Efficient triads related to transportation problem with common pivotal time

Abstract

The present paper discusses a transportation problem with three objectives corresponding to the concept of common pivotal time. There may be a situation when different conflicting objectives have same pivotal time but routes consuming that pivotal time for those objectives are different. This may create a trade-off situation between the objectives over that pivotal time and thus create a desire for the associated efficient solutions. This paper explores such a situation by considering three linear conflicting objectives associated with the transportation problem. An algorithm has been proposed to obtain the desired triads of three objectives corresponding to all common pivotal followed by a theoretical justification. To exhibit the algorithm, a numerical illustration has been given at the end.