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Presentation of my projects in modeling domain
Presentation of my projects in modeling domain
- Aggregates exploitation and transport flow (France)
- Artisanal Gold Mining (Burkina Faso)
**    Paper Award
- Ultra-pure Quartz exploitation (Madagascar)
- Collective management of animal wastes (La Réunion)

Ultra-pure Quartz exploitation (Madagascar)

(Photos: © BRGM)

1- Background and issues

What is Ultra-pure quartz ?

ultra-pure quartzSilica (SiO2), of which quartz represents the most common mineralogical occurrence, constitutes a natural resource long associated with human history. The degree of evolution of the first hominids was, for instance, identified 2.5 millions years ago by the way these hominids manipulated silica stones (Roche, 1989). Silica was also used in Egypt, 5000 years ago, to make the first synthetic material, glass, and the quartz itself was adopted as an ornamental stone in various proto-civilizations (Egyptian, Greek, Roman, etc.).

More recently, in the twentieth century, a particular category of quartz, ultra-pure quartz (i.e. in which the silica level is greater than 99.85%), has been exploited to deal with the evolution of many technological innovations, such as sonar for the detection of submarines, frequency control, time measurement, integrated circuits, optical fibers, etc.). This ultra pure quartz is also now mainly used for the production of high performance glass and artificially cultivated quartz crystals. As such, the ultra-pure quartz is then important for the development of international industries.

Ultra-pure quartz and Madagascar

Since the start of the twentieth century, Madagascar is the second ultra-pure quartz producer in the world behind Brazil. At the beginning, the annual production of both countries was respectively of (around) 15 tons and 200 tons. Throughout that century, they continuously increased their production. By 2000, for an annual world production totaling nearly 2000 tons, Madagascar production accounted for a quarter (500 tons), while the remaining 1500 tons were mainly provided by Brazil.

In Madagascar, the exploitation of quartz, generally undertaken through artisanal mining  operation, is necessary since it is considered as a complementary activity within a rural economy, for the most part oriented toward the production of mainly food crops (rice) but also other crops such as vanilla and cloves.

quartz fieldAn analysis of the quartz network illustrates its societal anchoring and its important role as a non-seasonal activity providing income at a crucial period for the familial economy during the crop breakdown and the plantation period, but also in the case of climate disorders such as cyclones or other phenomena like locust swarm invasions, which sometimes occur in Madagascar. This local necessity involves that the production of ultra-pure quartz will be sure to exist for a long-time yet in Madagascar. And since the population does not actually needs them (it only requires the money counterpart of its extraction), most exploited products will be sent abroad, for international industries uses, as mentioned above, assuring the existence of this necessary product in the world market.

This local exploitation is considered as a first stage of the ultra-pure quartz production in the world. We then start our (long-time) study of the quartz exploitation at this (micro-economical) level.

2- Introduction to Modeling and Simulation

In fact, although the impact of quartz collection on the local population seems indisputable, a real understanding of this impact is still lacking. Thus, throughout this work, we have attempted to obtain a better understanding of this issue. More precisely, by taking the region of Rantabe in northeastern Madagascar as a case study , we have attempted to model this activity and aimed to asses the possible impact of the value of quartz on the socio-economic evolution of the local population.

This application was developed in order
- to help in decision making with regard to a strategy of local governance for the reduction of poverty and
- to design a system of sustainable development in northeastern Madagascar. In this paper, we hereafter formally note this application Qz.

As for the modeling, we have used the Multi-Agent System (MAS) approach. This type of approach is appropriate because MAS is often used to model phenomena, i.e. situations where it is impossible to predict all future evolution of a system by a purely mathematical or statistical approach and in which the behavior of the actors is non-linear and non-deterministic.

We started this work in accordance with the real field study (i.e. observation of the population's behavior and the quartz network organization, inquiries …) lead by Barthélemy and Bouchut and we tried to follow the study as close as possible. After this modeling, and in order that the model fits the evolution of the real world more closely, a return to this real field is necessary for further progress to obtain information which may not have been forcely considered in this former study, as we will see later.

quartz collect

3- The exploitation network model

The figure below presents a high-level presentation of the model. The explanation is the following: as a natural resource, the geographical location of quartz can be anywhere in the physical environment. The persons responsible for quartz searching and collecting are farmers. As long as the quartz is transferred from actors to actors, a step of transformation (e.g. pre-grinding, purification) occurs.

quartz model

As a result, the quartz weight progressively decreases. In the figure, we assume that a farmer has found 100 kg of quartz. The farmer family sells the remaining 80 kg of the quartz to a collector which, in turn, after a possible transformation process, searches for conveyors in order to deliver the quartz (remaining: 68 kg) to the Rantabe exportation company. The 61.2 kg resulting from the company handling is then shipped from Rantabe to Toamasina, the only location from which the quartz may be exported. Inversely, after an exportation process, a distribution of the financial ratio of the quartz value occurs (we present here the Free On Board value).

The socioeconomic parameters

The socioeconomic unit of the model is "family".
Economic parameters are:
- family stock of rice
- family status: poor, middle, rich
- family goal (for each status): ok, amelioration, survival
- key: satisfaction threshold
Social parameters are:
- age class: [0-15], ]15-30], ]30-40], ]40-55] and >55
- life: death, birth, wedding
- key: family foundation threshold

The family behaviors

According to its goal, a family adopts different strategies, balancing between searching quartz and going to ricefield for cultivation. The principle is that the more a family is poor, the more it adopts quartz collection than cultivation. The strategy for survival, adopted by most families is the extreme case.

quartz strategy

4- MAS modeling of the system

In order to maximize the scope of our analysis, to increase the degree of our certainty and reduce any doubt about some results, to improve some hypothesis and scenario alternatives and to open a wider discussion about the study, we have implemented our model on two MAS platforms: ADK/RDK and Cormas.
Our modeling & simulations are analyzed from the results of both platforms. We call Qz-Cormas the version of the Qz application developed from Cormas and Qz-RDK the version of the Qz application developed from ADK/RDK.


Modeling pproach
- time management: based on a static structure, ie 1 day = 6hours, 1 month = 4 weeks and 1 year = 12 months.
- aggregation of parameteres computation: most usage of averages instead of going into details

- High-level Approach for Qz-Cormas design
- agent behavior pre-programmed at application level; based on if-then rules
- as a result, -> simulation performance: high

Periods for action evaluation during a simulation
- actions and strategies: daily
- family status: per month
- birth, death and weddings: at the beginning of every year for all families
- goal: yearly


Modeling approach
- time management: the Gregorian Calendar, ie january, etc. with leap years
- going into details for most parameters

- Low-level Approach for Qz-RDK design
- agent behavior driven by generic mechanism; based on natural motivations
- as a result, -> simulation performance: low

Periods for action evaluation during a simulation
- actions and strategies: daily
- family status (introducing a more reactive behavior):  
      per month for poor families
      per 15 days for middle families
      per day for rich families
- birth, death, and weddings: randomly distributed throughout a year for each family
- goal: yearly but in a random manner

The next figure presents additional information about the differences between concepts and approaches introduced in the two platforms.

 two environments

5- Example of simulations results

We present here the evolution of the parameter "stock of rice" of the three categories of families: poor, middle, rich, and when the price of rice (noted ro) increases. In the selected simulations presented here, we successively allot   to 1 then 5 then 7.


The figure presented has both vertical and horizontal views. Vertically, we can see the upper part (noted Figure a), which is related to the Qz-Cormas results, and the lower part (noted Figure b), which is related to the Qz-RDK results. Horizontally, we present the successive results (here the evolution of stock of rice) of the two platforms when ro increases.
The crossing (platform, ro) is called cell and corresponds to 25 years simulation. Each figure has then 6 cells (from the 3 values of ro times the two platforms). Each cell contains the evolution of three curves, associated, in a generic way, to the three  status (poor, middle and rich).

siumlation results

The results from both platforms show that when ro increases, the stock of poor families tends to be better. However, the figure shows that unlike in Qz-Cormas, ro increases starts, in Qz-RDK, to affect rich families (cf. from [c1] to [c7]). In our opinion, this situation is due to the reactivity behavior that we only introduced in Qz-RDK. Indeed, rich Qz-RDK families are more reactive about the management of their situation (status evaluated daily) than those in Qz-Cormas (status evaluated monthly). It is also the case for middle families (status evaluated every 15 days).

One interpretation of this result is that the notion of reactivity as a possible factor for, on the one hand, a reduction in the overall poverty and, on the other hand, a progression of wealth for rich families when ro increases.

In addition, one can note that the evolution of the family situation is not linear, i.e. it is not proportional to the variation of ro. This means that an exact measurement (except by simulation) of the relation between the ro-variation and the family status is currently difficult.

Overall, it is clear that the ro-increase certainly has positive impacts on the socio-economical evolution of the population. The problem is rather related to the degree of influence of this increase on the three family status introduced in this model.

6- Analysis and conclusion


The exploitation of ultra-pure quartz is based on the strategy for survival. It means that once the family satisfaction threshold  is reached, which is the situation especially when  ro increases, the family largely reduces or even ceases the quartz production, involving, at a more global level, a general decrease of the activity intensity. In other words, in artisanal mining activity, a ro-increase will quickly tend to decrease the quartz production activity. This is quite the opposite of what happens in industrial mining where, on the contrary, an increase of the price of quartz will also involve an increase of the production intensity since the global behavior of industries is to follow the evolution of markets.

Example of proposals for deciders

The conclusion here is that artisanal mining should have its specific policies distinct from the “traditional” law of economy and market since the objectives behind the production are not the same.

The following policies could be proposed to the real actors (situated at any level of decision). On the one hand, they should adopt factors such as reactivity in order to keep the idea of improving the socio-economical status of the population. On the other hand, they should adjust the value of   at a certain intermediate level only (ex: around [3-4]), instead of increasing it as high as possible, such as is the case in industrial mining. This latter policy will warrant continuation of ultra-pure quartz exploitation and then that of the ultra-pure quartz exportation (cf. Figure 1 showing the global scenario).

However, it should be borne in mind that such propositions are based on strategy for survival, which is certainly not the optimal strategy for attaining real sustainable development. According to us, an adequate mixing of artisanal and industrial mining is a better proposition for population to really progress towards sustainable development. We agree that carrying out this latter idea is not an easy task, at both research level (determining the meaning of the term “adequate” above) and socio-economical level (e.g. convincing the population to slightly change its way of life), but it is worth making further investigation about this way.

Whatever the adopted propositions, it is also necessary to train the population as a whole to improve its understand as to how to best manage its quartz activity in a more efficient manner.

(Photos: © BRGM