a multi-parametric approach to solid transportation problems under flexible constraints

Transportation is one of the most practical issues in operations research. since the uncertain parameters in the real world are more realistic, in this research, the solid transportation problem with imprecise constraints in flexible conditions and triangular fuzzy cost is taken into consideration. despite the non-deterministic parameters, the problem is transformed into a parametric deterministic form and the function is written accurately by using jaeger's ranking of the fuzzy cost and then by using the two-stage approach and the expectation limits for the supply and demand constraints and vehicles and with the opinion as a decision maker, we have reached the effective answer. one of the positive results of reducing transportation costs is increasing satisfaction as a result of more profit for companies.