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Userlevel 6
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Carbon sequestration is the process of capturing and storing atmospheric carbon dioxide. It helps in the fight against climate change by trying to reduce the CO2 levels in our atmosphere.

Popular techniques for carbon sequestration are reforestation and afforestation. They are both similar but slightly different:

1. Reforestation is restoring forests on lands that were once forests but are no longer, because of deforestation for farming, commercial activities etc.
2. Afforestation is creating forests on lands that were not previously forests. This could be repurposing land that was used for farming, or mining etc. into forest land.

We at AIMMS have started a new program, AIMMS Forest, to contribute to the fight against climate change.

## The challenge description is as follows:

Area is available to plant trees in 4 different regions (provided in p_area(i_region)).

We have about 20 different types of trees which belong to 5 different families (provided in ep_treeFamily(i_tree)).

The tree families differ in the area required to plant a single tree that belongs to the family – each tree is planted in a square plot with a given length of side (provided in p_dimension(i_family)).

Not all families of trees can be planted in all regions. The families that are suitable for each region is provided in p_regionFamilies(i_region, i_family).

In addition to that, some families of trees cannot be planted in the same region as they will adversely affect each other’s growth. This data is provided in p_forbidden(i_family, j_family) – if this = 1, then those two families of trees cannot be planted in the same region.

The cost of planting each tree type (\$) and the amount of carbon each tree recovers (Ton/year) is provided in p_cost(i_tree) and p_sequestration(i_tree).

Can you formulate a mathematical model to maximize the amount of CO2 recovered if there is a total budget of \$400,000?

1. What is the amount of CO2 recovered?
2. How will your answer change if the budget is divided equally amongst the 4 different regions?

### Where will your trees be planted?

To maximize the impact of our donations, One Tree Planted will allocate them to where they are needed most. Here are some examples:

• Peruvian Amazon: reforestation in the Western Arc of the Amazon Rainforest across the Loreto and Ucayali regions. This is one of the most biodiverse places on Earth and of critical importance for conservation.
• US, California: Post-fire reforestation of Edison Forestry land surrounding Shaver Lake. 3,000-acres burned in the 2020 Creek Fire.

C. Vanlisuta and S. Prombanpong, A Mathematical Approach for Afforestation to Mitigate Climate Change, International Journal of Innovation, Management and Technology, Vol. 4, No. 1, February 2013

### 16 replies

Userlevel 1

Fun challenge! I solved it using only linear constraints, and the solution was found ‘immediately’ (definitely within 1 second).

Userlevel 6

Fun challenge! I solved it using only linear constraints, and the solution was found ‘immediately’ (definitely within 1 second).

@martijnbdv awesome! We will contact you by email when we have your tree-planting certificate

Fun challenge and a great way to engage the community. Sent my entry to your mail @Gloria Quintanilla . Hope its the correct solution :)

Userlevel 1

What can be better on a chill saturday evening?

I really enjoyed this, I hope won’t be the last one!

Userlevel 6

What can be better on a chill saturday evening?

I really enjoyed this, I hope won’t be the last one!

@Boglarka Balogh thanks for participating! We’ll be in touch soon with your tree planting certificate!

Userlevel 6

Fun challenge and a great way to engage the community. Sent my entry to your mail @Gloria Quintanilla . Hope its the correct solution :)

Thanks again @mrugankmodiya

This initiative moved me as it is a great way to engage our community in this critical topic. Thank you, AIMMS and One Tree Planted, for hosting this beautiful project. I sent my solution to your email @Gloria Quintanilla . I really enjoyed it!

Userlevel 6

This initiative moved me as it is a great way to engage our community in this critical topic. Thank you, AIMMS and One Tree Planted, for hosting this beautiful project. I sent my solution to your email @Gloria Quintanilla . I really enjoyed it!

Thanks Daniel! We will be in touch soon with your tree certificate!

Userlevel 6
+2

Really liked to do the challenge myself as well. I sent the solution to @Gloria Quintanilla.

Keep m coming so we will plant more trees!

Thanks for the interesting challenge.

Userlevel 3
+1

As a graduate and researcher at St. Petersburg Forest Technical University, I could not pass by such a wonderful and important event! Thank you very much! I sent the answers and the project by email.

Userlevel 1

I work for a company in the forest industry developing mathematical models. Therefore, I was especially pleased to participate in the Reforestation Modeling Challenge. Thank you very much, AIMMS team and One Tree Planted.

Userlevel 6

Thanks for the interesting challenge.

@bacherikov_iv thank you for participating! We will be in touch soon with your tree planting certificate.

Userlevel 6

I work for a company in the forest industry developing mathematical models. Therefore, I was especially pleased to participate in the Reforestation Modeling Challenge. Thank you very much, AIMMS team and One Tree Planted.

@anastasiiasimonenkova thank you for participating!! We will send you your certificate by email soon

Userlevel 4
+2

Fun challenge and great initiative!!

Thought this was a perfect opportunity to not just solve the problem, but also work on small application around it to show the power of integrated optimization app building that AIMMS provides! Instead of sticking to the winUI (which I know pretty well…  ), decided to play a bit with the WebUI again.

That resulted in the following UI

(Have to say, it is going easier and faster the more I play it. However, when working on models or developing models I still think the winUI is easier to have some rudimentary developer GUI quickly up and running)

Userlevel 6

Fun challenge and great initiative!!

Thought this was a perfect opportunity to not just solve the problem, but also work on small application around it to show the power of integrated optimization app building that AIMMS provides! Instead of sticking to the winUI (which I know pretty well…  ), decided to play a bit with the WebUI again.

That resulted in the following UI

(Have to say, it is going easier and faster the more I play it. However, when working on models or developing models I still think the winUI is easier to have some rudimentary developer GUI quickly up and running)

Very nice @gdiepen! It’s great to hear from you again. We will follow up with your tree planting certificate shortly.