Warning: Lost Mine of Phandelver Chapter 1 spoilers below.
When playing LMOP, my PCs cleared out the the west side of the cave in part 1, namely area #6. They then decided that since the area had only one entry and exit, they would basically just wait there and ambush anybody who came by. They subsequently ambushed two goblins who came to check on the goblins that used to be in that area.
One of my players then pushed the party into moving out, probably because he's also a DM and could see that I was struggling to find a response other than sending more goblins into their ambush.
Had he not done so, what interesting ways could I have used to move the game along?
I have no problem with them playing tactically, but knowing that someone was wiping goblins sent into that part of the cave, I don't think the rest of the goblins in the dungeon would reasonably try to push into it.
Best Answer
You tell or show the party why they need to move on
It is always better to show rather than tell, so I would do something like this:
2 goblins appear coming down the cave, the party ambushes them, and mid-way through that ambush a straggler appears running to catch up to his friends. He sees the fight and runs back into the cave screaming that they are under attack.
You then narrate something like "The goblins are now clearly aware of your presence, you sense that if they simply wait it out they will have potentially several week's worth of supplies, worse with their darkvision they may be gathering strength to attack en-mass during the night when they would have the advantage - what would you like to do?"
If they continue to camp the spot:
Say "24 hours pass and there has been no sign of goblin activity, you are fairly sure they are trying to wait this out and you will need to leave, or press forth. Which do you do?"
Or in the middle of the next night have the now prepared goblins charge the party en-mass. This will lead to a hard fight but remember that the goblins are just trying to drive the party off, so they wouldn't pursue, and would allow a tactical retreat. If the party return maybe the cave has been abandoned.
Also consider why the party are there in the first place
The party are probably there to rescue people, use this to your advantage and narrate something like "You get the sense that every minute that passes brings them - if they are even alive - closer to death.
What if they still insist on camping?
After a reasonable period of time I would either have a few emaciated goblins come out under a peace banner, as a mass attacking force, or narrate "It has now been 6 weeks, you suspect the goblins wouldn't have the discipline to ration so most if not all have probably starved to death by now, you should probably investigate". If they go in maybe they find the corpses of the goblins, maybe one ate his dead brethren and has gone mad. Either way you need to consider the impact those 6 weeks had on the town and the overall campaign, specifically the last boss will have had more time to complete his plans and any time sensitive missions (Such as the aforementioned rescue) will have been failed. The town also won't be happy that your slow tactics potentially caused the deaths of the captives.
Generally it is ok to be slow, and you can't force a party to move on, but give them their win (I wouldn't give them xp for that tactic if I decided to let the goblins starve) and show them the cost of the failed missions.
What if they don't care about the cost and do it at the next cave entrance?
This is probably the time you say "Looks guys and gals, D&D is about adventure, if these are the tactics you are going to use maybe we need to discuss the aims and tone of the campaign", and have a session zero if you haven't already (Or refresh the one you did have).