First we will investigate your assumption that the sanitation workers perform melacha for individual homeowners on Shabbat.
The workers carry the garbage four amot[2] in a public domain and then deposit it into a private domain (the truck), but this constitutes a melacha only if there is no eiruv in the neighborhood. Regarding the operation of the truck, in many cases, no part of this operation is performed specifically for you or other Jews; the workers would perform the same actions even if none of the Jews in town put out their garbage.[3] However, handling the garbage is a (Rabbinic) violation of muktzeh. Although it is often permitted to take garbage out of the house on Shabbat, that leniency is based on the need to remove a bad smell,[4] which, while important inside a house, is rarely a significant need once the garbage is outside.
If we assume that it is forbidden for a Jew himself to throw garbage into the garbage truck on Shabbat, may non-Jewish workers do so for him? A potential factor for leniency is that the Jewish homeowners do not request – and in this case, presumably do not even care – if the sanitation crew comes specifically on Shabbat.[5] (This might not be true if they have not come for several days, if they never work after sunset or on Sunday, or if residents would have significant hardship or complaints if they did not come on Saturday. In those cases, it might be implicit that the Jewish residents are requesting that they come on Shabbat.[6])
However, this leniency helps only if the work the crew is doing at that time is halachically considered performed for their sake, not for yours. This condition is most commonly fulfilled when the worker is paid per job (kablan), in which case we consider the situation as one in which he is doing the work in order to receive the money to which the results entitle him.[7] If, however, he is paid by the day or by some other unit of time (po’el), he is considered to be paid in order to fulfill the Jew’s requests, whether explicit or implicit, which is forbidden.[8]
Categorizing the status of a sanitation crew is not simple. They are presumably paid by the day/month (po’el), and not, for example, by the amount of garbage they remove. On the other hand, perhaps we should consider the relationship between the homeowners and the municipality. The homeowners pay (usually through municipal taxes) for a host of services, including garbage disposal, which makes the municipality kablanim. The sanitation workers are working directly for the non-Jewish municipality, not for the homeowners, and the workers’ pay scheme is therefore irrelevant. In addition, one can possibly consider the sanitation workers kablanim on different grounds. The Shulchan Aruch[9] rules that a long-term worker whose responsibility is to perform one specific job is equivalent to a kablan. This is the situation in our case, provided the employer does not mind if the worker takes off days here and there as long as the job gets done.
One can argue that it is forbidden for the non-Jew to work for a Jew on the Jew’s property due to marit ayin,[10] as people will think he is violating Shabbat.[11] However, people usually put the garbage cans in the public domain before pickup. One might argue that this is a technicality, as the workers are still clearly doing work for the homeowner. However, since everyone knows that the homeowner has no special arrangement with the crew, and the general setup is permitted, marit ayin is not a problem.[12] We are also not supposed to have non-Jews take things on Shabbat from a Jew’s house, even when there is no intrinsic violation.[13] However, this too is due to marit ayin issues,[14] which should not apply here.
With regard to the Jew’s action of moving the garbage to the curb on Shabbat, there is more to say on this than we can discuss in this context. However, as mentioned, in standard cases, there will be a problem of muktzeh. Therefore, we would clearly recommend to simply take the garbage out to the curb before Shabbat.
There are similar analyses of the topic in Minchat Yitzchak[15] and Teshuvot V’Hanhagot.[16] Note that we have simplified several nuances in these matters. The bottom line is that in standard cases, it is permitted to put out the garbage before Shabbat even when the pickup will be on Shabbat.