I stumbled on how badly broken the AI is by accident. The premise here is that you can funnel the Orge into a wall of firepower that it finds intimidating. It will freeze up, and not go forward. Then repeated sniping by GEVs will whittle it down. The "4 Howitzer" defense that this is based on isn't my idea -- I vaguely remembered an old magazine article on it, and while trying to recreate it I came upon the strategy presented here and was surprised at the AI's reactions.
(EDIT: found the article http://www.sjgames.com/ogre/articles/fourhwz.html )

Select 4 howitzers, 3 GEVs, and 2 light tanks (infantry will stay with the howitzers)


The howitzers form a funnel, the GEVs stay out of range as a hit-and-run force, and the light tanks...well...let's just say the crews will all get posthumous Orders of Merit.

Use the light tanks to draw missle fire. Stay out of range of the Ogre main gun but in missle range. The Mk III will waste both its missles on the light tanks. (see Japanese Diversionary Force in WW II, especially the Battle of Coral Sea)











Keep your GEVs back until the missles are gone. The Mk III will come forward until it hits "the wall"
At this point, the GEVs do a bunch of hit-and-run snipes at the Ogre's treads. Start five hexes away and under the howitzer umbrella, dart in three hexes, dart back three hexes.
Eventually (20+ turns unless you are lucky) you will take off all the Ogre's treads and win. As you are doing this the Ogre will continue to sit there and take it.

I tested this once on the Mk V scenario, figured this would be harder since it has 6 missiles.
Had 6 light tanks as bait, but couldn't get the Mk V to waste its missiles on them (Yay!).
Sure enough, the Mk V stopped just out of howitzer range. I closed the light tanks in to try and take down the main guns.
Five GEVs left, six missiles for the Mk V? Did it even try to use them? No.
First I got the last main gun, then whittled down the treads as before.
The Mk V was defeated with all six missiles unfired. A human player might have either used the missiles on the GEVs to force a stalemate, or tried to flank one of the howitzer batteries (and risk taking free shots from the howitzer in return for a chance to use the missiles).

It seems like the howitzers form a wall of firepower that the Ogre doesn't want to go through.
I see three issues here:

• Once the Ogre stops, it's locked into a "dead end" strategy and can't see that it will eventually get whittled down by the GEVs.
  
• Saving the missles and charging a pair of howitzers, or even just heading straight fo the command post would be a much better option.
  
• As long as there are GEVs on the board, they can snipe the Ogre with impunity. The counter to this would charge on the the GEVs even though it would mean exposing the Ogre to howitzer fire.

Not wasting missles on light tanks would be a good start. Unlaunched missles will draw fire away from other systems on the Ogre, and I don't think the AI keeps this into account.

Never doing a zero move (at least for the Command Post defense scenarios) would be another improvement. At the very least, not allowing two zero-hex turns in a row would help keep the AI from being stuck in a "local minimum" of decision making.

Another way of fixing this would be, no matter what, to have a small random chance that the Ogre will charge the command post.

A final suggestion would be to have a time limit on these Ogre vs Command Post scenarios, and give the Ogre's decision making more incentive for heading for the Command Post. That is the whole point of the scenario, after all.

(added May 25, 2018)

Been thinking the last few months about the Ogre AI issues in the classic scenarios (Mk III attacking, etc), and it seems like there could be a reasonable solution. Way back in the day, I tried to come up with a pencil-and-dice algorithm to play the classic Ogre solitaire. My notes are long gone, but I've playtested this strategy, below, by playing as both sides and trying different set-ups for the defenders.

Beaking the AI down into a movement algorithm and firing algorithm:

Movement AI: 50% chance of overiding normal orders and take the most direct path towards the CP, ramming units along the way if needed (unless it would take treads to zero)

Firing AI: Missles are on WEAPONS HOLD unless they can hit, in priority order:
1. the CP
2a. a unit that has the highest attack strength armor currently on the board (not just in range)
2b. if no armor left, then only target an infantry stack with the highest combined strength

ex: Defenders deploy a mix of howitzers, GEV, light tanks (see "4 howitzer defense" section in my guide) then the Ogre will hold missles until howitzers are in range.
ex: Defenders have just GEV and light tanks, missiles will target any armor in range
ex: Defenders have heavy tanks and GEV, missiles will only target heavy tanks if in range
ex. Defenders have howitzers but the CP is in missile range, missiles will only target CP

Holding the missiles until a worthwhile target is in range might draw fire away from other Ogre systems (treads and main gun). I'm trying to mimic how a human player would solve this issue.

The Ogre is the strongest unit on the board, and it's unpredicability is an asset (see "Madman theory"). About 50% of the time, charging the CP is the best strategy. Also adding some randomness to the Ogre strategy keeps snarky gamers from posting guides on how to develop strategies for killing Ogres!

I like the Ogre game family a whole lot. I really enjoyed the classic "microgames", and felt that they packed lots of variety in a small rule set. I was excited that the computer version of this was released, and want to see the AI get the treatment that it deserves.
EDIT On 10 July 2018 I tested this again, and managed to get lucky with the Ogre's missile rolls and only lost one light tank. Its first missile shot only disabled a tank. So did it switch fire to the other one and clean up the disabled tank with the main gun next turn? No. Second missile killed the first light tank, leaving the second light tank able to flee,