Optimize expansion

[Lissa]

Hi,

I'm currently completely overhauling the structure of my base to switch to a more “scalable” model. I'm trying to calculate exactly how fast my iron plate stock will grow if I reinvest every surplus into new smelter lines. Does anyone use external tools or calculators to project this curve over the long term? I’d like to estimate my final resource balance after about ten hours of constant production, factoring in my regular ore contributions, just to see if my logistical bottlenecks are manageable.

[mmmPI]

imo it may be quite tedious to use an external calculator to model an existing factory, if you have trains bottleneck for example, it will create a discrepancy between what the calculator predict and the actual behavior in game and this would be difficult to tell the calculator, if you try to make it more accurate. Here my advice would be to use the production statistic in game, you can see the "last hour" or "10 minutes" production/consumption, and use this to extrapolate the result. "what if it stays like this for longer". Because it will incorporate all additionnals interactions that occurs in a factory compared to the idealized calculator.

To me calculator are more used "before" making the factory, and during the game looking at the production statistic allows to verify if the blueprint is working as intended, if the production is the expected one, if no material are lacking in production, if nothing is saturated in a way that prevent the math done with the calculator to properly apply.

[Tertius]

I know no such tool, but the math isn't too complicated.

As simplification to understand the concept in general, first assume we just have furnaces to build and just one material to build a furnace.

If you reinvest every product into the production of new furnaces and add the new furnaces to the production immediately, its math can be described as exponential growth.

The basis of the growth is the question: how long does it take 1 furnace to craft the ingredients for 1 furnace?

If we know this time, we know the time after production will double. After this time we have 2 furnaces. Another time and we have 4 furnaces, then 8, then 16, and so on. This starts slow and explodes after about 8-10 steps, depending on your view.


So all you need to do is to find the time how long it takes in your setup for one production line to craft the ingredients for one production line. Then apply the exponential growth:
steps = whole time / time per 1 production line
amount of production lines after steps = 2^steps

"whole time" is 10 hours for you. "time per 1 production line" can be calculated by classic calculators such as Rate Calculator. The time will probably not just include the raw production time but also the time you need to actually build the additional production lines on the map and supply it with ore.

[mmmPI]

So all you need to do is to find the time how long it takes in your setup for one production line to craft the ingredients for one production line. Then apply the exponential growth:
steps = whole time / time per 1 production line
amount of production lines after steps = 2^steps

That's a question of perspective i think, you see the exponential where one could see harmonics series

I tried to make a little drawing of what the production statistic would look like in game (imo ) :

ironstock.jpg (44.02 KiB) Viewed 49 times

You need to imagine all the red rectangle have the same area.

At first your production rate is "y", this is the production of 1 furnace array. 100 iron plate per minute maybe.
After "x" amount of time, you have produced enough so that you can create a second furnace array. maybe 10 minutes.

This means x*y is the amount of iron that was produced and transformed into more furnaces. ( 1000 iron plate ).

But then your production is double than what it was before, it is "2y", 200 iron plate per minute. Thus you only need half the amount of time to create the same quantity of iron (x/2) because 2y * x/2 = y*x ( 5 minutes at 200 plates per minutes makes another 1000 plates )

So really each "step" takes less and less amount of time, x/3 when you have 3 furnace arrays machines and produce 3 times as when you started.

Again , i feel your abstraction is also valid, it's just a different perspective but in game, when you have 2 furnaces array, you don't wait untill you can double the number, and then wait the same time so you can add 4 furnace arrays, you will add them when they are ready, 1 by 1 everytime 1 is available "maybe".

When looking at the in game statistic you can monitor the production per minutes, to make sure when you add a furnace array it reaches the expected level, and therefore know when/if there is a bottleneck that has appeared in the factory and you need to debug before expanding again.