Machines interference problem with several operators and several service types that have different priorities

This paper proposes a model for a special case of the machine-repairman problem, which is also known as the machine interference problem (MIP), where each of N identical machines randomly requests several different service types that are provided by a group of K identical operators. Each service type has a different priority and the operators serve the machines according to these priorities. The model allows the calculation of the expected number of machines that are waiting for each type of service, based on the multinomial distribution. The model enables us to determine the optimal number of operators and the optimal queue discipline that minimises the total manufacturing cost per unit (TCU). The paper provides a proof that the sum of the expected number of machines that are waiting for all service types is a constant, and does not depend on the service priorities. The conclusion is that queue discipline has no influence on throughput or loads. To demonstrate the applicability of the model, a theoretical analysis and a real case study are presented.