In 2.7, you cannot create convoys at will -- no automatic generation. Instead, they must be created in the scenario editor. You may want to increase their RCP in order to ensure they can survive more than a pinprick; the defaults leave them extremely vulnerable to bad guys weilding sharp mangos.
(I'm not sure which button you are saying is grayed out, Nils.)
The AI cannot manage logistics in 2.7, and I believe the AI simply plays with it turned off. It's way to complex for the AI to manage.
However, the human player can certainly play logistics while the computer does not.
Step by step (and please let me know where this breaks down; I've worked with this version long enough that I'm likely forgetting something that's hard for you and automatic for me

)
- 2.7 should have come with upgraded scenarios that have some logistics capability. If not...
- Open the scenario in the editor
- Open each side and add convoys, brigade supply battalions, DSBs, etc., using Add/Edit Units
- Check that Logistics is enabled (no "red circle with a line through it" icon, third button from the right hand end of the button bar); you can toggle this via the button or via "Options - Logistics" (remember that the grayed out option is currently active.)
- Save the scenario
- When you open the scenario for playing in whatever mode, you might want to double-check that logistics is set the way you want.
You can transfer supply between (a logistics unit) and (any unit); a log unit has to be in the operation somewhere. Footprints must overlap to transfer supply.
Select the log unit. Click the log management button.
You have an upper list of units: you log units.
You have a lower list of units: all the units whose footprints overlap with the footprint of the unit selected in the upper window.
Between these windows is an "A to B" or "B to A" selector -- transfer from the upper unit to the lower, or vice versa? This also tells you how much supply the receiving unit requires.
Put the amount you want to transfer into the small window at the bottom, and click Apply. Ta-da!
Bugs and troubles:
Sometimes, you click the log management button and DA freezes. Hit alt-tab to bring the log management screen to the front.
Sometimes, you open log management and the data is absent - no units shown. Use the +/- buttons on the log management window to force it to populate.
And, there's some kind of a recursive calculation bug in the unit's requirement that kicks in when they get hammered. This means the amount of supply a unit needs gets smaller and smaller and smaller, and eventually rounds off to zero. It causes two problems:
1) Eventually, the requirement is 0. Any unit listing its current supply state as N/0 should be left alone and not resupplied or DA will crash with a div/0 error.
2) When the requirement is tiny but still non-zero, units will start to report gargantuan percentages of supply on hand. When the unit has, say, 100 point on hand, and a requirement of 0.1 points, it has 1000% supply....
Hope all this helps.