What realistic data for a game based on management of polluting plants?

Question

I am not a writer nor an artist but I am creating a video game and I am looking for a realistic imaginary world based on science. I am looking for realistic data to support the strategical framework of the game that follows:

It is based on a company that wants to select $p$ locations among a set of $m$ possible sites for constructing polluting plants in a contemporary world. The $m$ candidate sites are located on a territory containing different cities. We have:

• $d_{ij}$ the distance between city $i$ and site $j$
• $P_i$ the population (in thousand of inhabitants) of city $i$

I imagined experts that thought that a city was threatened if there was a polluting plant located less than 2 km from it.

There are two different factions :

1. The authorities' point of view that wants to minimize nuisance. They want to minimize the number of inhabitants threatened by the $p$ selected plants.

2. The company point of view that wants to minimize the transportation costs.
   They take into account the volume of goods transported between the $p$ plants and the $n$ clients. The transportation cost from a plant $j$ to a client city $i$ is $1.5€$ per kilometer and per $m^3$ of transported good. The annual demand of city $i$ is $V_i$ (in $m^3$). It will be needed to transform the first model so that :

   • At most 5% of the population of $n$ cities are threatened (constraint imposed by the authorities).
   • The demand of a city is delivered by a single plant
   • The company minimizes its total transportation cost

I'm specifically looking for data, real or fictional, that would support this game framework, for instance the number of city in a given environment that would make it realistic in a given context (for example: are 10 sites for a population of 60 million people in 36,552 cities realistic? What would be the distances in this case?)

Answer 1

The main issue you seem to be neglecting are the carriers of pollution. Flows of water and air and even the local rotational velocity of the earth (higher closer the equator) are vital factors in determining your answer.

Air and water flows are mostly governed by climate and geographical features (which all in turn also influence each other, of course. Nobody said this would be simple).

Interestingly, in real life many factories have smokestacks SO high that it is no problem at all for the communities they are serving, but the pollution actually comes down hundreds of kilometers away to cause smog.

If your climate, flows and geography are relatively neutral and we ignore friendly-neighbor-policy smokestacks we can (greatly) simplify our models by assuming all plants pollute in a perfect circle with quadratic fall-off based on distance. At this point the model is so simple, unfortunately, that real-life data simply fails to accomodate. This does lend itself to heatmapping the area, and you can still use recorded smog and water polution levels in real life cities as reasonable benchmarks for tolerance.