Developing a M/G/C-FCFS queueing model with continuous review (R, Q) inventory system policy in a cement industry

Queueing models, in which the arrival and/or departure procedure do not follow the Poisson assumption, are more complex and may produce less tractable systematic results. In a production network, each stage or echelon can be portrayed with a lining framework with stock, especially when the procedure is liable to a long sitting tight time for retailers to meet the item. In particular, these problems lead to the uncertainty in demand and lead-time, both of which can be assumed as a probabilistic problem. Therefore, it is vital to create a mechanism to facilitate and reduce the long waiting time in the system. This paper considers an M/G/6-first come first service queueing model under the continued review (R, Q) policy. The DMEI-FCFS model is developed to reduce the long expected waiting time of the retailers in the system. The proposed model is able to reduce the expected waiting time in the system from 13 hours and 30 minutes to 6 hours and 2 minutes. From the model, the optimal expected number of the retailers and also the expected waiting time for both the queue and the system can be determined. Finally, the evaluation of the DMEI-FCFS model is conducted based on the performance measures of the expected waiting time in the system and also sensitivity analysis by using a simulation.