From reading discussions on Reddit, the general feeling at the moment is that explorers meet more difficult challenges and find better items the longer they're out on a particular journey. As such, it's not so much a matter of how many explorers you should have out as it is how many dwellers you can train up and equip while still being able to maintain your vault. There also seems to be a special opportunity that comes up after 60h of exploring (but can be passed or failed).
Also, it's not just endurance or luck that help out. All stats seem to have some impact on how the explorer deals with events (e.g. unlocking a box, healing a person), so you should train explorers in multiple stats. The better your explorers' stats, the longer they'll be able to stay out and the more successful they'll be.
TL;DR:
The events during exploration seem to occur according to the elapsed time, discounted the distance covered on any partial return trips.
Since the return speed is double of that of exploring, the time spent returning counts twice as the time going forward. This feature is reflected on the clock that is shown on the top of the screen.
Also, major events occur only once, regardless of how many times you hit their mark.
The Details
To answer my own question, I carried out one of the experiments suggested by Svj0hn in his comment. I sent Jericho exploring for about 59h, recalled him and let him return for 1h and then sent him back exploring again. The path looked something like this -
(*) <----------------------------------------------|vault
59h exploring
(*) ------------> |vault
1h returning (at double the exploring speed)
(*)<------------------ |vault
3h exploring (to reach the 60h reward mark)
At the end of the hike (after the last leg of exploring), the clock showed 60h (2d 12h). It was when the National Guard event occurred (see 4th picture below). Unfortunately to me, I didn't get my legendary loot :(
The Evidence
Below are the relevant screenshots I've taken during the experiment.
This picture below was taken moments before I recalled Jericho, at around 59h (58h 56min) into exploration.
This next one was taken just after I recalled him. Notice that the clock immediately goes down to half the time of exploration, to about 29h (29h28min), meaning that the returning speed is double of that of exploration.
Next one is when I sent Jericho around exploring again, after letting him return for about 1h.
And that's the final picture where we can see when Jericho got to the National Guard Depot, after 3 more hours of exploring, just 3 minutes past the 60h mark.
Conclusion
Given the evidence I have, I can tell that the effects of recalling an explorer in the middle of his trip are the following:
The explorer will return at double the speed of exploring. So, to compensate for 1 hour returning your hero will have to spend 2 more hours exploring. That will be taken into account by the clock on top of the screen.
Regardless of how many times you recalled your explorer in one trip, you'll get the 60th hour reward when the clock gets past 60h of equivalent exploring time. Just remember that, according to Robert Wertz's question and answer (Is it possible to repeatedly trigger sixtieth hour events?), you'll get that reward at most once per trip. That is, you'll need to take the explorer back to the vault and start the trip once more to get the reward again.
Although I haven't tested it, it's likely that other timed events follow the same pattern.
Best Answer
Dwellers will find items every hour in the wastes, plus some time fixed events such as: Broadcast Tower, National Guard, etc.
However, their inventory do have a limit of 100 items. After picking 100 items, they won't pickup anymore, although they show up in the log that they have found something.
SPECIALS do affect the chance of finding items and caps. And their level will increase their HP.
Currently as of update
1.031.1, there's no way to sell or ignore items while exploringPlease refer to the community spread sheet: Fallout Shelter Efficiency Sheet.
SOURCE: REDDIT