Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers (original) (raw)

Stochastic Inventory System with Reneging of Customers from the Service Facilities

American journal of operational research, 2020

This paper analysis an (s, S) perishable inventory system with postponed demands with service facilities. We assume that customer arrive to the service according to Poisson process with parameter λ. In this system, there is a finite buffer whose capacity varies according to the inventory level at any given time. When the maximum buffer size is reached, further demands join a pool which has finite capacity M (<∞) with probability γ and with probability (1-γ) it is lost forever. When inventory level is larger than the number of customers in the buffer, an external demand can enter the buffer for service. A pooled customer is transferred to the buffer for service at a service completion epoch with probability p if the inventory exceeds s+1 and provided the number of customers in the buffer is less than the number items held in the inventory. It is assumed that initially the inventory level is S. When inventory level reaches s an order for replenishment is placed. The lead time is exponentially distributed with parameter β. When at least one customer is available in the buffer then reneging will be occurred with parameter. We obtain the steady state analysis is made. Some performance measures are obtained and a few numerical illustrations are provided.

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sa...

A Relook at Queueing-Inventory System with Reservation, Cancellation and Common Life Time

2016

ABSTRACT: In this paper, we study an M/M/1 queue with a storage system having capacity S which have a common life time (CLT ), exponentially distributed. On realization of common life time or the first time inventory level drops to zero in a cycle whichever occurs first, a replenishment order is placed so as to bring the inventory level back to S (zero lead time). Customers arrive to the system according to a Poisson process and their service time is exponentially distributed. Reservation of items and cancellation of sold items is permitted before the realization of common life time. Cancellation takes place according to an exponential distribution. In this paper we assume that the time required to cancel the reservation is negligible. When the inventory level becomes zero through service completion or CLT realization, a replenishment order is placed which is realized instantly. We first derive the stationary joint distribution of the queue length and the on-hand inventory in produc...

A queueing-inventory system with two classes of customers

International Journal of Production Economics, 2011

We consider a queueing-inventory system with two classes of customers. Customers arrive at a service facility according to Poisson processes. Service times follow exponential distributions. Each service uses one item in the attached inventory supplied by an outside supplier with exponentially distributed lead time. We find a priority service rule to minimize the long-run expected waiting cost by dynamic programming method and obtain the necessary and sufficient condition for the priority queueinginventory system being stable. Formulating the model as a level-dependent quasi-birth-and-death (QBD) process, we can compute the steady state probability distribution by Bright-Taylor algorithm. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters to the system performance measures.

Comparison of discrete time inventory systems with positive service time and lead time

The Korean Journal of Mathematics, 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto SSS policy where as the second model is based on order placement by a fixed quantity QQQ, where Q=S−sQ=S-sQ=S−s, whenever the inventory level falls to sss. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

Discrete Time Queueing Inventory Models with Inventory Dependent Customer Arrival Under (s; S)

Neural, Parallel, & Scientific Computations, 2020

In this paper, we presents two discrete queueing inventory models with positive service time and lead time where customers arrive according to a Bernoulli process and service time follows a geometric distribution. In model 1, we assume that an arriving customer joins the system only if the number in the queue is less than the number of items in the inventory at that epoch. In model 2, it is assumed that if the inventory level is greater than reorder level, s at the time of arrival of a customer, then he necessarily joins. However, if it is less than or equal to s (but larger than zero) then he joins only if the number of customers present is less than the on hand inventory. We analyse this queueing system using the matrix geometric method and we derive an explicit expression for the stability condition of the model-2. We obtain the steady-state behaviour of these systems and several system performance measures. An average system cost function is constructed for the models and are investigated numerically. The influence of various parameters on the system performances are also discussed through numercal example.

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

Research article, 2018

This paper presents an inventory system where eligible customers are screen out at the first stage of servicing. The arrival of demand for fresh items and for rework items follows Poisson process with parameter λ and β . 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 αλ and rest of the arriving customer will be rejected to serve with a rate (1-α)λ. when inventory level for fresh items reaches to the reorder level s an order takes place which follows exponential distribution with parameter γ. The defective items will dysfunction before expire date, a service will be provided once it returns to the service center with parameter μ. If the store of rework items is full then the 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 arrival customer will be lost forever. A suitable mathematical model is developed and the solution of the developed model using Markov process with Rate-matrix is derived. Also the systems characteristics are numerically illustrated. The validation of the result in this model was coded in Mathematica 11.

DOI 10.1007/s11134-006-8710-5 M/M/1 Queueing systems with inventory

2004

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous re-view and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system.

A multi-server perishable inventory system with negative customer

Computers & Industrial Engineering, 2011

In this paper, we consider a continuous review perishable inventory system with multi-server service facility. In such systems the demanded item is delivered to the customer only after performing some service, such as assembly of parts or installation, etc. Compared to many inventory models in which the inventory is depleted at the demand rate, however in this model, it is depleted, at the rate at which the service is completed. We assume that the arrivals of customers are according to a Markovian arrival process (MAP) and that the service time has exponential distribution. The ordering policy is based on (s, S) policy. The lead time is assumed to have exponential distribution. The customer who finds either all servers are busy or no item (excluding those in service) is in the stock, enters into an orbit of infinite size. These orbiting customers send requests at random time points for possible selection of their demands for service. The interval time between two successive request-time points is assumed to have exponential distribution. In addition to the regular customers, a second flow of negative customers following an independent MAP is also considered so that a negative customer will remove one of the customers from the orbit. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.