Cost Optimization of a Queueing Inventory System with Two Level Supply mode, Retrial Demands and Multiple Vacations Using Genetic Algorithm

The paper investigates the queueing inventory miniature with single server uses multiple vacations, two-level supply mode with different lead time. Two level supply modes mean stocks can be reloaded from two brokers with distinct lead times and cost. There are two suppliers A and B. The supplier B has lesser lead time than supplier A but higher inventory cost. The second supplier option is considered for fast delivery of articles needed urgently by the customer. The Quasi-Birth-and-Death process employed, analysed, and stationary probabilities are derived using matrix-analytic approach. The effect of the parameters on performance measures are illustrated using graphs and tables. Genetic algorithm is utilized to optimize total cost as 4-dimensional function including size of retrial orbit, maximum inventory level utmost stock level and minimum stock level for orders to both suppliers.