The Queuing Model for Perishable Inventory with Lost Sale Under Random Demand, Lead Time and Lifetime

This paper we propose a continuous review inventory system for perishable inventory with lost sales. We consider a single demand types and a single unit for placing and depleting the demand. The demand, lead time and life time is random variables according to an exponentially distributed. We develop the inventory system as a Markov process with impatient customer. We formulate the model as a M/M/∞ queuing model given a (r, S) and (r, K) policies. The state of system is a number of on-hand inventories and obtains the limited steady state probability at state n. The limited steady state probability approach is based on a basic rule of the rate of transition out equal to the rate of transition into the state. Numerical results indicate that the model provides no difference of the limited steady state probability comparing to the results of the augmented generator matrix. Furthermore, the results show that the (r, S) policy provides more efficiency than the (r, K) policy as (K > r) on the probability of lost sale (P0) whereas the (r, S) policy provides a larger on-hand inventory than the (r, K) policy as (K > r).