations are mixed-integer nonlinear mathematical models. Exact mixed-integer linear programming formulations are presented by applying linearization techniques. An exact branch-and-cut algorithm, which applies violated subtour elimination cuts to deal with the sequence-dependent production and cutting setups, is developed to solve the non-polynomial formulations. In addition, a Benders-based branch-and-cut algorithm using Benders cuts and violated cuts is also presented to solve the integrated problem. A computational study is conducted in order to analyze the impact of the proposed approaches to model sequence-dependent setups and the exact solution methods used to solve the coupled bin-packing and lot-sizing problem.</p>
2021-09-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28872021-10-12T15:01:25-04:002021-10-12T16:19:33-04:00G-2021-48 : Predicting COVID-19 incidences from patients? Viral load using deep-learningAthar Khalil, Khalil Bassam Al Handawi, Ibrahim Chamseddine, Zeina Mohsen, Afif Abdel Nour, Rita Feghali, Michael Kokkolaras
<p>The transmission of the contagious COVID-19 is known to be highly dependent on individual viral dynamics. Since the cycle threshold (Ct) is the only semi-quantitative viral measurement that could reflect infectivity, we utilized Ct values to forecast COVID-19 incidences. Our COVID-19 cohort (n=9531), retrieved from a single representative cross-sectional virology test center in Lebanon, revealed that low daily mean Ct values are followed by an increase in the number of national positive COVID-19 cases. A subset of the data was used to develop a deep neural network model, tune its hyperparameters, and optimize the weights for minimal mean square error of prediction. The final model's accuracy is reported by comparing its predictions with an unseen dataset. Our model was the first to capture the interaction of the previously reported Ct values with the upcoming number of COVID-19 cases and any temporal effects that arise from population dynamics. Our model was deployed as a publicly available and easy-to-use estimator to facilitate prospective validation. Our model has potential application in predicting COVID-19 incidences in other countries and in assessing post-vaccination policies. Aside from emphasizing patient responsibility in adopting early testing practices, this study proposed and validated viral load measurement as a rigid input that can enhance outcomes and precision of viral disease predicting models.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28862021-10-12T14:38:17-04:002021-10-12T14:38:17-04:00G-2021-47 : Self-image and the stability of international environmental agreementsMichèle Breton, Lucia Sbragia
<p>Nous étudions la stabilité des accords environnementaux
internationaux portant sur une cible commune pour le niveau d'émissions
polluantes. En signant l'accord, les parties développent un sens des
responsabilités vis-à-vis de l'engagement pris, acquérant une
image de soi qui contribue à leur utilité.</p>
<p>Nous analysons un jeu dynamique en deux étapes où tous les pays
agissent de manière indépendante. Nous étudions comment deux
composantes fondamentales du modèle, à savoir le niveau (ambition)
de l'engagement et l'importance relative accordée par les signataires au
respect de leur engagement, affectent la stabilité et l'efficacité
de l'accord en termes de bien-être global et d'émissions totales.</p>
<p>Nous constatons que la participation à l'accord constitue le moteur clé des résultats. La participation diminue avec l'ambition de
l'engagement et augmente avec le niveau de préoccupation des pays pour
les questions environnementales.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28852021-10-12T14:29:53-04:002021-10-12T14:29:53-04:00G-2021-46 : Multi-agent hierarchical reinforcement learning for energy managementImen Jendoubi, François Bouffard
<p>The increasingly complex energy systems are turning the attention towards model-free control approaches such as reinforcement learning (RL). This work proposes novel RL-based energy management approaches for scheduling the operation of controllable devices within an electric network.
The proposed approaches provide a tool for efficiently solving multi-dimensional, multi-objective and partially observable power system problems. The novelty in this work is threefold: We implement a hierarchical RL-based control strategy to solve a typical energy scheduling problem. Second, multi-agent reinforcement learning (MARL) is put forward to efficiently coordinate different units with no communication burden. Third, a control strategy that merges hierarchical RL and MARL theory is proposed for a robust control framework that can handle complex power system problems. A comparative performance evaluation of the proposed control approaches is also presented. Experimental results of two typical energy dispatch scenarios show the effectiveness of the proposed approaches.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28842021-09-24T15:37:48-04:002021-09-24T15:37:48-04:00G-2021-45 : The equilateral small octagon of maximal widthChristian Bingane, Charles Audet
<p>A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with <code>\(n=2^s\)</code> vertices is not known when <code>\(s \ge 3\)</code>. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximatively 3.24 % larger than the width of the regular octagon: <code>\(\cos(\pi/8)\)</code>. In addition, the paper proposes a family of equilateral small <code>\(n\)</code>-gons, for <code>\(n=2^s\)</code> with <code>\(s\ge 4\)</code>, whose widths are within <code>\(O(1/n^4)\)</code> of the maximal width.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28832021-09-24T15:31:55-04:002021-09-24T15:31:55-04:00G-2021-44 : Robust integration of electric vehicles charging load in smart grids capacity expansion planningSajad Aliakbarisani, Olivier Bahn, Erick Delage, Rinel Foguen Tchuendom
<p>Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain the network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable generation expansion planning problem, called R-ETEM, in which demand responses of EV users are uncertain. Then, we employ a linear quadratic game to simulate the average charging behavior of the EV users. The two models are coupled through a dynamic price signal broadcasted by the utility. Mean field game theory is used to solve the linear quadratic game model. Finally, we develop a new coupling algorithm between R-ETEM and the linear quadratic game with the purpose of adjusting in R-ETEM the uncertainty level of EV demand responses. The performance of our approach is evaluated on a realistic case study that represents the energy system of the Swiss "Arc Lémanique" region. Results show that a robust behaviorally-consistent generation expansion plan can potentially reduce the total actual cost of the system by 6.2% compared to a behaviorally-inconsistent expansion plan.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28822021-09-24T15:26:38-04:002021-09-24T15:26:38-04:00G-2021-43 : A dual bounding framework for binary quadratic combinatorial optimizationMahdis Bayani, Borzou Rostami, Yossiri Adulyasak, Louis-Martin Rousseau
<p>Binary quadratic programming (BQP) is a class of combinatorial optimization problems comprising binary variables, quadratic objective functions and linear/non-linear constraints.
In this paper, we propose a unified framework to reformulate any BQP problem with linear constraints to a new BQP problem defined on a graph. This framework relies on the concept of stars in the graph and partitioning the quadratic costs into in-star and out-of-star interactions.
We exploit the star-based structure of the new reformulation to develop a decomposition-based column generation algorithm. In our computational experiments, we evaluate the performance of our methodology on different applications with different quadratic structures in which the quadratic component of the problem is dealt with in the column generation master problem and in its subproblem. Results suggest that the framework outperforms the state-of-the-art solver in almost all the instances having zero out-of-star interactions both in terms of dual bound and computational time.</p>
2021-08-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28912021-10-26T14:41:19-04:002021-10-26T14:41:19-04:00G-2021-42 : Adaptive simultaneous stochastic optimization of mining complexes: Where is the value coming from?Maria Fernanda Del Castillo, Roussos Dimitrakopoulos
<p>This paper aims to identify the sources of value created in the strategic plan of a mining complex when the adaptive simultaneous stochastic optimization of mining complex (ASSOMC) approach is used. This approach considers operational and investment alternatives dynamically within the simultaneous stochastic optimization of mining complex (SSOMC) framework, providing an adaptive strategic plan that manages technical risk and maximizes value. A case study on a world-class mining complex illustrates the effects of this optimization model, comparing the adaptive alternatives of the ASSOMC with the fixed SSOMC case. Results show that considering the SSOMC without alternatives as a starting point, including either investment or operational alternatives in a fixed manner, provides an increase in NPV of 4.4% and 2.8%, respectively; whereas considering both jointly increases the NPV by 10.3%. On the other hand, when adaptive changes are considered over investments, such as additional crushers or conveyor belts, the NPV increases further, by about 20%. The focus is placed on identifying the location and components where this extra value is created within the mining complex, understanding the effect that the alternatives have, and capitalizing from them. This study finds that, due to the non-linear synergies that exist between the different components of a mining complex, the adaptive aspect of the approach allows the production plan optimization to be proactive and to tailor its configuration according to possible changes and future developments.</p>
2021-07-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28812021-09-24T15:23:40-04:002021-10-21T11:30:56-04:00G-2021-41 : Stochastic stope design optimization under grade uncertainty and dynamic development costsMatheus Faria, Roussos Dimitrakopoulos, Clàudio Pinto
<p>Stope design optimization defines mineable three-dimensional material
volumes to be extracted from a mineral deposit, aiming to maximize
cashflows subject to geotechnical, geological, and operational
constraints related to the selected stoping underground mining method.
The current industry practice considers a stope design as the input into
subsequent optimization steps: development network layout and production
scheduling, leading to life-of-mine planning and related forecasts.
Available stope layout optimization methods are deterministic and are
based on conventionally estimated orebody models; thus, they fail to
consider the geological uncertainty and variability that affects the
stope locations and sizes. A two-stage stochastic integer programming
formulation for stope design optimization is proposed. The model
integrates grade uncertainty, quantified through geostatistical
simulations of a mineral deposit, level allocation, variable stope
sizes, pillar requirements, development costs and slope stability
parameters for different geotechnical zones. An application at an
underground gold mine employing sublevel open stoping is presented.
Results highlight how the integration of grade uncertainty and
variability define a risk-resilient stope design, capturing the upside
potential in terms of metal recovered.</p>
2021-07-01GERADinfo@gerad.catag:www.gerad.ca,2005:Paper/28802021-09-24T15:18:48-04:002021-09-24T15:18:49-04:00G-2021-40 : Integrating geometallurgical Ball mill throughput predictions into short-term stochastic production scheduling in mining complexesChristian Both, Roussos Dimitrakopoulos
<p>The geometallurgical models that predicting the throughput/comminution performance of the a processing plant often rely on rock hardness models, which are based on very sparse information, and are not typically are not designed to interact with mine production scheduling, and while ignoringignore the non-additive nature of hardness. This article presents a novel approach to integrate a geometallurgical throughput prediction model for the ball mill into short-term stochastic production scheduling in industrial mining complexes. The utilized datasets for this prediction model include penetration rates from blast-hole drilling, truck cycle data and measured throughput rates of the operating ball mill, offering an easily accessible and cost-effective method compared to other geometallurgical programs. Firstly, the comminution behavior of the mineral reserve is geostatistically simulated by building additive hardness proportions using blast-hole penetration rates. Then, a material tracking approach considers all material movements in the mining complex to inform the throughput prediction model about rock properties of blended materials sent to the ball mill. Subsequently, a multiple regression model is constructed, which predicts throughput rates as a function of blended rock properties. Finally, the prediction model is integrated into a stochastic integer programming model for short-term production scheduling in mining complexes. A case study at the Tropicana Gold Mining Complex in Western Australia shows that ball mill throughput can be predicted with an error of less than 30 t/h (RMSE) and a correlation coefficient between predicted and observed values of up to 0.8. By integrating the prediction model and newly proposed stochastic components into the optimization, the resulting production schedule can achieve weekly planned production reliably because scheduled materials can now be matched with the predicted performance of the ball mill. Comparisons to optimization using conventional mill tonnage constraints reveal that expected production shortfalls of up to 7% per period can be mitigated this way.</p>
2021-07-01GERADinfo@gerad.ca