The problem is there is no utility function and choices are path dependent.
-"there is no utility function" is an odd claim. A function can obviously be defined, so what's the objection? Note that in any case there is an implicit utility function for which each action you do take has the maximum utility. Of course, there's the recursive problem of choosing the "best" utility function, which just highlights that at some point we stumble upon certain fundamental principles of physics and ethics which are ultimately arbitrary in which we would guide our actions consistently.
Ok, so list its definition in a programming language of your choice.
Utility theory applies when we define "utility" as a linear function of some number of real-valued variables inside a model of the world. For instance, if we say "utility world = sumOfMoney world", then we've defined a VNM utility function.
This doesn't mean that total hedonic utilitarianism possesses any such function, or that we've neatly uncovered any such function which accurately describes the desires of real people. It just means someone wrote down a bit of math that works well for trivial cases.
So here's one utility function (for a company, for example): "Utility = Capital ^ (2/3)". It's one valid utility function (even in accordance to VNM theorem), which is why I don't understand the saying "there is no utility function".
If you read what I wrote in response to gress below, I of course have no hope that utility theory would unveil a good utility function in itself; indeed you cannot do it within mathematics exclusively. I just think it's a useful tool that exposes whatever fundamental motivations you have with clarity. Which again is why I don't see why criticizing utilitarianism is a thing at all.
Because utilitarianism is doing utility-theory consequentialism with the utility function strictly defined to be summed-up quantities of pleasure across the whole population. Utilitarianism doesn't mean "consequentialist, VNM-rational decision making", it means, "the maximally effective way of creating and enforcing pleasure for everyone". It's not the utility function anyone really wants, which is why utility theory is such crap. It doesn't matter to have a coherent mathematical formalism if you get given not the slightest idea how to come up with a good value for the infinite-dimensional free parameter.
What I mean by the utility function being arbitrary is there is no way to derive it from within utility theory, or within mathematics for that matter. In this sense the laws of physics are arbitrary; what you define as good principles of utility are also arbitrary, but that doesn't make them useless -- in fact the stochastic version of the theory is widely applied in decision making and artificial intelligence. It let's you scrutinize the basic principles and act consistently based on that. Not unlike other mathematical tools, it's a way to find the best course of action given a small set of assumptions, and not more than that (i.e. doesn't provide a way to find the assumptions, because it's impossible).
Ultimately we're just certain animals of a species, and things like happiness, ethics, morality, are the outcome of our traits and can't be defined in a vacuum.
As noted, there's also the equality interesting reverse utility theory -- that is, finding utility functions that approximately match our choices. It's just as useful, it shows clearly how we instinctively prioritize things like money, time, feelings; I think it's all quite valuable analysis.