Formula for bonus structure calculations

[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 ]