Study on possibislitic multiobjective solid transportation problems

The Solid Transportation Problem (STP) arises when bounds are given on three item properties. Usually, these properties are supply, demand, and type of product or mode of transport (conveyance). In this paper, the efficient solutions and stability of multiobjective solid transportation problem (Poss MOSTP) with possibilitic coefficients and / or possibilistic supply quantities and / or possibilistic demand quantities and / or possibilistic conveyances are investigated. We consider the problem by incorporating possibilistic data into the objective functions coefficients, supplies, demands and conveyances. The concept of α-possibly efficient is specified in which the ordinary efficient solution is extended based on the α-cut of a possibilistic variables. A solution of the weighting problem of Poss MOSTP is deduced. A necessary and sufficient condition for such a solution is established. The basic notions like the solvability set and the stability set of the first kind are defined and characterized that's to characterize the parametric optimal solution for the auxiliary problem. An algorithm for the determination of the stability set is proposed. Finally, a numerical example is given to illustrate the aspects of the developed results.