In this paper we consider workforce management in repair/maintenance environments in which repairmen are cross-trained to attend more than one type of machine. In this context, we study the machine-repairman problem with heterogeneous machines but with partially cross-trained repairmen. We introduce simple repairman-assignment rules as well as machine-priority rules that are effective in minimizing the machine downtime costs, or balancing the percentage of working machines of different types. We show that static machine priority rules are effective in minimizing systems downtime costs, while a generalized version of the longest queue policy is effective in balancing the percentage of working machines. We also introduce the concept of hidden symmetry in repair environments, and show that the well-known chain repairman skill set structure performs very well in repair environments with hidden symmetry. Finally, we provide insights into the design and control issues of repair/maintenance systems with cross-trained repairmen.machine-repairman problem, quasi-birth-and-death process, cross-training, preemption, myopic approach
We consider a finite-population queueing system with heterogeneous classes of customers and a single server. For the case of nonpreemptive service, we fully characterize the structure of the server's optimal service policy that minimizes the total average customer waiting costs. We show that the optimal service policy may never serve some classes of customers. For those classes that are served, we show that the optimal service policy is a simple static priority policy. We also derive sufficient conditions that determine the optimal priority sequence.
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