Question: Can we inflate an air-bed with a foot-pump on Shabbos for an unexpected guest?
Answer: The Shulchan Aruch (OC 340:8) writes that one can put feathers back into a cushion on Shabbos though one can’t replace it with fresh feathers as this is tikkun mana, fixing an object (See Mishna Berura 340:32). Based on this, R’ Yitzchak Yaakov Weiss (Minchas Yitzchak 6:30) forbids pumping up a mattress on Shabbos, as one is putting ‘new air’ into the mattress. Additionally, one should avoid acts that involve a lot of tircha, exertion on Shabbos.
R’ Pesach Eliyahu Falk (Machazeh Eliyahu 69:2), however disagrees. There is a big difference between a cushion that is considered broken minus its stuffing, and an inflatable mattress, that is more like a water bottle that is supposed to be emptied and filled as needed (See Minchas Shlomo 1:11:5)
Similarly, R’ Bezalel Stern (Betzel Hachachma 4:92:1; 93) writes that one may inflate a mattress on Shabbos. One can’t compare air that has no real substance to feather stuffing (See Igros Moshe CM 2:47:3).
R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 15:89; 34:24) writes that one may only inflate the mattress if it had previously been inflated, though not for the first time it’s been used.In conclusion, while it is ideal to inflate mattresses before Shabbos, one can do so on Shabbos for a guest, especially if the mattress has been used before.