Comparison of (s, S) and (s, Q) type discrete time queueing inventory model and cost optimization using genetic algorithm with some fuzzy interpretation using PFNs

This research paper examines and compares two discrete queuing inventory models with different replenishment policies and with positive lead time including some fuzzy interpretation. Performance parameters of the models are obtained through the application of quasi birth and death (QBD) Process. The paper presents a significant contribution by integrating fuzzy parameters for comparison of the two models by analysing the influence of different input parameters on performance measures and utilizing the genetic algorithm to optimize the overall cost. In this analysis, all parameters are treated as pentagonal fuzzy numbers (PFNs). Numerical examples in the paper illustrate the impact of these parameters.