Modeling the Multi-channel Section in the Supply Chain System using the Multiserver Queue Analogy

The industry generally consists of a supply chain system. The main constituents of any supply chain system are suppliers, manufacturers, distribution centers, and retailers. The system configuration can be straight chain, branched, cyclic, or a combination of all. An analytical model is needed to study system behavior as a result of the dynamics of its constituents. Modeling a multi-channel section becomes quite a challenging job in this regard. A method of modeling the multi-channel section will be discussed in this paper by adopting multi-server queues. As is well known, in a multi-server queue, there is a branching point at which the flow of entities begins to spread across several parallel servers. In the modeling perspective of this paper, the branching point is in the buffer (finished good warehouse in the factory, i.e., the focal echelon). That is the end of the waiting line from which the entity specifically moves to one of the servers, or in this context; it is called a channel. In this paper, the number of channels can be any, generalizable, can be more than two. Hence, the subsystem studied includes a factory, finished product warehouse, and several distribution centers. The factory produces by the mechanism of, where and r are stopping point and production restarting point, respectively. Production stops when the quantity of finished product in the warehouse reaches units and will restart the production when the quantity drops to the same or lower than units. The model is developed under Markovian assumptions by considering the quantities of production rates, the number of distribution centers (channels), travel time from factories to each distribution center, delivery lot size, and the time between the arrival of orders from distribution centers. The system under study is seen as a case of two echelons, namely factories and distribution channels. The numerical model obtained is applied to one case example with certain conditions. Comparisons with discrete simulation results give relatively small and acceptable differences. So, in the future, this model can complement the overall modeling of the supply chain system, a multi-echelon system with multi-channel distribution.