An Inventory System with Postponed Demands

Abstract

In this article we consider a continuous review perishable inventory system in which the demands arrive according to a Markovian arrival process MAP . The items in the inventory have shelf life times that are assumed to follow an exponential distribution. The inventory is replenished according to an s S policy and the replenishing times are assumed to follow a phase type distribution. The demands that occur during stock out periods either enter a pool which has capacity N < or leave the system. Any demand that arrives when the pool is full and the inventory level is zero, is also assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s with interval time between any two successive selections is distributed as exponential with parameter depending on the number of customers in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are derived and the total expected cost rate is also calculated. The results are illustrated numerically.

A continuous review (<i>s</i>, <i>S</i>) inventory system with postponed demands at service facility

“…dealt with the problem of optimally controlling the service rates for a perishable inventory system with service facility postponed demands and finite waiting hall. Nevertheless, this notion of postponement of work has been introduced into inventory by a few researchers (see Krishnamoorthy and Islam, 2004;Arivarignan et al, 2009;Manuel et al, 2007;Sivakumar and Arivarignan, 2008;Padmavathi et al, 2015). Recently, Venkata and Udayabaskaran (2018) considered a continuous review of single product perishable stochastic inventory system in which a reorder can be placed only after the expiry of a compulsory waiting period even if the inventory position of the system demands an earlier placement of a reorder.…”

Optimal Control Policy of an Inventory System with Postponed Demand

“…Krishnamoorthy and Islam [3] considered an inventory system with Poisson demand, exponential lead time and the pooled customers were selected according to an exponentially distributed time lag. Sivakumar and Arivarignan [9] considered an inventory model in which the demand occurr according to a Markovian arrival process, lead time was distributed as a phase type, exponential life time for the items in the stock and the pooled customers were selected exponentially. Paul Manuel et al [6] dealt an inventory system in which the positive and negative demand occurr according to independent Markovian arrival processes, lead time of the reorder, life time of the items, inter-selection time of customers from the pool and the reneging time points of the customers in the pool were independent exponential distribution.…”

A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

“…Krishnamoorthy and Islam [21] considered an inventory system with Poisson demand, exponential lead time and the pooled customers are selected according to an exponentially distributed time lag. 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. Manuel et al [23] dealt with an inventory system in which the positive and negative demands occur according to an independent Markovian arrival processes, the lead time of the reorder, the life time of the items, the interselection time of customers from the pool and the reneging time points of the customers in the pool are independent, and each has the exponential distribution.…”