Fuzzy Transportation Model Technique to Determine the Minimum Total Cost Using a Novel Ranking Function

Abstract

The transportation problem (TP) is employed in many different situations, such as scheduling, performance, spending, plant placement, inventory control, and employee scheduling. When all variables, including supply, demand, and unit transportation costs (TC), are precisely known, effective solutions to the transportation problem can be provided. However, understanding how to investigate the transportation problem in an uncertain environment is essential. Additionally, businesses and organizations should seek the most economical and environmentally friendly forms of transportation, considering the significance of environmental issues and strict environmental legislation. This research employs a novel ranking function to solve the transportation problem (TP), where fuzzy triangular numbers represent the fuzzy demand and supply (DAS). The fuzzy model is transformed and compressed to a crisp model (CM), and the results are compared using the northwest corner method and the least cost method. In addition, a numerical example of the fuzzy transportation model (FTM) is shown.

Keywords

• fuzzy transportation model
• fuzzy set, ranking function
• triangular fuzzy number
• membership function