Is it possible to accurately estimate production in mining operations?

1. Mines are �Complex Systems�

Mine operations consist of multiple �stochastic dependent processes� interconnected through a wide range of complex relationships. 

Let�s analyze this proposition.

1.1. Mining processes are stochastic in nature

Variability is inherent to mining operations. Each mining process is subject to variability. Examples of this inherent variability are:

• Time to load truck 'A' is not equal to the time to load truck 'B'. 
• Travel time between an extraction point and the crusher, varies for the same truck �A� during the day. 
• Even if trucks �A� and �B� are of the same model type, travel times are different for the same pair origin-destination.
• Big particles generate unplanned stops at the crusher. These stops generate uneven conveyor loading rates.

In the presence of variability delays, slowness, and lags in production appear.

1.2. Mine processes are 'dependent events'

As in many production environments, mine operations are composed by a sequence of interconnected dependent processes. Let�s consider the following sequence: 

Extraction ? Truck loading ? Transportation ? Truck unloading ? crushing

Upstream delays due to variability will negatively affect flow and generate lags downstream. For example, delays in the truck loading process will delay the arrival of loaded trucks to the crusher.

1.3. Complex interrelationships

Operation managers know how difficult mine operations are. Synchronizing the different processes is a complex endeavor. Examples of this complexity are:

• The same truck �A� could serve different pairs origin-destination during the same day
• Crusher operation is highly dependent on the rock fragmentation process
• Unplanned truck downtime affects the dispatch process
• Unplanned crusher stops generate truck lines at the crusher, and could reduce shovel�s utilization upstream

2. Aggregate Variability of the Mine as a �System�

Mine production as a whole, also presents statistical fluctuations so-called 'Aggregated variability'.

2.1 Why we need to know the aggregate variability?

For planning, budgeting, and control purposes, operations managers need to estimate the production volume for a given period of time (e.g. month, year). 

Due to the existence of aggregate variability production volumes could take on multiple values. In other words, it is a random variable with an unknown probability distribution.

Being a random variable, we cannot calculate/estimate production volumes with 100% certainty. A typical approach is to use averages to make this estimation. There are two important problems with this approach: 

• Using averages totally ignores the presence of variability throughout the system, and
• The average is only one of the infinite possible values that this random variable can take on.

2.2. How to calculate the aggregated variability?

Unfortunately, the aggregated variability is not equal to the sum of the variability in each of the dependent processes. As well, it is almost impossible to develop an analytical or mathematical model to represent mine operations. To calculate the aggregate variability, it is necessary to use sophisticated computational tools such as 'Computer Simulation'.

2.3 How Computer simulation works?

Computer simulation consists in developing a computational model of the mine. The model is composed of a set of entities. These entities represent elements of the mine (e.g. trucks, shovels). Each entity has its own characteristics and could be tracked during the simulation. Entities are interconnected through a series of hypotheses about the mine operations expressed as mathematical, logical, and statistical relationships among them.

Processes are represented through probability distributions. Therefore, during the simulation, a single process could take on different values. In order to allow the model to generate these random values, data collection in the field is necessary. Based on the collected data, the modeler fits probability distributions and populates the model with them. In this way, during each run the model replicates the real operations using the same variability observed in the reality.

For example, when simulating the truck loading process, the 'entity truck' is positioned near to the 'entity shovel'. The model generates a random loading time keeping the truck near the shovel for this simulated time. The model also generates a random value to simulate the tons of material to be loaded in the truck. This value will be stored in the 'entity truck'.

The model is capable of recording and storing a large number of data, allowing the modeler to process it when the run is completed. 

The model should be validated and calibrated to accurately represent the reality. Once calibrated and validated, the model can be used to estimate the aggregate variability of the process. To do this it is necessary to run the same scenario multiple times. Modern computers allow the modeler to run long periods of time in seconds. This means that a year can be simulated many times in a few minutes.

Each run will generate one value for the production volume. Collecting these values for a series of runs, allows the modeler to build a probability distribution. Using this distribution, different statistical analyses can be performed (e.g. confidence intervals).

Simulation models can also be used to perform experiments in order to fully understand the system performance and evaluate different operational strategies.

HERE you can find more information about a comprehensive mine simulation model.

3. In Summary

Due to the inherent variability of mining processes, aggregate variability appears making it difficult to estimate the production level for a given period of time.

Averages hide and ignore the presence of variability throughout the system and therefore lead to errors when used to estimate production levels.

So, is it possible to accurately estimate production in mining operations? The answer is yes. The use of computer simulation is the appropriate way to do it.

Rene Alvarez, IE, MEng

www.SmartSimulation.ca