Analysis of the fuzzy machine repair problem with spares using parametric nonlinear programming

Machine repair models find various applications in real-life problems. We carry out a systematic analysis of the classical machine repair problem with N machines and c servers, along with S spares in a fuzzy environment. The machine repair problem is essentially a queueing system with finite calling population. We use trapezoidal membership to model fuzziness in the parameters of the system, namely the service rate and the breakdown (arrival) rate. We propose an approach that uses parametric nonlinear programs to determine the alpha cuts of relevant performance measures of the system. This allows us to construct their membership maps. The problem of determining system characteristics is effectively reduced to an optimization problem. Finally, we present a numerical example to establish the validity of the approach.