A MAP/PH/1 Production Inventory Model with Perishable Items and Dependent Retrials

Abstract

This article studies a perishable inventory system with a production unit. The production process is governed by (s, S) policy and it is exponentially distributed. The primary arrival follows Markovian arrival process(MAP) and the service time is phase-type distributed random variable. The inventoried items are subject to decay exponentially with a linear rate. A newly arriving customer realizes that system is running out of stock or server busy either moves to infinite waiting space with a pre-assigned probability or exit system with complementary probability. Customers in the waiting space make retrials to access the free server at a linear rate. If the system is running out of stock or the server is busy upon retrial, customers go back to orbit with different pre-defined probabilities according to the level of inventory or exit the system with corresponding complementary probabilities. The system is analysed using Matrix Analytic Method(MAM) and the findings are numerically illustrated.