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..

Mathematical Programming of Peirce-Smith Converting

RÉSUMÉ : Le convertissage par méthode Pierce-Smith (PS) est l'étape clé de la production de cuivre et du nickel. Cette opération se poursuit par des étapes séquentielles et présentent un cas idéal pour la programmation mathématique. Ce travail démontre les complexités thermochimiques et les étapes du convertissage au moyen d'un programme linéaire (PL) en nombres entiers mixtes. Ceci est la première fois que le convertissage PS est abordé dans un cadre de programmation mathématique et représente un avancement majeur de l'application de la recherche opérationnelle aux étapes de production des fonderies de cuivre et de nickel. Les résultats démontrent que le cadre mathématique est fonctionnel, et peut être utilisé quotidiennement pour la gestion optimale des séquences d'opération de l'élaboration de cuivre et de nickel. Le cadre est flexible quant à la définition des contraintes du système et de la fonction objective. Cette flexibilité évoque la formulation de divers modes d'opération des fonderies. Le cadre pourra être exploité en forme de logiciel industriel que les fonderies pourraient utiliser pour coordonner la production journalière, et de varier leur mode d'opération selon les conditions de l'usine et du marché. Le cadre a été formulé suivant une méthodologie qui est typique de la programmation mathématique, mais qui n'avait jamais été adaptée au convertissage PS. Premièrement, le problème se pose en forme générale. En effet, Le problème de convertissage consiste de la coordination des convertisseurs PS avec d'autres opérations dans la fonderie afin de maximiser la production durant une période fixe, tout en respectant les contraintes chimiques, volumétriques et thermiques. Deuxièmement, les diverses composantes et dimensions du système sont représentées par des structures algébriques générales; c'est-à-dire, des ensembles, des paramètres et des variables. Troisièmement, ces composantes sont liées de telle manière à ce que la formulation puisse être supportée par des techniques de résolution. Les techniques de résolution par la programmation linéaire (PL) en nombres entiers mixtes sont bien établies. Par contre, il a été nécessaire d'introduire des simplifications pour pouvoir résoudre le problème des convertissages par l'adoption d'un cadre hypothétique de PL en nombres entiers mixtes. En considérant la vaste gamme de problèmes qui ont été déjà abordées dans ce type de cadre, il semblait raisonnable que le convertissage PS nécessiterait seulement des simplifications mineures. En fait, le nouveau cadre mathématique exige certaines simplifications. En particulier, il impose une rigidité artificielle sur deux températures variables : la température nominale d'effluent gazeux, et la température d'écrémage de la scorie. Ces simplifications peuvent être considérées mineures, puisqu'il existe des logiciels qui ne traitent même pas ces quantités comme variables. En outre, il semble maintenant plausible de formuler un cadre non linéaire qui fournirait un traitement plus robuste et réaliste qui tient compte de ces températures. Les résultats de cette étude ont un attrait considérable pour les industries de cuivre et de nickel, puisque l'opération efficace d'une fonderie dépend directement de la coordination quotidienne de la production. Suivant les succès du travail actuel, des efforts superficiels provoqueront des changements majeurs dans les opérations journalières des fonderies de cuivre et de nickel.----------ABSTRACT : Peirce-Smith (PS) converting is central to the production of copper and nickel, and is a lucrative, yet previously undeveloped, context for mathematical programming. The thermochemical complexities of PS converting have now been represented within a mixed-integer linear program (MILP). This is the first time that PS converting has been treated within a mathematical programming framework, hence a major advancement in the operations research of copper and nickel smelters. The MILP framework is now functional, and can be used to construct optimal daily production schedules. The framework offers flexibility in the definition of system constraints and objective functions. This flexibility can accommodate the formulation of alternative modes of operation for smelters. The MILP framework can now be marketed as industrial software, to produce optimal daily schedules, and allow smelters to change their mode of operation in accordance to plant and market conditions. The framework has been created using a methodology that is typical of mathematical programming, but which had never been adapted to Peirce-Smith converting. Firstly, the problem has been posed in appropriately general terms; indeed, the PS Converter Problem is to coordinate Peirce-Smith converters with other objects in the smelter, so as to maximize production within a fixed period of time, while respecting chemical, volumetric and thermal constraints. Secondly, the various components and dimensions of the system have been represented using general algebraic structures, such as sets, parameters and variables. Thirdly, these components have been related to each other in a manner that can be supported by solution techniques. The solution techniques for MILP are well established. However, it was initially unclear what degree of simplification would be required in order to fit the PS Converter Problem into a hypothetical MILP framework. Given the vast scope of problems that have already been treated using MILP, it seemed plausible that the PS Converter Problem would require only minor simplifications. The new MILP framework has indeed required some simplification. More precisely, the framework imposes an artificial rigidity on two classes of temperature variables: nominal offgas temperatures, and skimming temperatures. These simplifications can be considered minor, since there are existing software tools that do not even treat these quantities as variables. Moreover, it now seems plausible to extend the current formulation into a nonlinear framework that would provide a more intensive and realistic treatment of the offgas and skimming temperatures. The results of this study have a considerable appeal to the copper and nickel industries, since the efficient operation of a smelter is directly linked to its scheduling practice. Following the successes of the current work, superficial efforts will cause major changes in the daily operations of copper and nickel smelters