Retrial Inventory System Research Articles

Modeling, Performance Evaluation and Optimization of (s, Q) Retrial Inventory System with partial backlogging demands: A GSPN Approach

Modeling, Performance Evaluation and Optimization of (s, Q) Retrial Inventory System with partial backlogging demands: A GSPN Approach

An inventory model with self-generation of priorities and retrial of customers

This paper mainly focuses on a single server retrial inventory system. The arrival of customers follows the Poisson process, and when the inventory level depletes to the reorder level s due to service, replenishment order placed according to (s, Q) policy. The lead-time governed by an exponential distribution with parameter β. A customer who finds the server busy or inventory dry moves to an orbit of infinite capacity with probability σ. Customers in orbit independently tries to access the server at a rate of θ, which depends on the number of customers in orbit. A retrial customer returns to the orbit with probability δ if the server is busy or inventory is dry. Each customer in orbit generates priority according to an exponential distribution with rate γ. If the server is free, a priority generated customer will get immediate service. Else such a customer have to wait in a space A 1 of capacity one, which is reserved only for priority generated customers. The service times follows exponential distribution with different rates for ordinary and priority generated customers. The model turned out to be a level-dependent quasi birth-death(LDQBD) process, and we use Matrix-Analytic Method as a tool for obtaining a solution.

<i>MAP/PH</i>(1), <i>PH</i>(2)/2 finite retrial inventory system with service facility, multiple vacations for servers

<i>MAP/PH</i>(1), <i>PH</i>(2)/2 finite retrial inventory system with service facility, multiple vacations for servers

A retrial inventory system with an unreliable server

A retrial inventory system with an unreliable server

A retrial inventory system with an unreliable server

In this paper, we analyse an unreliable (s, S) inventory system with infinite capacity orbit. Customers join the retrial orbit if they are interrupted by a server breakdown and repeatedly attempt to access the server at iid intervals until it is found functioning and idle. We provide stability condition and steady state system size probabilities of the underlying stochastic process. Also, we provide several other characteristics of the system like average waiting time of a customer in the orbit, average number of breakdowns of the server, average duration of a failed service, etc. We obtained a total expected cost function which is optimal in both s and S and provided some numerical illustration.

A retrial inventory system with priority customers and second optional service

In this paper, we investigate a single server (s, Q) perishable inventory model consisting of two priority customers, say, type-1 and type-2. The customers arrival flows are independent Poisson processes, and the service times of the type 1 and type 2 customers are exponentially distributed. The server offers two different types of services - first with ordinary service (essential service) and the second with optional service. The idle server first gives ordinary service to the arriving customers (type 1/type 2). Upon first essential service completion, then the server gives additional service (second optional) only to the type 1 customers. We assume that the type 1 customers have both types of priorities (non-preemptive priority and preemptive priority) over the type 2 customers. We discussed retrial concepts only for type-2 customers. The stationary probability distribution of the inventory level, status of the server, number of customer in the orbit and number of customers in the waiting line are obtained by matrix methods and some numerical illustrations are provided.

Retrial inventory system with multiple working vacations and two types of customers

Retrial inventory system with multiple working vacations and two types of customers

Retrial inventory system with negative customers and service interruptions

In this paper, we consider a single server queueing system wherein demands arrive according to Poisson process, each demanding exactly one unit of inventory item. The operating policy is (s, S) policy in which an order is placed for a quantity up to S whenever the inventory level falls to s. The ordered items are received after a random time which is exponentially distributed. The service may be interrupted according to Poisson process in which case it restarts after an exponentially distributed time. The demands that occur during the server breakdown period or stock-out period may turn out to be ordinary or negative and they enter into the orbit of infinite size. These demands retry after a random time, which is again exponentially distributed. Matrix geometric solution is obtained for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results.

An (s, S) retrial inventory system with impatient and negative customers

In this paper, we consider a continuous review inventory system with an orbit of infinite size. A customer turns out to be an ordinary customer and a negative customer. On arrival, an ordinary customer joins the queue and the negative customer does not join the queue and takes away one waiting customer from the orbit if any. If there is no customer when a negative customer arrives, then the negative customer will be serviced. The customers in the orbit are assumed not only to retry for their demand, but may renege from the orbit after a random time. We consider this situation by assuming Poisson arrivals for both types of customers, exponential lead time for orders placed under (s, S) ordering policy, exponential time between successive attempts of retrial of a customer and exponential times for reneging by customers at the orbit. The condition for ergodicity of the system is obtained. The joint probability distribution of the number of customers in the system and the inventory level is obtained in steady...

A retrial inventory system with single and modified multiple vacation for server

This paper considers a continuous review stochastic (s,S) inventory system with Poisson demand and exponentially distributed delivery time. The demands that occur during the stock out period or during the server vacation period enter into an orbit of infinite size. These orbiting demands retry to get satisfied by sending out signals so that the time durations are exponentially distributed. We consider two models which differ in the way that server go for vacation. The joint probability distribution of the inventory level, the number of demands in the orbit and the server status is obtained in the steady state case. Various system performance measures in the steady state is derived and the long-run total expected cost rate is calculated. Several numerical examples, which provide insight into the behaviour of the cost function, are presented.

A Retrial Inventory System with Non-Preemptive Priority Service

We consider a queueing-inventory system with two types of customers, say, high priority and low priority, arrive according to Poisson processes. The service times are exponentially distributed. The inventory is replenished according to an (s; S) policy and the replenishing times are assumed to be exponentially distributed. Retrial is introduced for low priority customers only. The orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution of the number of customers in the waiting area, the number of customers in the orbit and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived. Several numerical examples are presented to illustrate the effect of the system parameters and costs on these measures.

A continuous review retrial inventory system with impatient customers

This paper examines a retrial inventory system with an orbit of infinite size. An arriving customer, finding the stock out in the system, proceeds to the orbit with probability a and is lost forever with probability (1 – a). The customers in the orbit are assumed not only to retry for their demand, may renege from the orbit at random time. We model this situation by assuming Poisson arrivals for customers, exponential lead time for orders placed under (s, S) ordering policy, exponential time between successive attempts of retrial of a customer and exponential times for reneging by customers at the orbit. The condition for ergodicity of the system is obtained. The joint probability distribution of the number of customers in the system and the inventory level is obtained in steady state case. The measures of system performance in the steady state are derived and the long run total expected cost rate is derived. The results are illustrated with numerical examples.

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.