Analysis of a build-to-order manufacturing system with a standby facility

In recent years, build-to-order manufacturing systems have been increasingly adopted, because of their ability to meet the various needs of customers and progress in Internet businesses. Therefore, it is necessary to construct a build-to-order manufacturing system that is capable of reducing the inventory cost of components and opportunity loss in busy periods and decrease the operating cost of manufacturing facilities and wages for employees in idle periods. Therefore, we consider a build-to-order manufacturing system with a standby facility in addition to a permanent facility, and investigate the performance of the system. In this case, we describe the investigated system as a queueing model with a permanent service counter and a standby service counter that has different functions than the permanent service counter. We adopt the graph technique developed by Billinton and Kumar for the purpose of obtaining the formulae of the steady-state probabilities of the system, and the number of times per unit of time that operation of the standby facilities begins and is ended. Further, optimal operation for the activating time interval of the standby facility is investigated.