Non-linear programming for the optimization of machine repair problems in fuzzy environments

Machine repair models have wide applications in many systems such as production line systems and maintenance operations. A procedure is developed to derive the fuzzy objective value of the cost-based machine repair optimization problem, in that the cost coefficients and the machine breakdown rate are fuzzy numbers. On the basis of the extension principle, a pair of non-linear programs are formulated to calculate the lower and upper bounds of the fuzzy minimum expected total cost at the possibility level α. The membership function of the minimum expected total cost is constructed by enumerating different values of α. A numerical example is solved successfully to demonstrate the validity of the proposed method. Since the minimum expected total cost is completely expressed by a membership function rather than by a crisp value, the fuzziness of the input data is conserved, and more information is provided for decision-making. Furthermore, since the optimum repair rate obtained is fuzzy, a crisp optimum repair rate based on the Yager ranking indices is recommended for practical use.