Analysis of the (Q, r) inventory model for perishables with positive lead times and lost sales

We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q, r) policy, where r < Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q, r) policy with respect to a time-based benchmark policy and find that the (Q, r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.