A transportation problem with m origins and n destinations becomes a trans-shipment problem with

The correct answer is (m + n) sources and (m + n) destinations.

Key Points

• In case of transportation problems, the amount to be sent from each origin, the amount to be received at each destination, and the cost per unit shipped from any origin to any destination are specified and transshipment is not considered.
• Thus each point acts as a shipper only or as a receiver only. We may extend this problem to permit transshipment with the additional feature that shipments may go via any sequence of points rather than being restricted to direct connections from one origin to one of the destinations. 
• Suppose that, we have m origins and n destinations. Since in a transshipment problem, any origin or destination can ship to any other origin or destination it would be convenient to number them successively so that the origins are numbered from 1 to m and the destinations from m + 1 to m + n.

So, A transportation problem with m origins and n destinations becomes a trans-shipment problem with (m+n) sources and (m+ n) destinations.

Additional Information 
Transportation problems:

• A transportation problem refers to a class of linear programming problems that involves the selection of the most economical shipping routes for the transfer of a uniform commodity from a number of sources to a number of destinations.
• In case of an unbalanced transportation problem, the total availability is not equal the to total demand, thus some of the source and/or destination constraints are satisfied as inequalities.

Trans-shipment problems:

• In the transshipment problem, all the sources and destinations can function in any direction.
• Usually, in the absence of the transshipment, the transportation cost goes higher. Hence transshipment is also very useful for the transportation cost.
• Both the transportation problem and the transshipment problem are also quite widely used for planning bulk distribution.

Hence, the correct answer is (m+n) sources and (m+ n) destinations.