Perishable Inventory Control in Retrial Service FacilitySemi Markov Decision Process

This article deals the problem of optimally controlling the perishable inventory with exponential perishable rate and exponential lead time in a finite capacity retrial service facility system. Arrival of demands to the system is assumed as Poisson and service times are assumed to follows an exponential distribution. Here, the customers are not allowed to form a queue. A customer who sees the server busy joins the orbit and reattempts the system with exponential distributed time. For the given values of maximum inventory and reorder level, we determine the optimal ordering policy at various instants of time. The system is formulated as a Semi-Markov Decision Process and the optimum inventory control to be employed by using linear programming method so that the long–run expected cost rate is minimized. Numerical examples are provided to illustrate the model.