A mechanical model for the transportation problem
  We describe a mechanical device which can be used as an analog computer to solve the transportation problem. In practice this device is simulated by a numerical algorithm. Tests show that this algorithm is 60 times faster than a current subroutine (NAG library) for an average 1000 x 1000 problem. Its performance is even better for degenerate problems in which the weights take only a small number of integer values. 
Michel Henon