Productivity module examination

[aober93]

Hey,
I have collected some numbers here ,the effect of productivity modules on saving resources (without taken into account the cost of modules and energy production). I have wondered how much resources you actually save and besides whats the production ratios of intermediate products. This is for the biggest production chain of Rocket + Satellite. Has anyone gotten similar results? I may be wrong...

Lets assume the infamous 1Rocket per Minute. Lets also assume, no speed modules. So you need:

~289/sec Copper Ore (without productivity you need ~1421/sec) (you save 1132/sec) (roughly 80% savings)
~563/sec Iron Ore (without productivity you need ~1712/sec) (you save 1149/sec) (roughly 70% savings)
~265/sec Crude Oil (without productivity you need ~900ish/sec) (you save 635/sec) (roughly 70% savings)
~54/sec Coal (without productivity you need ~165/sec) (you save 111/sec) (roughly 70% savings)

Throwing this in: In all required 7473 Buildings, you can spend 21278 Productivity 3 Modules. Aside from requiring 10's of hours to build they cost: (assuming your chain is already full with productivity modules)

~13651864 Copper Ore (without productivity modules you need ~42557479 Copper Ore)
~9980871 Iron Ore (without productivity modules you need ~23300220 Iron Ore)
~6500000 (very roughly) Crude Oil (without productivity modules you need ~16000000 (very roughly) Crude Oil)
~2189394 Coal (without productivity modules you need ~4042960 Coal)
~21278 Alien Artifacts

These Modules inserted require an additional maximum of 3,54 Gigawatt Energy. I dont know how much the average energy consumption is. But my example has all machines busy at 100%. So then the energy should be at the limit i think. This amount of Energy needs solar panels. And for every 100 panels i have 90 accus and like 1 roboport and 10 substations. I think you can remove or add small things and it wont change much at this point. Although you need 59010 solar panels lol. Lets assume that we produce the panels, all the while we insert the production modules. So while producing them we profit from the modules already. But not fully ,im thinking half. To build them we need:

~1100587 Copper with productivity modules (2148343 Copper without productivity modules)
~2461017 Iron with productivity modules (3766701 Iron without productivity modules)
~2000000 Crude Oil with productivity modules (4500000 Crude Oil without productivity modules)
~27441 Coal with productivity modules (46101 Coal without productivity modules)

Summary and time it takes to amortise:
Lets have a rough calculation and assume you produce all 21278 productivity modules without inserting them and also assume a relativly high throughput right of the beginning that is very roughly resembling that from above.
Additionally and more practical ,lets also assume that if we inserted the modules right away and over time and kinda spend evenly, the time and resources required for the modules itself is down like 35% flat. This is because without modules there were 0% saving and with full modules the resource and therefore timesavings are like 70%, and we are looking at the average. This calculation is trivial for many reasons, but its an orientation.
Lets also assume we produce solar panels as from above all the while we insert modules and the resource saving amounts to the same 35% flat because of the same assumption.

Looking at Copper.. How long does it take to produce the modules:
You need 42557479 (for the productivity modules) + 2148343 (for the solar field) Copper Ore (for 21278 modules without them already inserted and a 3,54GW Solarfield). With a high throughput comparable to that of a 1Rocket/min factory of say 300/sec it takes 149019 seconds that is ~41 hours.
Once inserted how much longer does it take to amortise:
You spent 42557479 + 2148343 Copper Ore to build modules and solar. But you now save 1132/sec once you have them all. Now having the above 1Rocket per minute situation. To have saved these it takes 39492 seconds. It amortises after ~11 hours.
Together this is 41hours + 11 hours = 52 hours. For the above case if we insert the modules right away lets deduct 35% flat and we are left with 34 hours.

For all resources this is:
---------------------------------------------
to make: 42557479 + 2148343 Copper Ore and a throughput of 300/sec it takes ~41 hours
to amortise: 42557479 + 2148343 Copper and 1132/sec saved = ~11hours
Sum = 41+11 = 52 minus 35% = 34 hours
--------------------------------------------
to make: 23300220 + 3766701 Iron Ore and a throughput of 300/sec it takes ~25 hours
to amortise: 23300220 + 3766701 Iron and 1149/sec saved = ~7hours
Sum = 25 + 7 = 32 minus 35% = 21 hours
--------------------------------------------
to make: 16000000 + 4500000 (very roughly) Crude Oil and a throughput of 265/sec it takes ~21 hours
to amortise: 16000000 + 4500000 Crude Oil and 635/sec saved = ~9hours
Sum = 21 + 9 = 30 minus 35% = 20 hours
--------------------------------------------
to make: 4042960 + 46101 Coal and a throughput of 54/sec it takes ~21 hours
to amortise: 4042960 + 46101 Coal and 111/sec saved = ~10 hours
Sum = 21 + 10 = 31 minus 35% = 20 hours

So yea, it takes like 34 hours for this high end factory until productivity modules become worthwhile (and that is not even factoring in any other modules). In factories like this with 1000's of buildings you are likely to spend way more time in this. So anything beyond that time is profit. And since smaller factories need less productivity modules, they take linearly less time to make so that in any situation it should be worthwhile. The cost of energy production is only around 10% that of the cost of the modules depending on the resource. I have read in many posts that the cost to make these modules is higher than the reward but i dont think so?? I have one but this is from 2 years old and i think values changed but im not sure.

[aober93]

These are my Production Calculations based on the factory described above.

My calculation is initiated by defining 1,66 Rocket Parts / second , which equals 1 full Rocket per minute. And then its requirements trickle down the production chain. 1 Rocket part done in the rocket silo requires like 10 Rocket Controls, and 1,66 Rocket Parts require 16,6 of them. Factoring in the 40% productivity (16,6 / (1+40%)), 40% more output is created but viceversa less input is required . And it only requires 11,9. And thus 11,9 Rocket Control units /s have to be created in some Assembling machine 3. And to create 11,9 of them ,only 8.5 Blue Circuits/s are required. Again Factoring in 40% productivity. And so on.

Last down the chain 347 Copperplates require 289 Copper Ore when factoring in 20% Productivity, but normally they are 1:1. The assembling speed is 3,5 seconds but the electric smelter has a speed factor of 1,4 when having 2 productivity modules inside. So these have to be multiplied (actually the inverse of 1,4 because a higher speed factor lowers the numer of assemblers required) and this is the speed a machine achieves for a single item without productivity effects (at 60UPS). This is multiplied by how many items are to be created per second, and also multiplied by the (inverse) productivity effect as the 20% production bonus is on top of the given production speed. And this gives you the required amount of machines. 3,5sec * (1/1,4speed factor) * (1/1,2 Production factor) * 347 Units/sec = 722 Machines

347 Copper plates are used by 283 for cables, 48 for Low Density parts, 8,33 for Solar Panels,6,94 for Accumulator

289/sec Copper Ore -> 347/sec Copperplate at 20% Productivity. Timed at 3,5seconds, modified Machine Speed Factor at 1,4. (347/sec*3,5sec/1,4/(1+20%))=723 Machines (Smelting) with 2 Modules each = 1448 Modules
563/sec Iron Ore -> 675/sec Ironplate at 20% Productivity. Timed at 3,5seconds, modified Machine Speed Factor at 1,4. (675/sec*3,5sec/1,4/(1+20%))=1407 Machines (Smelting) with 2 Modules each = 2815 Modules
283/sec Copperplate -> 794/sec Copper Cable at 40% Productivity. Timed at 0,5seconds, modified Machine Speed Factor at 0,5. (794/sec*0,5sec/0,5/(1+40%))=567 Machines with 4 Modules each = 2270 Modules
265/sec Crude Oil -> 175/sec Petroleum at 20% Productivity. Timed at 0,909seconds, modified Machine Speed Factor at 0,7. (175/sec*0,909sec/0,7/(1+20%))=190 Machines (Refinery) with 2 Modules each = 379 Modules
269/sec Crude Oil -> 145/sec Light Oil at 20% Productivity. Timed at 1,111seconds, modified Machine Speed Factor at 0,7. (145/sec*1,111sec/0,7/(1+20%))=192 Machines (Refinery) with 2 Modules each = 384 Modules
266/sec Crude Oil -> 32/sec Heavy Oil at 20% Productivity. Timed at 5seconds, modified Machine Speed Factor at 0,7. (32/sec*5sec/0,7/(1+20%))=190 Machines (Refinery these 3 are 1 refinery) with 2 Modules each = 380 Modules
32/sec Heavy Oil -> 29/sec Light Oil at 20% Productivity. Timed at 1,6666seconds, modified Machine Speed Factor at 0,875. (29/sec*1,666sec/0,875/(1+20%))=45 Machines (Cracking) with 2 Modules each = 91 Modules
98/sec Light Oil -> 78/sec Petroleum at 20% Productivity. Timed at 2,5seconds, modified Machine Speed Factor at 0,875. (78/sec*2,5sec/0,875/(1+20%))=187 Machines (Cracking) with 2 Modules each = 374 Modules
76/sec Light Oil -> 91/sec Solid Fuel at 20% Productivity. Timed at 3seconds, modified Machine Speed Factor at 0,875. (91/sec*3sec/0,875/(1+20%))=260 Machines with 2 Modules each = 520 Modules
91/sec Petroleum -> 73/sec Sulfur at 20% Productivity. Timed at 0,5seconds, modified Machine Speed Factor at 0,875. (73/sec*0,5sec/0,875/(1+20%))=34 Machines with 2 Modules each = 69 Modules
54/sec Coal + 162/sec Petroleum -> 130/sec Plastic at 20% Productivity. Timed at 0,5seconds, modified Machine Speed Factor at 0,875. (130/sec*0,5sec/0,875/(1+20%))=62 Machines with 2 Modules each = 124 Modules
631/sec Copper Cable + 210/sec Iron Plate -> 294/sec Green Circuits at 40% Productivity. Timed at 0,5seconds, modified Machine Speed Factor at 0,5. (294/sec*0,5sec/0,5/(1+40%))=210 Machines with 4 Modules each = 842 Modules
81/sec Green Circuit + 162/sec Copper Cable + 81/sec Plastic -> 57/sec Red Circuits at 40% Productivity. Timed at 8seconds, modified Machine Speed Factor at 0,5. (57/sec*8sec/0,5/(1+40%))=652 Machines with 4 Modules each = 2608 Modules
73/sec Sulfur + 14/sec Iron Plate -> 17/sec Sulfur Acid at 20% Productivity. Timed at 0,2seconds (per 1 item), modified Machine Speed Factor at 0,875. (17/sec*0,2sec/0,5/(1+20%))=3,3 Machines with 2 Modules each = 6,7 Modules
145/sec Green Circuit + 14/sec Red Circuit + 4/sec Sulfur Acid -> 10/sec Blue Circuits (CPU) at 40% Productivity. Timed at 15seconds, modified Machine Speed Factor at 0,5. (10/sec*15sec/0,5/(1+40%))=218 Machines with 4 Modules each = 872 Modules
42/sec Red Circuit + 42/sec Green Circuit -> 9/sec Speed Module 1 at 0% Productivity. Timed at 15seconds, modified Machine Speed Factor at 1,25. (9/sec*15sec/1,25)=102 Machines with 0 Modules each = 0 Modules
9/sec Speed Module 1 + 9/sec Blue Circuits -> 12/sec Rocket Control at 40% Productivity. Timed at 30seconds, modified Machine Speed Factor at 0,5. (12/sec*30sec/0,5/(1+40%))=510 Machines with 4 Modules each = 2041 Modules
438/sec Iron Plates -> 105/sec Steel Bar at 20% Productivity. Timed at 17,5seconds, modified Machine Speed Factor at 1,4. (105/sec*17,5sec/1,4/(1+20%))=1097 Machines (Smelting) with 2 Modules each = 2193 Modules
91/sec Solid Fuel -> 13/sec Rocket Fuel at 40% Productivity. Timed at 30seconds, modified Machine Speed Factor at 0,5. (13/sec*30sec/0,5/(1+40%))=546 Machines with 4 Modules each = 2184 Modules
97/sec Steel Bars + 48/sec Copper Plate + 48/sec Plastic -> 13/sec Low Density Stuff at 40% Productivity. Timed at 30seconds, modified Machine Speed Factor at 0,5. (13/sec*30sec/0,5/(1+40%))=581 Machines with 4 Modules each = 2326 Modules
12/sec Low Density Part + 12/sec Rocket Control + 12/sec Rocket Fuel -> 1,66/sec Rocket Part at 40% Productivity. Timed at 3seconds, modified Machine Speed Factor at 0,4. (1,666/sec*3sec/0,4/(1+40%))=8,9 Machines with 4 Modules each = 36 Modules
8,3/sec Steel Bars + 25/sec Green Circuit + 8,3/sec Copper Plate -> 1,666/sec Solar Panel at 0% Productivity. Timed at 10seconds, modified Machine Speed Factor at 1,25. (1,666/sec*10sec/1,25)=13,3 Machines with 0 Modules each = 0 Modules
7/sec Iron Plate + 7/sec Copper Plate + 14/sec Sulfur Acid -> 8,3/sec Battery at 20% Productivity. Timed at 5seconds, modified Machine Speed Factor at 0,875. (8,3/sec*5sec/0,875/(1+20%))=40 Machines with 2 Modules each = 79 Modules
3,3/sec Iron Plate + 8,3/sec Battery -> 1,66/sec Accumulator at 0% Productivity. Timed at 10seconds, modified Machine Speed Factor at 1,25. (1,66/sec*10sec/1,25)=13,3 Machines with 0 Modules each = 0 Modules
0,41/sec Green Circuit + 1,66/sec Iron Plate (with Gear Wheel) -> 0,083/sec Radar at 0% Productivity. Timed at 0,5seconds, modified Machine Speed Factor at 1,25. (0,083/sec*0,5sec/1,25)=0,033 Machines with 0 Modules each = 0 Modules
1,66/sec Low Density Part + 1,66/sec Solar Panel + 1,66/sec Accumulator + 0,083/sec Radar + 1,666/sec Blue Circuit (CPU) + 0,833/sec Rocket Fuel -> 0,0167/sec Satellit at 0% Productivity. Timed at 3seconds, modified Machine Speed Factor at 1,25. (0,0167/sec*3sec/1,25)=0,04 Machines with 0 Modules each = 0 Modules

[DaveMcW]

In all required 10060 Buildings

This seems really high. Are you using speed beacons to reduce the number of buildings needed?

[Ranakastrasz]

He explicitly said he wasn't using speed modules, so probably not.

Wasn't there a thing about a combo of speed and producitivity gave you more than pure productivity?

[aober93]

This is without speed modules to have an easier calculation. I was only trying to show the benefit of productivity. Speed modules have their own benefits, but i want meant to factor these in. I can disclose my calculation later but i doubt this is visually and mentally attractive? But i will because i hope it helps someone check my results.

However you apply speed modules, you will need less buildings. A rough overview. With 1 beacon and 2 speed modules in it affecting each building and 1 beacon per 6-8 buildings as a highly optimal case, then you will only need 5281 (edit: more like 4000) buildings and these fit 14405 (edit: more like 11000) productivity modules. So requirements for productivity modules about half once you have speed modules.
For those 15000 (edit: more like 11000) productivity modules saved , you will need around 700 beacons and 1400 speed modules. 1 Beacon per 6-8 buildings ,having 5281 buildings.

This is an interesting insight. Because you save productivity modules, you suddenly profit from speed modules. Something you woudnt if you used speed modules on their own right?

[aober93]

In all required 10060 Buildings

This seems really high. Are you using speed beacons to reduce the number of buildings needed?

Right i think its 7374 actually. I have to triple check. This is only productivity and no speed.

[vanatteveldt]

TL;DR: (calculations on) prod modules without speed modules to offset the speed penalty are useless.

I admit I didn't read your complete post, but let me just chip in that prod modules without speed beacons are pretty silly due to the high cost and the way in which the speed boost/penalty and productivity boost are added instead of multiplied.

For a better comparison, I would make either of two assumptions:
- You build one beacon for each assembler, and each assembler is affected by 4 beacons (this is a very easy target, most optimized setups have more like 6-8+ assemblers per beacon), giving +40% prod and +155% speed at the cost of 6 modules per assembler
- You build 3 prod modules and 1 speed module in each assembler3, giving +30% production and +5% speed at the cost of 4 modules per assembler

As you can see, the beacon setup is vastly superior, since it produces more than twice the material (especially with >4 beacons per assembler) with only 50% more module cost, obviously at the cost of power consumption and more complex setup.

For a concrete example, 4 copper + 4 circuit assemblers fill a blue belt when properly boosted (e.g. viewtopic.php?f=18&t=30332&start=10#p192129) , consuming about half the normal copper, which would require (40 * 0.5 / 1.25=)16 circuit assemblers and around 25 cable assemblers without boosting, or an astounding (40 * 0.5 / ((1.25 - .6)*1.4)=)22 cable and 22 circuit assemblers with 4*prod3 modules. So, without speed beacons you require 44*4 = 176 modules, with beacons you require 9*2 + 6*4=50 modules, a saving of 72% (!) on module costs, and I'm pretty sure the boosted result uses less power per unit produced as well.

[bobucles]

The actual payoff for productivity modules depends on how many raw resources it can churn through.

The rocket is a prime example of maximum return. It blasts an entire factory's worth of resources in mere seconds. Every time it eats up hundreds of ore worth of parts you're getting 10% free, so you're getting 10 free ore in the same time a mine is churning out a tiny fraction of free ore.

The important metric here is "resources per second". Anything that grinds more will pay itself off in less time.

[Jupiter]

... This amount of Energy needs solar panels. And for every 100 panels i have 90 accus and like 1 roboport and 10 substations. I think you can remove or add small things and it wont change much at this point. Although you need 59010 solar panels lol.

59010 panels seems too low. May it is enough if every panel produces 60 W but you forgot to include the extra's to charge up your accums. I've done some research myself some time ago and when you account for this the average output of a panel is 42 W. Scaling your number by 60/42 to account for this gives me 84300 solar panels.

This number stills seems low to me because my factory is consuming just under 1 GW (to produce 1 rocket every 10 mins) and it needs around 30k panels (including a couple of hundreds MW as buffer capacity for when I expand).

On another point, the optimal accum/panel ratio is 0.84. This saves you 6.667% of accumulators you would otherwise build. This is equal to 5058 accums if you consider 84300 solar panels (just 6% of no of panels).

[aober93]

Yea thanks and i know that my stuff was visually not appealing but i dont know how to write it down. I could have put it short, like you receive 300% productivity with these modules if used on the whole chain, go figure. I havent found this result anywhere so i guess nobody has done it, so why do you think its worthless? Speed doesnt influence this rate.

First i thought speed just makes it faster, but to realize that speed modules save resources as well was a side effect of this thread. Without it i wouldnt know it. I noted in the 5th post that you can get an easy 50% resource saving on modules with just a rough calculation. Which is kinda astounding. Seeing that the common opinion i received on this forum was ,that speed modules are worthless basically for one or the other reason. And why would speed modules save resources.
But this thread helped me with this. Afaik there is no comprehensive overview to this.

[aober93]

... This amount of Energy needs solar panels. And for every 100 panels i have 90 accus and like 1 roboport and 10 substations. I think you can remove or add small things and it wont change much at this point. Although you need 59010 solar panels lol.

59010 panels seems too low. May it is enough if every panel produces 60 W but you forgot to include the extra's to charge up your accums. I've done some research myself some time ago and when you account for this the average output of a panel is 42 W. Scaling your number by 60/42 to account for this gives me 84300 solar panels.

You are right, i ignored that. It does have an impact like 3% of resource cost for the modules, i wont recalculate it tho.

Btw the 3,54 GW enery was the ADDITIONAL energy required by productivity modules for this product chain. This goes on top of the energy needed by the assemblers normal energy requirement and base defense. This was my basis to calculate the additional resources needed.

[MadZuri]

TL;DR: (calculations on) prod modules without speed modules to offset the speed penalty are useless.

This is absolutely true. The beacon example given is the most effective, but the 1spd3 and 3prod3 per assembler should make overall calculations for the whole system a lot easier. Productivity modules alone vastly increase the energy/item and space/production, and speed modules greatly offset both of those factors. Also, you can fit a solar blueprint with 196 solar, 160ish accumulators, 1 roboport, and 16 substations, for an average power production of 8MW per stamp (that's accounting for the power cost of the port).

My back-of-the-napkin calculations are that speed modules cut the initial investment costs in about half. This would then reduce time to amortize by half as well. Therfore, it start paying for itself after 10 hours for some products, and finished well before 20 hours. If you're running your factory for hundreds of hours, it is well worth the investment.

[Frightning]

The reason speed modules are useless by themselves is that it's cheaper to just parallelize (make more assemblers) than it is to use speed modules to increase throughput. Now, with productivity modules, speed has wonderful synergy, as the speed effect is additive against the speed penalty from the prod modules. They actually end up decreasing energy cost/unit while also greatly speeding up the assembly machine and thus reducing the number of machines that you need to put modules into and thereby greatly reducing resource costs to set up production as well. Thus it amortizes dramatically faster than prod modules alone.

[Helfima]

I have made MOD for these calculation
https://mods.factorio.com/mods/Helfima/helmod
Check my wiki to use

[vanatteveldt]

Yea thanks and i know that my stuff was visually not appealing but i dont know how to write it down. I could have put it short, like you receive 300% productivity with these modules if used on the whole chain, go figure. I havent found this result anywhere so i guess nobody has done it, so why do you think its worthless? Speed doesnt influence this rate.

First i thought speed just makes it faster, but to realize that speed modules save resources as well was a side effect of this thread. Without it i wouldnt know it. I noted in the 5th post that you can get an easy 50% resource saving on modules with just a rough calculation. Which is kinda astounding. Seeing that the common opinion i received on this forum was ,that speed modules are worthless basically for one or the other reason. And why would speed modules save resources.
But this thread helped me with this. Afaik there is no comprehensive overview to this.

Sorry, I didn't mean to say your thread was worthless, I meant purely that looking on any kind of 'return on investment' or amortization of the upfront cost of modules is mostly useful when combining speed and prod modules.

If you look at any of the end game designs floating out there they almost always combine prod modules and speed beacons, as you get insanely fast and resource-efficient factories that way, without having to invest an insane amount of resources building 100 assemblers with 400 prod modules to fill a blue belt with circuits...

The reason speed modules are useless by themselves is that it's cheaper to just parallelize (make more assemblers) than it is to use speed modules to increase throughput. Now, with productivity modules, speed has wonderful synergy, as the speed effect is additive against the speed penalty from the prod modules. They actually end up decreasing energy cost/unit while also greatly speeding up the assembly machine and thus reducing the number of machines that you need to put modules into and thereby greatly reducing resource costs to set up production as well. Thus it amortizes dramatically faster than prod modules alone.

Exactly. It's the double effect of being additive wrt the speed penalty (and -50 + 50 > .5 * 1.5) while the productivity is multiplicative wrt the speed bonus for total output (and 2*1.4 > 1+1+0.4; i.e. +100% speed and +40% producitivity -> 2*1.4=2.8 speedup of output). Of course, giving that beacons don't accept prod modules means that the setup is a fairly mindless "first maximize productivity and then add as many beacons as feasible" (some corner cases excepted)....