In many areas, due to situational complexity, conceptual imprecision, or informational imperfection, management accounting is faced with a high degree of uncertainty or ambiguity. Many of these uncertainties spring from emotional and or lingual causes. Until the Fuzzy Set Theory (FST) was introduced, people learned how to model these uncertainties arising from the human mind and the environment. The present study explores the applied potentials of fuzzy sets and Genetic Algorithms (GA) in different areas of management accounting, especially logistic issues. Logistic issues in a dynamic business environment primarily involve allocating specific resources to several corresponding consumption destinations. Each resource supplies certain goods, whereas each destination demands certain quantities. In this type of issue, the goal is to identify the most economical transportation route that meets the demand without violating the supply constraints. This paper suggests using fuzzy sets to supply appropriate information regarding price, demand, and other variables. The suggestions include the calculation method of the shortest route with the least cost prices for the distribution cycle (network). Finally, as a solution for this complex problem, a GA in combination with a well-suited fuzzy function is recommended.