A production inventory model with deteriorating items and retrial demands

This paper considers a single server perishable inventory system in which customers arrive in a homogeneous Poisson stream. The system has a production unit which produces a single item in an exponentially distributed time interval. At the time of arrival, a customer leads to service if the server is available with a positive level of inventory. Otherwise, the customer goes to a waiting place(orbit) of infinite capacity with pre-determined probability or exits the system with complementary probability. Each customer in the orbit tries to access the server in an exponentially distributed time interval. After every unsuccessful retrial, the customer returns to the orbit with a pre-allotted probability or is lost forever with complementary probability. An algorithmic solution to the problem is obtained using Matrix Analytic Method. The mean number of customer loss before and after entering the system, the rate of successful retrials among overall retrials and some other performance measures of the system are derived. The impacts of system parameters on different measures are numerically studied. A suitable cost function is constructed and the optimum control policy is numerically obtained.