Probabilistic analysis and multicriteria decision for machine assignment problem with general service times

In this paper we carried out a probabilistic analysis for a machine repair system with a general service-time distribution by means of generalized Markov renewal processes. Some formulas for the steady-state performance measures, such as the distribution of queue sizes, average queue length, degree of repairman utilization and so on, are then derived. Finally, the machine repair model and a multiple criteria decision-making method are applied to study machine assignment problem with a general service-time distribution to determine the optimum number of machines being serviced by one repairman.