• Feasible solution:when non negative values of xij where i= 1 , 2 , …m and j= 1 , 2 , …n satisfy the constraints of availability or supply and demand or requirement is called the feasible solution of the transportation problem.
  • Basic feasible solution: it is that feasible solution that contains only m + n -1 non-negative distribution.
  • Optimal solution: when the transportation cost is minimum then the feasible solution is said to be the optimal solution.
  • Balanced transportation problem: a transportation problem in which the total supply from all the sources equals the total demand in all the destinations.

Mathematically, i=1 ʃm ai = j=1ʃn bi

  • Unbalanced transportation problem: such problems which are not balanced are called unbalanced.

Mathematically,   i=1ʃm ai ≠ j=1ʃn bi

  • Matrix terminology: transportation problem is also solved by the matrix system. As we all know in matrix the vertical cells are called columns and horizontal cells as rows.


1                          2                      3                        4

Plants          A               4                          2                      10                      3

B               6                          8                       7                        8

Demand      15                         7                       8                       12


The intersecting point that is row B and column 4 also written as (B, 4) is the unit cost 5.

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