The challenge of knapsack in practice

Every item in my house has to be placed in one of three categories: (1) moving to France, (2) going into storage, and (3) to be disposed of. For each item, there is a cost for (1), another smaller cost for (2), and possibly a profit from (3). Each item has a value if it is in France and another value if it is in the US.

This is an instance of combinatorial optimization that is very close to research problems I have worked on, so one would expect that I would be an expert at handling this.

Yet I am paralyzed by indecision. Why? Because every information is "soft". I don't know how to evaluate each item! I don't have a hard bound on the maximum cost of moving! There are too many items for me to be able to ponder carefully the value of each object! In addition, that value depends on the unknown future, and I cannot model it with scenarios and probabilities. That's not how life works.

There will be only a single execution of that algorithm that is my life. Only one future, many unknowns on which it depends, and no probabilistic model to represent it.