The Halacha prohibits instructing a non-Jew to perform melacha on Shabbat. This restriction applies even when the Jew gave the instructions before Shabbat. Nevertheless, it is permitted to engage the non-Jewish worker as a "Kablan," i.e. based on a fixed price per task. As long as the Jew does not specify to perform the work on Shabbat, and the work is not performed on the Jew’s premises, any work done on Shabbat is the Non-Jew’s initiative for his own convenience.
One application of this Halacha is dropping off laundry at the dry cleaners on Friday afternoon. It is permitted to do so since the cleaners is a "Kablan," charging a fixed price per garment. Even if he chooses to do the work on Shabbat, it was not done on the Jew’s premises or at the Jew’s request.
However, the Magen Abraham (Rav Abraham Gombiner, Poland, 1637-1682) holds that dropping off the laundry very close to Shabbat and ordering it to be ready on Mosei Shabbat is prohibited. This is tantamount to instructing the non-Jew to work on Shabbat, since there is no other time he could do it. Hacham Ben Sion Abba Shaul (Israel, 1923-1998) applied this reasoning to prohibit bringing a car for repair at the garage on Friday afternoon, in order to pick it up right after Shabbat.
However, Hacham Ovadia in Yehaveh Da’at (Vol. 3) and Hazon Ovadia (Vol. 1, p. 159) says that the Shulhan Aruch (siman 307) is lenient in such cases, based on the opinion of the Ran, who holds that as long as the Jew did not explicitly tell the non-Jew to execute the task on Shabbat, it is permitted. This is also the opinion of the Minhat Kohen, as well as Rav Yehuda Ayash. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work, Rav Berachot, is also lenient, even though in his halachot he was more stringent. Hacham Ovadia rules that under extenuating circumstances, one may be lenient in accordance with these opinions.
It is important to note that in any case that the workload will be in the hands of the non-Jew over Shabbat, Sepharadim require engaging the non-Jew as a "Kablan," even if the work was submitted before Friday. Ashkenazim are more lenient and do not require this arrangement, if the work was submitted before Friday.
SUMMARY: It is permitted to drop off clothes at the cleaners on Friday afternoon. Under extenuating circumstances, it is even permissible to have the order ready on Mosei Shabbat.
