CF: Ophidian

Vice-Admiral Tunguska stood upon the strategium deck of HDMS Atlantia, staring at the verisim actuality sphere that displayed his command. The warship contingent rode at high anchor above 43-Dobre, every one of them keeping perfect station on the Exorcist-class grand cruiser that was his flagship.

The auxilliaries and fleet support vessels were another matter. Half of them were still mustering from across the sector, and he'd been forced to detach Implacable to chase down stragglers and escort them here. In a way, the merchantmen that had arrived on schedule were even more of a headache: they wandered about the system without so much as a by-your-leave, cluttered up vox channels with inane chatter and insisted on sending small craft out between ships. He was certain that at least some of them were providing contraband to the naval crews, but short of ordering every shuttle blown out of the sky if it wasn't sanctioned by a command officer, there wasn't much he could do...



One of the things often forgotten in naval fiction, whether sci-fi, fantasy or historical, is the need for supply chains. In historical or fantasy settings, this is not so much of a problem, as there is virtually always going to be a coast nearby they can 'recquisition' food and water from, if not a friendly port from which to obtain munitions and other supplies. But in space, especially in 40k, with its manpower-intensive technology, things become more problematic. You need to consider keeping a force of millions (quite literally- even a light cruiser's complement can be on the order of 10,000 or so) in air clean enough to breathe, with enough food and water to tide them over until their next resupply. And that resupply could well be months, if not years away, thanks to the ...eccentricities of warp travel, combined with the exigencies of the service.
It can be alleviated somewhat by tithing the local infrastructure whenever you make planetfall, even if the tech base is too crude to support the other needs of the fleet, in much the same way that an age-of-sail captain might put in to a deserted cove to find water. However, that can only work to a certain degree- as air, food and water are not the only needs of a starship: spare parts, other consumable supplies (pots of paint, fabric for uniforms, tools, etc.), fuel, and of course munitions.
Yes, some would put munitions down as 'other consumable supplies', but when it comes to warships (whether mere escorts like frigates and destroyers, or full blown Ships-of-the-Wall such as cruisers and larger), I think it proper to give it a category all its own. After all, without anything to shoot, a warship is just a large, sturdy freighter with an inefficient and wasteful deck plan.

So, we have a general list of what a fleet of warships would need to remain operational, yes?
Actually, no: not quite, anyway. There is one other commodity that would need regular replenishment, and that is crew. Not officers, or even NCOs, necessarily, but crewmen.
An 18th century RN frigate (average complement around 200, officially), could expect to have one death aboard every six days or so, assuming no sickness swept among the crew, and the ship didn't see action. Given that 40k tends towards the grim and bleak, I suspect it is safe to say there would be a higher rate of death per hundred men or so. When you consider that the overall crew complement is much larger, I suspect that most ships (of cruiser size, anyway) see 20 or 30 deaths a week.
Of course, most of these would be amongst freshly pressed ratings: without the experience or training to know how to survive aboard ship, doing the thankless, ridiculously labour intensive and highly dangerous tasks, like scrubbing out and re-galvanizing the ship's central heating from inside the pipes; it isn't surprising they die off quickly, but they are easily replaced by another draft of slave-ratings.

So now we know a fleet needs food, water, fuel, air, spare parts, fresh crew, munitions and miscellaneous other consumables to keep going (those with too much time on their hands can work out which will be the biggest need). To get all of these, it needs a flotilla of fleet colliers to make the run back to the nearest supply depot (be it agri-world, hive-world manufactory or even or forge world) to pick up whatever supplies it is tasked with and then travelling to catch up with the fleet.

Obviously, those supply ships need to be either fast, lucky, or defended. Preferably all three.
Fast ships can make the run in very little time (obviously), reducing the risk of it being ambushed or simply lost. Defended ships (whether by convoy, or their own guns or by an assigned escort) have a chance at fighting off an ambush, but if they are escorted, that means more supplies are needed, so more supply runs, so more danger...

All in all, a neat little problem in logistics...