Theorem 1. A solution obtained by the blocking method to the BTP, (P) is optimal.
Proof : Let T0 be the time transportation of a feasible solution of the given problem.
Let W be the time transportation of the feasible solution to the given BTP by
the blocking method. It means that all transportation can be made in the time of W . In
the active table, maximum time is W. As per the Step 3 to 5, W is the minimum time to
transport all items from the origins to destinations.
If T 0 ≥ W , the solution obtained by the blocking method is optimal.
If T 0 < W , it means that all transporting work can be made in the time of T0 and
T 0< W . Therefore, T0 is a time for transportation which is less than W . This is not
possible.
Thus, the time for transportation obtained using the blocking method to the
bottleneck transportation problem is optimal .
Hence the theorem.
The blocking method for solving a BTP is illustrated by the following example.