Evaluation of performance measures for multi-part, single-product kanban controlled assembly systems with stochastic acquisition and production lead times

We consider the following kanban-controlled, multi-stage production assembly system. A number of raw parts are acquired from various suppliers and assembled into a single product. The raw-part acquisition lead times, the production lead time and demand arrival are all random variables. The raw-part acquisition order is made when the inventory level of the common part buffer, consisting of a number of sets of raw parts where a set of raw parts forms a single product, depletes to a reorder point. A production stage consists of the input queue, the output buffer, and the kanban board. The finished product can be backordered with a given allowable quantity. The problem is to evaluate the various system performance measures for a given set of design parameters: the raw-part batch order size, the common buffer size, the reorder point, the number of kanbans circulating in each production stage. A system is decomposed into a number of semi-autonomous Markov processes. A mathematical model is formulated and an ite...