The USSR had about 12 million types of goods. If you cross them over about 1000 possible locations, that gives you 12 billion variables, which according to Cosm

The USSR had about 12 million types of goods. If you cross them over about 1000 possible locations, that gives you 12 billion variables, which according to Cosma would correspond to an optimization problem that would take a thousand years to solve on a modern desktop computer. Modern (commercial and open-source) solvers of linear programming (LP) tackle problems of millions of variables in minutes. Most of those 12 billion variables would be cleared out (e.g. fixed to their lower bound, zero) in a pre-processing step. Problems with variables that are constrained to be integer can take much longer, but they are orders of magnitude more efficient today than a few years ago.