A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

R Jayaraman,B Sivakumar,G Arivarignan

doi:10.1155/2012/620960

R Jayaraman, B Sivakumar + Show 1 more

Open Access

https://doi.org/10.1155/2012/620960

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Abstract

A mathematical modelling of a continuous review stochastic inventory system with a single server is carried out in this work. We assume that demand time points form a Poisson process. The life time of each item is assumed to have exponential distribution. We assume(s,S)ordering policy to replenish stock with random lead time. The server goes for a vacation of an exponentially distributed duration at the time of stock depletion and may take subsequent vacation depending on the stock position. The customer who arrives during the stock-out period or during the server vacation is offered a choice of joining a pool which is of finite capacity or leaving the system. The demands in the pool are selected one by one by the server only when the inventory level is aboves, with interval time between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The joint probability distribution of the inventory level and the number of customers in the pool is obtained in the steady-state case. Various system performance measures in the steady state are derived, and the long-run total expected cost rate is calculated.

Highlights

In most of the inventory models considered in the literature, the demanded items are directly delivered from the stock
Sivakumar and Arivarignan [22] considered an inventory model in which the demand occurs according to a Markovian arrival process, lead time has a phase type distribution, life time for the items in the stock has exponential distribution, and the pooled customers are selected exponentially
Since φ(i,k,p,m) denotes the steady state probability when the number of demands in the pool is i, the server status is k, the status of reorder is p, and the inventory level is m, the mean inventory level is given by the server, status of the reorder, and the inventory level, the expected number of customers in the pool is given by ηI = ⎝ mφ(i,0,0,m) +

Summary

Introduction

In most of the inventory models considered in the literature, the demanded items are directly delivered from the stock (if available). In the context of inventory system, any arriving demands during the server vacation either enter a pool or leave the system These pooled customers are selected at a later time, preferably after the stock is replenished. Sivakumar and Arivarignan [22] considered an inventory model in which the demand occurs according to a Markovian arrival process, lead time has a phase type distribution, life time for the items in the stock has exponential distribution, and the pooled customers are selected exponentially. Sivakumar and Arivarignan [24] considered an inventory system with independent Markovian arrival processes for positive and negative demands, exponential lead time for the reorders, exponential life times for each item in the stock, and the pool size is infinite.

Problem Formulation

Analysis

Steady-State Analysis

Cost Analysis

Numerical Illustrations