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 iterative algorithm is proposed to evaluate system performance measures. Extensive numerical experiments with simulation analyses show that the computational time is very short and the model proposed is reasonably accurate. Thus, resorting to a genetic algorithm we can find an optimal set of system design parameters.