Fractional two-stage transshipment problem under uncertainty: application of the extension principle approach

In this paper, a fuzzy fractional two-stage transshipment problem where all the parameters are represented by fuzzy numbers is studied. The problem uses the ratio of costs divided by benefits as the objective function. A solution method which employs the extension principle is used to find the fuzzy objective value of the problem. For this purpose, the fuzzy fractional two-stage transshipment problem is decomposed into two sub-problems where each of them is tackled individually using various alpha levels to obtain the fuzzy objective function value and its associated membership function. To deal with the nonlinearity of the objective function the Charnes-Cooper transformation method is embedded to the proposed approach. The superior efficiency of the presented formulation and the proposed solution method is examined over a numerical example as well as a case study comparing to the literature.