Modèle d’optimisation pour la planification à moyen terme des mines à ciel ouvert

RÉSUMÉ L’exploitation d’une mine à ciel ouvert requiert un grand nombre d’étapes de planification, que ce soit au niveau de l’analyse du site, de l’organisation des installations ou de la gestion des activités de production. Cette planification est complexe puisque les opérations à planifier sont nombreuses et fortement dépendantes les unes des autres. Dans ce projet, nous nous intéressons principalement au problème de planification à moyen terme (i.e. une période allant jusqu’à 3 mois) de ces activités. Ce problème consiste à trouver l’ordre de traitement des blocs d’une mine, tout en minimisant les coûts de production. Ces séquences doivent respecter les liens de préséances entre les blocs et les contraintes de mélange, ainsi que considérer le déplacement des pelles et le groupement des blocs pour le forage/dynamitage. Ce niveau de planification pour les mines à ciel ouvert a reçu peu d’attention dans la littérature jusqu’à présent. Ainsi, nous proposons un modèle composé d’entiers mixtes (MIP) avec lequel nous établissons l’organisation des opérations et la séquence d’extraction des blocs de la mine. Deux méthodes de résolution sont développées afin d’exploiter ce modèle. En premier lieu, une méthode optimale faisant l’usage de stratégies de résolution est présentée. Parmi ces stratégies, nous retrouvons la fixation de variables, l’établissement de priorités pour l’arbre de branchement et l’inclusion de contraintes et de paramètres ayant la propriété d’éliminer les symétries dans les solutions. L’utilisation de ce type de stratégies est indispensable et améliore le temps de résolution de façon drastique. Par la suite, une méthode heuristique exploitant le caractère intuitif d’extraire les blocs en séquence directe est développée. Cette méthode repose sur l’établissement d’une séquence intuitive qui sera ensuite proposée au solveur, lors de la résolution, par l’entremise de rabais dans la fonction objectif. Les résultats démontrent que cette façon de faire permet d’obtenir de bonnes solutions rapidement pour des modèles de taille très supérieure aux modèles pouvant être résolus de façon optimale.----------ABSTRACT Operating an open pit mine requires a large number of planning steps, either for the site analysis, the organization of facilities or the management of production activities. Such planning is complex as the activities to plan are numerous and highly co-dependent. In this project, we are primarily concerned with the problem of planning in the medium term (i.e. a period of up to 3 months) of these activities. This problem consists of finding the processing order for the blocks of the mine, while minimizing production costs. These sequences must respect the precedence relationships between blocks, the mixing constraints, the movements of the shovels and the grouping of blocks for drilling / blasting. This level of planning for open pit mining has received little attention in the literature so far. Thus, we propose a model consisting of mixed integers (MIP) with which we establish the organization of operations and the removal sequence for the blocks of the mine. Two resolution methods are developed to use this model. First, an optimal method making use of resolution strategies is presented. Among these strategies, we find the setting of variables, the setting of priorities for the tree branching and the inclusion of constraints and parameters with the property of eliminating symmetries in the solutions. The use of such strategies is essential and improves the solution time dramatically. Subsequently, a heuristic exploiting the intuitiveness of extracting blocks in a direct sequence is developed. This method relies on the establishment of an intuitive sequence which is then strongly suggested to the solver during the resolution through discounts in the objective function. The results show that this approach achieves very good solutions quickly for models of size much greater than the models which can be solved optimally

A Mixed-Integer Programming Model for an In-Pit Crusher Conveyor Location Problem

RÉSUMÉ Les coûts de transport représentent environ la moitié du coût total de fonctionnement (d’exploitation) dans les grandes mines à ciel ouvert. Une manière de réduire les coûts de transport est de raccourcir les distances de transport en rapprochant le point de déchargement du camion ou même de le placer dans la mine. Il y a une tendance à utiliser des systèmes de convoyeurs à grande vitesse et à grande capacité, lesquels ont été très productifs. Les systèmes de transport camion-pelle qu’utilisent des convoyeurs comparés aux conventionnels offrent une rentabilité opérationnelle supérieure et une grande fiabilité du concassage dans la fosse, ce qui les rend plus attrayants pour les activités minières modernes. Les principaux éléments à considérer dans la planification minière pour implémenter un système de concassage dans la fosse sont la disposition du convoyeur et la position du concasseur.---------- ABSTRACT Haulage costs account for around a half of the total operating costs in large open-pit mines. One way to reduce the haulage costs is to shorten the haulage distances by bringing the truck dump point closer or even into the mine. There is a tendency in the direction of the high speed, large capacity conveyor systems, and these arrangements have been very productive. Conveying and truck-shovel systems compared to conventional truck-shovel systems alone, provide operating cost efficiency and high reliability of in-pit crushing, making those types of systems more appealing to be implemented in modern mining activities. The main elements to be considered in mine planning to implement an in-pit crusher system are conveyor layout and crusher position

Multi-variable models of management in mining

osetljivost i rizik. Više pobuda generiše ovakvu atribuciju. Prva je, multivarijabilnost ambijentalnih uslova i funkcionalna i strukturna složenost rudarskih sistema (čovek - priroda (radna sredina) - mašina – okruženje); Druga se odnosi na ne postojanje opšte naučne saglasnosti oko ocene pogodnosti modela za podršku odlučivanju i upravljanje. Treća, ako bi saglasnost i postojala, nije sigurno da bi raspoloživi modeli, metode i taktike, dale ekvivalentne rezultate za iste rudničke uslove. Četvrta, sistemske nauke još uvek nemaju opšte prihvaćen i u praksi primenljiv algoritam izbora najboljeg rešenja u slučaju kolebanja multimodelskih poredaka alternativa. Prisutni su različiti pristupi u premoštavanju problema, oni se međusobno ne isključuju, ali ponuđena rešenja nemaju verifikaciju opšte i univerzalne primenljivosti. Ovo je uticalo da istraživanja u okviru disertacije, budu usmerena kritičkim stavom prema pristupima zasnovanim na izboru najboljeg modela za analizu i donošenje upravljačkih odluka u rudničkim uslovima, drugačijim od uobičajenih industrijskih uslova. U disertaciji se umesto izbora najboljeg, najpogodnijeg, ili najprikladnijeg modela za podršku odlučivanju, predlaže proceduralni prilaz. Ovakav prilaz podrazumeva istovremeno uključivanje u analizu više modela sa korektnom aproksimacijom multivarijabilnih rudničkih uslova. Pošto cilj nije izbor najboljeg modela već najboljeg rešenja zadatog problema, prema postavljenom algoritmu postupak izbora najbolje rangirane alternative ili najboljeg poretka alternativa, zavisi od kolebanja multimodelskih rangova. U slučaju ekvivalencije multimodelskih rangova, formirani poredak alternativa prihvata se kao definitivan, u suprotnom konačni poredak alternativa definiše se ponderisanjem. Ako je cilj najbolja (prvorangirana) alternativa, analiza je opciona zavisno od stepena ekvivalencije multimodelskih rangova. Primenljivost i operativnu korisnost postavljenog pristupa, odnosno algoritma „proceduralnog postupka’’, eksperimentalno je testirana sa četiri modela na šest rudničkih problema, različite strateške, taktičke ili operativne važnosti. Prosečna korelativnost multimodelskih i ponderisanih poredaka u 50% testova je u opsegu visoke – jake veze (0,70-0,89), a u preostalih 50% u opsegu veoma visoke-veoma jake veze (0,90-0,99). Prosečna korelativnost ponderisanih i multimodelskih poredaka (0,813) veća je za 5,58% od prosečne korelativnosti (0,77) multimodelskih poredaka. Primenjeni pristup u istraživanjima i metrični elementi eksperimentalnih rezultata, obezbeđuju objektivnost sagledavanja i vrednovanja predloženog algoritma za podršku odlučivanju u multivarijabilnim uslovima. Rezultujući ishodi ovih saznanja, potvrđuju validnost i praktičnu primenljivost postavljenog algoritma...The decision making and management in mining engineering are characterized by complexity, variability, ambiguity, sensibility and risk. There are several incentives for such attribution. The first is multi-variability of environmental conditions and the functional and structural complexity of mining production systems (Human – nature (working environment) – machine – narrower and wider environment). The second is related to the non-existing scientific consensus regarding the assessment on the suitability of decision making and management model. The third, even if such consensus existed, it is not sure that available models, methods and tactics would give equivalent results for different mining conditions. The fourth is that system sciences still do not have generally accepted and practically applicable algorithm for the selection of the best solution in case of instability of the multi-model order of alternatives. There are several approaches in overcoming this problem that are not mutually exclusive, but the offered solutions do not have verification of the general and universal applicability. This was a determining point that the research within the scope of this dissertation should be forwarded by a critical standpoint toward approaches based on the selection of the best model for analysis and management decision making in mining conditions, with major differences from conditions in other industries. In the dissertation, opposed to the selection of the best, the most adequate or the most suitable model for the support to decision making, the procedural approach is recommended. This approach means to include simultaneous models in the analysis, with accurate approximation of the multi-variable conditions in mines. Since the goal is not to select the best model, but rather the best solution for the task in question, the procedure of selection of the best ranked alternative, or the best order of alternatives is accomplished depends on the instabilities of multi-model ranks according to the algorithm set. In case of multi-model ranks equivalence, the order of alternatives is accepted as the final solution, otherwise the process of defining the final order of alternatives is achieved by pondering. If the goal is the best (the first ranked) alternative, the procedure is optional, depending on the multi-model ranks equivalence degree. The applicability and the operative usability of the approach set, i.e. the algorithm of the “procedural method” developed in this dissertation on four models, is tested with six mining engineering problems with different strategic, tactical or operational importance. The average correlation of multi-model and pondered orders for 50% of tests lies within the class of high – strong connection (0.70-0.89), and for other 50% within the class of very high – very strong connections (0.90-0.99). The average correlation of the pondered and multi-model orders (0.813) is larger by 5.58 % than the average correlation (0.77) of the multi-model orders. The applied approach in the research, and metric elements of the experimental tests results are ensuring the objective assessment and valuation of the suggested algorithm for the support to decision making in multi-variable conditions. The outcome of these findings are confirming the validity and practical applicability of the suggested approach..