I have to go in the opposite direction of the other answers and say that artillery isn't very useful. If you run sims to try and flesh out what is the optimal mix, you will probably find that using artillery is better. However I found that when actually playing the game, tanks have at least 3 significant advantages over artillery.
Retaining their offensive power
When attacking a territory that is well defended, you can count on losing a lot of infantry. Since the third point for offensive power of artillery is dependent on having an accompanying infantry piece, your forces will lose significant offensive power when you start losing those pieces. Since tanks aren't dependent on the infantry, you will retain your offensive power longer.
While this is covered in the simulations, it is important to realize that the simulations favor artillery if you limit the size of the forces by IPCs. If you limit your forces by number of units, tanks fare significantly better than artillery because they retain their power.
Gauging power by IPCs makes sense if you are talking about land battles in Europe, Asia and Africa. However if you are doing amphibious assaults(or your supply of troops comes from the sea) you are going to be limited by the number of transports and therefore the number of ground troops. When you have a navy offshore worth 100 IPCs and another 50 IPCs of aircraft supporting the invasion, I don't think it makes much sense to decrease your ground power just to save 2 or 3 IPCs(especially if you are losing planes to keep the last ground troop alive).
In my experience the main challenge isn't taking a territory but actually holding on to it. While artillery give a boost to offensive power, that extra IPC doesn't do anything for you when defending. Since tanks defend on 3, they also give an added boost for defense.
Moving 2 Spaces/Blitzing
This is the most important advantage. While it is not very important in some theaters, it is critical in the Germany/Russia land war. Artillery will take 1-2 turns longer to get where they need to be than tanks. While the math may show artillery is optimal in these battles, they won't have any value if they're not at the battle.
When I'm playing that theater, I will often purchase a couple turns of infantry, then tanks then fighters and bombers. I try to time it so that when the main battle is fought, all the units from previous turns will be able to participate. If you are running with an optimized infantry/artillery mix, the player on defense is going to have several more turns worth of units in the battle.
While you may purchase a 15 IPC industrial complex in one of the 3 IPC territories to counteract this, it will still take 5 turns of purchasing artillery before you break even and those artillery will still have the above disadvantages.
I get the impression that you are looking more for a math oriented answer to what the optimal ground forces are. My general point is that there is no optimal mixture because everything is too dependent on the situation.
A math based solution isn't capable of taking into account:
- the possibility(and costs) of the opponent's counterattack
- how long it takes to move your forces into position
- the added value of the territory you are conquering(and the loss of it from your opponent)
- the time component(since territories generate IPCs, they are more valuable if conquered sooner than later)
- and probably a bunch of others I haven't thought of