Analytical modeling of part supply process in a bin-kanban system with logistic trains

This paper deals with the part supply process in a mixed-model assembly line served by a logistic train. The mixed-model assembly line is made up of a number s of stations each of which is provided with bins of different parts. According to the concept of “bin-kanban”, when a bin becomes empty it represents a request for a replenishment at that station. In this system the empty bins are retrieved by a logistic train that transports them to a centralized warehouse area where they are refilled (supermarket). The duration of a tour of the logistic train is a stochastic variable depending on the number of stations that require a service and the number of bins that must be retrieved or supplied. We assume Poisson arrival processes and exponential service times. The aim of this paper is to analytically model the system described above as a “polling system”, that can be basically defined as a collection of queues served by a single server. In particular, we reformulate the model proposed by Blanc (1992a) for polling systems with limited service disciplines in order to model a polling system where the server has a finite capacity.