One of the greatest weaknesses of utilitarianism is the difficulty of weighing up “the greatest good for the greatest number.” How does one balance the concerns of several people in a community, who are sufficiently perturbed to make complaints but do not seem to be seriously affected by the man sleeping on the bench, with his more immediately pressing interest in having somewhere to sleep?
The police have a moral as well as a legal duty to uphold the law, which prohibits people from sleeping in public. However, they also have a general moral duty not to cause harm. The ethics of care, which emphasize benevolence, would also place this moral duty uppermost.
The ideal solution would be for the police to find the man a better place to sleep. This would benefit everyone, improving his situation and dealing with the concerns of the local residents. In many neighborhoods, the police would be able to find a bed in a hostel or other temporary housing for the man, without his having to pay. This might form the first step in a more long-term solution to his difficulties. Failing this, they might be able to accommodate him at the police station/precinct on a short-term basis. The ethics of care would demand that they consult him to find out what what he feels is in his best interests.