Decentralized scheduling algorithm to improve the rate of production without increase of stocks of intermediates

'Virtual kanban (VK) system' is presented as a scheduling method of pull-type. VK system is applicable to custom-made products in a large-scale and complex factory with multi-stage production system, such as an application specific integrated circuit (ASIC) manufacturing facility. In the factory, any scheduling method of push-type can hardly improve the production rate without increase of stocks of intermediates. For products whose specifications are known before their orders, a scheduling method of pull-type named kanban system has been developed and succeeded to improve the production rate without increase of stocks of intermediates. Kanban system, however, is not applicable to custom-made products whose specifications are not known before their orders. Furthermore, the effect of processing many lots at a single step simultaneously is not investigated. The simulation of ASIC manufacturing facility demonstrates the usefulness of VK system, and the effect of processing many lots at a single step simultaneously.