A new method for obtaining optimal solution of unbalanced transportation problem (Q2710528)

Considered is a transportation problem with \(m\) origins \(0_1,0_2,\dots, 0_m\) and \(n\) destinations \(D_1,D_2,\) \(\dots, D_n\) having \(a_i> 0\), \(b_j>0\) the amount of a commodity available and required, respectively. The authors show that the condition \(\sum^m_{i=1} a_i= \sum^n_{j=1} b_j\) is not necessary and sufficient for the existence of a feasible solution to the Unbalanced Transportation Problem (UTP). They propose a method for solving the UTP without balancing it. The method is illustrated by numerical examples.