Which algorithm to use for efficient resource assignment?
For the most part, this probably doesn't need a ML solution. Instead it'll probably be based on assigning rules based on business logic. For example, If the Customer is from a certain country, assign +5 points. Then the tickets are assigned out based on that.

This way, it captures a lot of information and goals you're wanting to achieve as business.

If you wanted to go down the ML route, my hunch is a model such as RandomForest or a tree based solution would be helpful as they're relatively explainable. At least as a starting point.

Uber Engineering team talk about how they prioritize their tickets here, which is an interesting read.