A mathematical programming approach to the machine interference problem with fuzzy parameters

Machine interference is an important problem frequently encountered in production and manufacturing operations such as semiconductor manufacturing and maintenance operations. Due to uncontrollable factors, parameters in the machine interference problem may be fuzzy. This paper proposes a mathematical programming approach to construct the membership function of the performance measure of the machine interference system with the machine breakdown rate and the service rate being fuzzy numbers. On the basis of the extension principle, a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy performance measure at possibility level α. By enumerating different values of α, the membership function of the system performance measure is constructed. A numerical example is solved successfully to demonstrate the validity of the proposed approach. Since the performance measure is completely described by a membership function rather than by a crisp value, the fuzziness of input parameters is conserved completely. Thus more information is provided for designing manufacturing systems. The successful extension of machine interference models to fuzzy environments permits machine interference models to have wider practical applications.