Solving bi-objective bi-item solid transportation problem with fuzzy stochastic constraints involving normal distribution

In today's competitive world, entrepreneurs cannot argue for transporting a single product. It does not provide much profit to the entrepreneur. Due to this reason, multiple products need to be transported from various origins to destinations through various types of conveyances. Real-world decision-making problems are typically phrased as multi-objective optimization problems because they may be effectively described with numerous competing objectives. Many real-life problems have uncertain objective functions and constraints due to incomplete or uncertain information. Such uncertainties are dealt with in fuzzy/interval/stochastic programming. This study explored a novel integrated model bi-objective bi-item solid transportation problem with fuzzy stochastic inequality constraints following a normal distribution. The entrepreneur's objectives are minimizing the transportation cost and duration of transit while maximizing the profit subject to constraints. The chance-constrained technique is applied to transform the uncertainty problem into its equivalent deterministic problem. The deterministic problem is then solved with the proposed method, namely, the global weighted sum method (GWSM), to find the optimal compromise solution. A numerical example is provided to test the efficacy of the method and then is solved using the Lingo 18.0 software. To highlight the proposed method, comparisons of the solution with the existing solution methods are performed. Finally, to understand the sensitivity of parameters in the proposed model, sensitivity analysis (SA) is conducted.