Optimal Solution for Transportation Problems Using Trapezoidal Fuzzy Numbers

Transportation problems (TPs) play important roles in today’s highly competitive world. To maximize profits, organizations are always aiming for more revenue. In this chapter, we present the selecting fuzzy-zero method (SFZM), which can help us to find the optimal solution for minimizing transportation costs while maximizing profit. We present this SFZM to solve a fuzzy transportation problem (FTP), in which demand, supply, and transportation costs (TCs) are trapezoidal fuzzy numbers (TFNs). By using the existing solution methods, we convert these TFNs to fixed values and thus solve the FTP. We also compare the methods of (Hamdy AT. Operations research: an introduction, 8th edn. Pearson Prentice Hall, Upper Saddle River, 2007; Pandian P, Natarajan G. A. Appl Math Sci 4:79–90, 2010; Reinfeld NV, Vogel WR. Mathematical programming. Englewood Cliffs, Prentice-Hall, 1958; Souhail Dhouib. Int J Oper Res Inf Syst 12:1-16, 2022.) with our SFZM. We illustrate how the SFZM works by laying out numerical examples with a working procedure.