Transient Analysis of a Stochastic Inventory System for Serving Eligible Customers with Reworks


Mohammad Ekramol Islam , Md. Sharif Uddin , Mohammad Ataullah ,

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Volume 7 - December 2018 (12)


this paper presents an inventory system where eligible customers are screened out at the first stage of service. The arrival of demand for fresh items and for rework items follows the Poisson process with parameter and  . From fresh items store, items will be provided to the arrival customer within a negligible service time. We assume that a certain portion of arriving customers will get service with rate  and rest of the arriving customer will be rejected to serve with a rate (1- when inventory level for fresh items reaches to the reorder level s an order takes place which follows exponean an ntial distribution with parameter . The defective items will dysfunction before expire date, a service will be provided once it returns to the service center with parameter . If the store of rework items is full then th,e next case will be served at home as early as possible. We considered two stores in the system one for fresh items and another for returned items. When inventory level is zero then ar,rival cu the stomer will be lost forever. A suitable mathematical model is developed and the solution of the developed model using Markov pa rocess with Rate-matrixisderived. Also the sys,,tems characteristics are numerically illustrated. The validation of the result in this model was coded in Mathematica 11


Inventory, Stochastic model, Re-order level, Replenishment, Reworks, Poisson process, exponential distribution


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