to me it's logical. first you deploy tanks & infantry and then artilery.
so if oyu want to move forward you should pack artilery in a truck and movie it first then move tanks in adjacent hexagon to protect it from the enemy (by doing this enemy can't reach the artilery by ground).
in fact this kindof movement is quite good as it makes your artilery unit aways safe from any ground attack.
so how to invade a city. move tank in the clear area next to it (prevents them form getting mor ereinforcements). move infantry closer. move packed artilery (or even better if you have those armoured ones) behind tank. move air defence next to artilery or fighter.
let the siege begin. next turn. bomb town (if you have bombers). fire artielry shots. check for their entranchement. if it's low enough andif you can move artielry forwad (bypass the town) then do so. now attack wiht light infantry (multiple attacks is prefered). if your forces get crushed then move them forward near artilery. if you clean the town occupy it. if not try the tanks on the now battered enemy infantry.
if you occupied the town move the tank forward to protect atrilery.
if you had a delay. no worries.... you can pack and move artielry later. they won't be able to fire on next front anyway as they need a turn to deploy.
use parashooters to cause confusion or to prevent the enemy purchasing any units in his cities as reinforcements. if you have a unit near a city no matter which he can not reinforce it or buy new units in them.
usefull if you just occupied one city then another one on your way is about to get fortified with some air defence, infartry, artilery etc. to prevent it all you need is a unit of parachuters (no matter how weak the are).
at lower AI you can also confuse him with parachuters into strengthening defences in the wrong areas/cities.
