What is utilitarianism and how can it be criticised?

Utilitarianism is the view that the action that one is morally compelled to take in any given situation can be characterised as that which produces the greatest total utility and the smallest total harm. For example, if one must distribute £100 between 5 people, a utilitarian must perform a calculus of utility to determine how to do this, by deciding which course of action would produce the greatest utility. If one person would be so happy to be given the whole £100 that this utility would be greater than that attainable by sharing the money equally, then the utilitarian is morally compelled to do so. A common criticism of utilitarianism is that the calculus of utility is incoherent. It implies that if I enjoy punching people in the face so much that it brings me more utility that it brings pain and unhappiness to whoever I punch, the utilitarian has it that I am morally compelled to punch as many people in the face as possible, and they are morally compelled to let me, but this conclusion is deeply troubling to our moral intuitions.