On a queueing inventory with common life time and reduction sale consequent to increase in age

Consider an inventoried item for which reduction in sales price is declared as the age of increases. Decision to maintain at same level/reduce, taken stages 2, · , k − 1, k. On items attaining CLT, they are sold scrap value, provided still left stock. Customer arrival forms a non-homogenous Poisson process, with rate increasing each reduction. Service time follows exponential distribution.The replenished according (S, s) policy positive lead time. Each stage CLT iid Phase type distribution representation(α, S) orderm. The k-fold convolution this items. problem modelled queueing-inventory continuous Markov chain (CTMC). stationary CTMC computed and various performance measures discussed. A cost function constructed compute optimal order quantity reorder level.The model compared queueing inventory Erlang Distribution