QMCD approach for perishability models: The (S, s) control policy with lead time

We consider cost minimization for an (S, s) continuous-review perishable inventory system with random lead times and times to perishability, and a state-dependent Poisson demand. We derive the stationary distributions for the inventory level using the Queueing and Markov Chain Decomposition (QMCD) methodology. Applying QMCD, we develop an intuitive approach to characterizing the distribution of the residual time for the next event in different states of the system. We provide comprehensive analysis of two main models. The first model assumes a general random lifetime and an exponential distributed lead time. The second model assumes an exponential distributed lifetime and a general lead time. Each model is analyzed under both backordering and lost sales assumptions. We consider a fixed cost for each order, a purchase cost, a holding cost, a cost for perished items, and a penalty cost in the case of shortage. Numerical examples are provided and show that variability of lead time is more costly than that of perishability time. Therefore, after reducing lead time and increasing perishability time, managers should focus on reducing variability of lead time.