Application and performance evaluation of assigning shortest mini-max method on trans-shipment problem with flow restriction over some path

Trans-shipment problem is an extension of transportation problem. Like transportation problem, it has a huge application in logistics. Trans-shipment problem may or may not have some additional trans-shipment nodes in addition to the source and destination nodes. In the present paper, we are trying to classify the trans-shipment problem and solve a trans-shipment problem out of these classifications. We convert the trans-shipment problem to a transportation problem and apply the recently introduced assigning shortest mini-max method for dealing the converted trans-shipment problem. The feasible solution obtained in this way is compared with the existing Vogel’s approximation method. Further, we extend this application to deal with a modified trans-shipment problem in which some paths are completely restricted or restricted to a finite limit. Therefore, strategy for solving constrained arcs trans-shipment problem is also discussed. This includes finding the solution of slightly modified trans-shipment problem. We have also found the optimal solution of the trans-shipment problem using the mathematical model of the corresponding transportation problem. The same is also done for the modified trans-shipment problem.