Constrained transportation problem with upper and lower bounds on row-availabilities and destination requirements

Motivated by dead mileage minimization problems in transport systems, the present paper studies a transportation problem with upper and lower bounds on source availabilities and destination demands, where the total flow is specified. Though apparently, it is a generalization of a classical transportation problem, yet it makes the model more important from an application view point. an equivalent transportation problem is constructed which can be handled by standard available techniques and packages and transformations are established which would transform its solution to the solution of the original problem. The proposed technique also identifies the paradoxical solution properties whenever present. A simple illustration in support of the theory is included.