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All factories are producing maximum elements.

T38 capacity 9, total produced, 0, 0 produced turn
T39 capacity 12, total produced 6, 6 produced turn
T40 capacity 15, total produced 15, 9 produced turn

From this, it appears that factories have produced 15 out of a maximum 36 units. Can anyone explain these production figures?

1) factories expand after production
2) on first turn factories produce less or even sometimes nothing

That doesn't explain figures for Ts 39 and 40. If expansion is done after production, still T39 begins with a capacity of 9 yet produces only 6 units. T40 begins with 12 capacity yet produces only 9.

Factory update is after expansion and after production. Also, you get only 80% production from German factories, rounded down.

Turn 38 - 3x3 factories of Pz IVf become 3x3 factories of Pz IVf2 (no production)
Turn 39 - 3x3 factories of Pz IVf2 produce 6 tanks (0.8*3=2.4 rounded down to 2, times 3) and expand to 3x4
Turn 40 - 3x4 factories of Pz IVf2 produce 9 tanks (0.8*4=3.2 rounded down to 3, times 3) and expand to 3x5

A side effect - when you have a lot of small factories and available production percentage lower than 100% (like the Germans do) you lose even more production due to rounding (if the number multiplied by fraction gives fractional value, of course).

80% of 3x3 becomes 67% (6 tanks).
80% of 9 would be 78% (7 tanks).

Yes - much to Rommel's surprise, 6 PzIVf2s will be shipped off to Africa every week.

One of the problems of using a "single front" system to depict a multi-front war is that the allocation of resources to the non-existent other fronts is fixed across the board without consideration for the actual composition of forces or combat situations of these non-existent fronts. In game terms that means that probably too much armor and not enough aircraft are going to the other fronts. Unfortunately you'll have to wait for WitE 2.0 for a better solution to this issue.

Ah, that starts to make sense, thanks all.

Of all things that need to be modeled, material to other fronts should be easy. Doesn't need to be randomized, either (for me.)