The Assignment model is a mathematical model that aims to express a real problem facing factories and companies which is characterized by the guarantee of its activity in order to make the appropriate decision to get the best allocation of machines or jobs or workers on machines in order to increase efficiency or profits to the highest possible level or reduce costs or time To the extent possible, and in this research has been using the method of labeling to solve the problem of the fuzzy assignment of real data has been approved by the tire factory Diwaniya, where the data included two factors are the factors of efficiency and cost, and was solved manually by a number of iterations until reaching the optimization solution, Where this method works on the treatment of Fuzzy by transfer the fuzzy assignment model into a fractional assignment model where the numerator represents maximizing performance and minimizing cost. Results show that the efficiency between the first goal is to maximize the performance to the ratio of the second goal is to reduce the cost (0.49) and cost (3,432,000) million dinars..
