Machine Learning - How to predict set of fixed fields based on past features
It's a supervised classification problem: you're trying to predict the destination (class) based on some categorical features (input columns). I would suggest starting with some simple algorithms such as decision trees or Naive Bayes.

However I'm guessing that logistical shipments can evolve over time: maybe a shipper business grows with country X but decreases with country Y, etc. If this is relevant, it might make sense to look into more advanced methods which could take the chronological evolution into account (time series).