Two stage approach to solve extended transportation problem

The main objective of transportation problem is to minimise the cost of shipping homogeneous commodity from various origins to various destinations. The classical transportation problem is extended by considering multiple incommensurate inputs and outputs for each shipment link. The relative efficiency concept is defined for each possible shipment link. Two linear programming models are proposed to determine the optimal transportation plan with maximum efficiency. A numerical example is discussed to show the applicability of said approach.