Formula for bonus structure calculations

[snakeye]

I have finally created a formula to calculate the benefit for remote mining taking into account cost of the vehicle, maintenance of both the constructor and vehicle. I have a excel spreadsheet also for it. Will update forum very soon with my results. My formula calculates the turns before a Remote mine structure or ship pays off all the ovberhead and for how long you can operate it till the overhead from maintenance is more than the profit, and it works for both ships and bases, decaying asteroids or static ones

[Loser]

Originally posted by snakeye:
I have finally created a formula to calculate the benefit for remote mining taking into account cost of the vehicle, maintenance of both the constructor and vehicle. I have a excel spreadsheet also for it. Will update forum very soon with my results. My formula calculates the turns before a Remote mine structure or ship pays off all the ovberhead and for how long you can operate it till the overhead from maintenance is more than the profit, and it works for both ships and bases, decaying asteroids or static ones

Woot.

[snakeye]

Ok here it goes!

Lets assume the following:
Pr=Production of an asteroid at any given time
Ov=overhead for production [total, will explain further below]
A=production of a mining component[for a resource]
N=number of components on board
P=starting percent bonus of asteroid [for a resource, ie 10%=0.1, 150%=1.5]
T=number of turns currently since the remote mining ship was operational
D=degradation degree. Normaly its a steady 0.01 per turn, but it can also be zero or any value for that matter.
Vm=maintenance cost of the vehicle that will perform the mining
Cm=maintenance of the vehicle that will build the mining vehicle, ie for a ship is anything, for a planet is zero
Tm=turns to move construction vehicle to position, ie for a ship could be from 1 to any, for a ship yard is zero
R=rate of building the mining vehicle. Calculations assume a STATIC value! If the contruction is conducted by a ship, then it is a fixed rate by default. If its constructed via a planet assumes a static [max if you like] population has been achieved.
Vc=mining vehicle cost

The overhead discussed above is:
Ov=Cost_to_move+Cost_to_build+Cost_of_remote_miner or

Ov=Cm*Tm+Cm*RNDUP[Vc/R]+Vc

We also assume the following:
-Player has at least one ship with a shipyard component on. The cost and build time of this ship falls outside the scope of the calculations here.
-Player has already built the ship that he is going to construct BEFORE, so the maintenance cost is known. [sorry guys, thats the only way i know how to get the maintenance values. if someone has a better way, please let me know!]

At any given time, the production on an asteroid is:

Pr1=A*N*P1-Vm

next turn it would be:

Pr2=A*N*P2-Vm

On the T turn it would be:

Pr[T]=A*N*P[T]-Vm [1]

Total product would be the total of the two sides of the equation, or:

Pr[total]=A*N*[P1+P2+...+P[T]]-T*Vm [2]

Now the sum P1+P2+...+P[T] is known since P2=P1-0.01, P3=P2-D or P3=P1-2*D, P[T]=P[T-1]-D or P[T]=P1-[T-1]*D. Replacing on [2] we have:

Pr[total]=A*N*[T*P1-[T-1]*D}-T*Vm

The above will give us the total production for a given resource on an asteroid AFTER turns T have elapsed. Since we want to find out after how many turns the output would have paid off the overhead Ov, we have:

Pr[T] must be equal to Ov[T] or more accurately:

A*N*[T*P1-[T-1]*D}-T*Vm must be equal to Cm*Tm+Cm*RNDUP[Vc/R]+Vc. Solving the above we have:

T=[Ov-D*A*N]/[A*N*P-D*A*N-Vm] [3]

After the above turn, the profit will be "clean" and will have paid off the initial cost.

But equation [1] has another use. We can derive the turn T at which the overhead of maintenance [excluding the initial overhead], is greater than the profit, due to asteroid degredation.

From [1] we have:

Pr[T]=A*N*[P-[T-1]D]-Vm must be greater or equal than zero or

A*N*[P-[T-1]D] - Vm >= 0

or A*N*[P-[T-1]D] >= Vm

or

T =< ROUNDUP[[A*N*P+D-Vm]/[D*A*N]] [4]

That is the Last turn that the remote vehicle will give some profit from a degrading asteroid. If the turn calculated by the [4] is less or equal to the turn calculated from the [3] then you have a very unworthy asteroid!!!!! I would upload the excell spreadsheet for all this [ so you guys can just use the thing!] but dont know how and where! Hope someone can help. Hope this is any use to anyone! But I sure had fun working it out, and yes I do use my spreadsheet since I created it! Best regards to all!

[ May 06, 2003, 14:08: Message edited by: snakeye ]

[snakeye]

I forgot to thank Loser for his/her motivation for me to do this. Took me back to my school days and was a nice trip down memory lane. Thank you again bud. I dont have the graphs on the spreadsheet you requested, but would be nice to create them.

[Loser]

Christ in Drag!

Snakeye you rock! This verbose post belongs in the FAQ, I'd think. I am ecstatic to have this lengthy and complete explanation and even more pleased that you enjoyed pursuing my suggestion. You are more than welcome.

I'm sure someone can tell you where and how to upload that spreadsheet, and I was just joking about the graphs and the rest of the Alro Guthrie gibberish.

[FadingSuns]

Rock! Now this is what I'm talking about, math finally coming in handy for something other than figuring out all the deductions out of my paycheck. Snakeye, this really should go into the FAQ, you've just solved one of those questions that everyone has sooner or later about remote mining. Great job

[Suicide Junkie]

-Player has already built the ship that he is going to construct BEFORE, so the maintenance cost is known. [sorry guys, thats the only way i know how to get the maintenance values. if someone has a better way, please let me know!]

Start at 25%. Subtract your maintenance reduction racial characteristic. (Commonly boosted to 20%; 25%-20% = 5%)
This is your actual maintenance cost per turn.

Multiply you ship's build cost by the above maintenance rate.
If you are looking at a base, rather than a ship, divide by 2.

If you have a crystalline restructuring plant in the system, take off another 5 to 15% depending on tech level.

This is how much you spend each turn for maintenance.