Optimization of shovel-truck systems using the queuing theory

Abstract Introduction
Off-highway dump trucks are the basic haulage equipment used in most of open pit mines. Since haulage cost may account for up to 50% of the operational cost and up to 25% of a total cost, it is crucial to minimize it. Effectiveness of the equipment employed then becomes a key factor for the mine.
One of the most reliable and realistic methods to optimize shovel-truck systems is the queuing theory. It considers a random character of truck cycle time and associated costs. This paper presents the application of queuing theory for the purpose of shovel-truck system optimization.
Objectives
The goal of the presented research was to develop a coherent methodology for optimizing shovel-truck systems. Two basic objectives were pursued:

Determination of the optimal ratio between volume of a shovel’s bucket and of a truck body.
Development of the methodology using the queuing theory and aimed at determination of the optimal number of trucks in the fleet.

Methodology
The methodology used in this study consisted of three stages:

Optimization of the ratio between volume of the shovel’s bucket and of a truck body. This approach was based on a ratio between relative productivity of shovels and trucks. Their matching is “ideal” when productivities of both are equal.
Modelling of shovel-truck systems using the queuing theory:

adapt this theory to shovel-truck systems;
calculate the optimal number of trucks for one or more shovels.

In order to find the latter, a criterion of minimal operational cost of the system has been employed. Cost parameters were determined through calculations of probability for different states of the above mentioned system.
Application of the developed methodology for a range of front shovels and trucks commercially available from Caterpillar.

Results Obtained
The methodology developed has been validated for a range of Caterpillar hydraulic front shovels and off-highway dump trucks. The process has proven the applicability of the theoretical model proposed by the authors.
At the first stage, it has been determined how the shovels should be matched with trucks in relation to truck cycle time. Results obtained are interesting and applicable with regard to planning loading and haulage operations in open-pit mines or at the procurement stage of the equipment. The approach proposed is universal, i.e. it is possible to calculate the optimal bucket/truck body volume ratio regardless of equipment supplier and/or equipment model.
The next stage consisted of determination of the optimal number of trucks working with each shovel in the system using a model based on the queuing theory. The complete example has been provided for CAT 5230 shovels working with CAT 793C dump trucks. The results clearly demonstrate the applicability of such an approach for the issues under study.
Conclusion
The methodology developed and presented in this paper has a potential to be useful for mine operators for loading and haulage planning in open-pit mines and/or at the stage of equipment procurement. Since operational cost of hydraulic shovels and trucks is several hundreds of dollars per hour, the application of this methodology has a potential for substantial savings.



Optimisation des systèmes pelles-camions en utilisant la théorie des files d’attente

Mise en contexte
Les camions (tombereaux) représentent probablement l’équipement le plus utilisé pour le transport dans les mines à ciel ouvert. Le coût de transport peut parfois monter jusqu’à 50 % du coût d’exploitation et jusqu’à 25 % du coût total. Il est critique pour une opération minière de le minimiser. La gestion efficace de l’utilisation des camions devient un facteur important dans le fonctionnement général de la mine.
L’une des méthodes les plus fiables et réelles de l’optimisation des systèmes pelles-camions se base sur la théorie des files d’attente. Elle prend en considération le caractère aléatoire du temps de cycle du camion et de son chargement ainsi que les coûts qui y sont attachés.
Cet article présente l’application de la théorie des files d’attente pour les fins de cette optimisation.
But et objectifs
Le but de cette recherche est d’élaborer une méthodologie cohérente d’optimisation des systèmes pelles-camions. Ce travail referme deux objectifs :

Détermination du rapport optimal: volume de la pelle/volume de la benne du camion.
Élaboration de la méthodologie de la sélection du nombre optimal de camions dans la flotte à l’aide de la théorie des files d’attente.

Méthodologie
La méthodologie utilisée dans cette étude se compose de trois étapes :

Optimiser le rapport du volume de la benne du camion/volume du godet. Cette approche prend en considération le rapport entre les productivités relatives : pelle-camions. L’appariement idéal du système pelle-camions survient lorsque ces productivités relatives sont égales.
Modéliser les systèmes de transport à l’aide de la théorie des files d’attente :

adapter cette théorie pour le système pelle(s)-camions;
calculer le nombre optimal de camions avec la (les) pelle(s).
Le calcul du nombre optimal de camions avec les pelles se base sur la minimisation du coût d’opération du système pelles-camions. La détermination des paramètres du coût résulte des calculs des probabilités de différents états dudit système.
Application de la méthodologie sur la série des pelles et des camions de Caterpillar.

Résultats obtenus
La méthodologie présentée est validée sur la série des excavatrices hydrauliques à pelle frontale et des camions à benne du manufacturier Caterpillar. La validation démontre la mise en pratique du modèle théorique proposé.
Dans la première étape on détermine comment les pelles analysées doivent être appariées avec des camions lors de la variation du temps de cycle du camion. Les résultats obtenus sont intéressants pour la planification des travaux de chargement et de transport dans une mine ou lors de la planification de l’acquisition de cet équipement. En utilisant cette approche, on peut calculer le rapport optimal du volume de la benne du camion/volume du godet pour n’importe quel manufacturier ou le modèle d’équipement.
L’étape suivante consiste à déterminer le nombre optimal de camions pour chaque pelle en utilisant le modèle basé sur la théorie des files d’attente. L’exemple concernant le nombre optimal de camions est calculé pour pelles CAT 5230 appariées avec des camions CAT 793C. Les résultats du calcul démontrent l’applicabilité de cette approche pour la problématique analysée.
Conclusion
Cette méthodologie peut être très utile pour les opérateurs des mines à ciel ouvert lors de la planification des travaux de chargement et de transport. En sachant que le coût d’opération des pelles et des camions est de l’ordre de plusieurs centaines de dollars à l’heure, des économies importantes pourraient être dégagées en utilisant cette méthodologie.
Keywords: Queuing theory, Mining trucks, Shovel, Truck fleet sizing, Open pit
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