The term “transportation” is somewhat deceptive it appears to be restricted only to transportation systems, but the case is different. In fact many of the resource allocation problems arising in production systems can be treated as transportation problems. Typical examples are production scheduling, transportation scheduling, etc.
This problem was first introduced by HITCHCOCK (1941) and KOOPMANS (1947), and was solved by DANTZIG (1947) using revised simplex method.
Consider m origins (production centres/warehouses) and n destinations (market places) in a transportation system.
The Origin i (i = 1, 2, … m) has si (si > 0) units of single product ...