Gary Grigsby’s War in the West 1943-45 is the most ambitious and detailed computer wargame on the Western Front of World War II ever made. Starting with the Summer 1943 invasions of Sicily and Italy and proceeding through the invasions of France and the drive into Germany, War in the West brings you all the Allied campaigns in Western Europe and the capability to re-fight the Western Front according to your plan.
put the supply mode on - you should have depots on the invasion beaches - as long as they can trace a line of supply (ie you control all the hex route), supply will arrive next turn.
watch out for the gap at the foot of the Adriatic, you can easily lose control so make sure you run naval patrol there.
also - HQs don't set priority for supply delivery, they set the demand for supply consumption
Hexes near and around my amphibious force are red, I have lost control of those naval hexes. Does taking control require a high enough level of air supremacy missions in the area?
you need at least +2 on the interdiction scores. So you can gain that via a naval patrol AD or by sailing your TF into the region and back. Neither actually reduce the enemy interdiction so you will pay a price in shipping but at least the isolation penalty will be lifted