The economic number of operators for the machine interference problem with heterogeneous machines and preemptive priority

This paper proposes a model for a special case of the machine interference problem, where several heterogeneous machines that produce the same product randomly request a service provided by a group of operators. Each machine (or a group of identical machines) randomly requests several different service types that are provided by groups of operators, such that each request for a service can be fulfilled by a qualified operator that is assigned to perform only this specific service. Presuming the preemptive priority in service between the heterogeneous machines, the model allows computing of the economic number of operators in the context of different objective functions via the binomial probability function. The advantages of the proposed model are that it is much easier to apply when compared to the Markovian models, and that it does not need any restrictive assumptions about failure rate and service distribution, as those of the Markovian models. To demonstrate the applicability of the model, a theoretical analysis and a real case study are presented.