A simple parametric method to generate all optimal solutions of fuzzy solid transportation problem

•A new method is proposed to generate all optimal solutions of the fully fuzzy version of the solid transportation problem.•Auxiliary programs construct the parametric form of the solutions.•A decision maker can attain the level of fuzzy supply–demand–conveyance quantities and also the fuzzy costs.•With our method, it is easy to reflect qualitative factors, market analysis, economic conditions, etc. for making real life decisions. This paper deals with the fuzzy solid transportation problem (FSTP) that has fuzzy cost coefficients, fuzzy supplies, fuzzy demands and fuzzy conveyances. All these fuzzy quantities of FSTP are assumed to be triangular fuzzy numbers. For this problem, we propose an approach to generate all optimal solutions parametrically. The first stage of our approach is to determine the feasibility range based on fuzzy supply–demand–conveyance quantities. In the second stage, the breaking points of fuzzy costs are found by intersecting the membership functions of the fuzzy costs. The last stage constructs the optimal solutions of FSTP by means of some proposed auxiliary programs. Also a numerical example has been provided to illustrate our solution procedure.