Multi-objective Linear Fractional Solid Transportation Problem with Uncertain Variables

In this paper, the multi-objective linear fractional solid transportation problem (MOLFSTP) under uncertainty is studied, where all parameters are treated as zigzag uncertain variables. For the uncertain MOLFSTP model, the expected value model (EVM) and the optimistic value model (OVM) were established using two different ranking parameters of the uncertainty principle. Using the principal basis of uncertainty, both models are converted to correlated deterministic form and then to a single-objective model using a two-resolution method. Fuzzy programming method using distance minimization and linear membership functions. Next, we use Lingo 17.0 optimization tools to solve a two-model single-objective problem and arrive at a Pareto optimal solution. Lastly, numerical outcomes demonstrate the application of the model and the algorithm.