Korean J. Math.  Vol 29, No 2 (2021)  pp.371-386
DOI: https://doi.org/10.11568/kjm.2021.29.2.371

Comparison of discrete time inventory systems with positive service time and lead time

Balagopal N., Deepthi C. P., Jayaprasad P. N., Varghese Jacob

Abstract


This paper investigates  two discrete time queueing inventory models with positive service time and lead time.  Customers arrive according to a Bernoulli process and service time  and lead time follow  geometric distributions. The first model under discussion based on replenishment of order upto $S$ policy where as the second model  is based on order placement by a fixed quantity $Q$, where $Q=S-s$, whenever the inventory level falls to $s$.  We analyse this queueing systems using the matrix geometric method and   derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems  performance measures and comparison on the cost analysis  are also discussed  through numerical example. 


Keywords


Queueing-inventory system, inventory policy, matrix-geometric method, sta- tionary distributions, cost analysis.

Subject classification

60K25, 90B05, 91B70.

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