Linear Programming applied on Transportation problem

Transportation Problems can be unbalanced:
     capacities≠requirements
     and the constraints functions are inequalities.

Transportation Problems can be balanced:
     capacities=requirements
     and the constraints functions are equalities.

Balanced Problems can be solved by the following algorithms

     First identify basic feasible solutions using:

• North West Rule
• Minimum Cost method
• Penalty Cost (Vogel's approximation)

    Then identify optimal solution, using:

• Stepping Stone
• MODI or UV (Modified distribution)

Minimize        ΣΣ c_ij x_ij

Subject to:     Σx_ij = Σa_i

                      Σx_ij = Σb_j

                      Σa_i=Σb_j

Where:           x_ij = amount transport from I to j

                      c_ij = cost of transport from I to j

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