Genetic algorithm in the single server inventory retrial queueing system with time and stock level dependent customer arrival rate

In this paper stock-dependent customer arrival rate and queue size dependent service rate in single server inventory retrial queueing system is discussed. The model consists of finite size queue. Impact of stock level on arrival rate is included in the concerned system. If the stock is positive and server is available, then arriving customer served directly else customer joins queue. If queue space is fully occupied the customer joins infinite size orbit. The orbited customer retrial for service with classical retrial policy. The service rates proportionate the queue size. The (s, Q) replenishment policy is used for stock management. The steady state probabilities are calculated using Quasi birth and death process with matrix geometric approximation. Impact of parameters on performance measures like number of waiting customers and total cost is discussed. Finally genetic algorithm is employed for optimization of total cost and adequate examples are included with graphical presentation. © 2023, The Author(s), under exclusive licence to Bharati Vidyapeeth's Institute of Computer Applications and Management.