https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

An integrated queuing-stochastic optimization hybrid Genetic Algorithm for a location-inventory supply chain network

Inventory with Positive Service Time: a Survey

This paper considers a single-server queueing model in which the customers are served in batches of varying size depending on predetermined thresholds as well as available inventory. There is a finite buffer for the inventory and the service of every customer requires an inventory item. An (s, S) -type inventory system is used for the models considered in this paper. Initially, the model is studied in detail using the matrix-analytic method by assuming all the underlying random variables to be exponentially distributed. Thereafter, an outline of the model in a more general set up is also presented. Due to complexity of the model when more general assumptions are made on the underlying random variables, simulation is opted after a satisfactory validation with the analytic counterpart of the exponential model. Finally, some illustrative numerical examples are also presented to accomplish our analysis.

An ‘( s , S )’ inventory in a queueing system with batch service facility

Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers

In this paper we model a queueing-inventory system that has applications in railway and airline reservation systems. Maximum items in the inventory is $$S$$
 which have a random common life time; this includes those that are sold in particular cycle. A customer, on arrival to an idle server with at least one item in inventory, is immediately taken for service; or else he joins the buffer of maximum size $$S$$
 depending on number of items in the inventory (the buffer capacity varies and is, at any time, equal to the number of items in the inventory). The arrival of customers constitutes a Poisson process, demanding exactly one item each from the inventory. If there is no item in the inventory, the arriving customer first queue up in a finite waiting space of capacity $$K$$
 . When it overflows an arrival goes to an orbit of infinite capacity with probability $$p$$
 or is lost forever with probability $$1-p$$
 . From the orbit he retries for service according to an exponentially distributed inter-occurrence time. The service time follows an exponential distribution. Cancellation of sold items before its expiry is permitted. Inventory gets added through cancellation of purchased items, until the expiry time. Cancellation time is assumed to be negligible. We analyze this system. Several performance characteristics are computed; expected sojourn time of the system in a cycle with “no inventory” and also “maximum inventory” are computed. Some illustrative numerical examples are presented. An optimization problem is numerically analyzed.

On a queueing-inventory with reservation, cancellation, common life time and retrial

In this paper we analyze two single server queueing-inventory systems in which items in the inventory have a random common life time. On realization of common life time, all customers in the system are flushed out. Subsequently the inventory reaches its maximum level S through a (positive lead time) replenishment for the next cycle which follows an exponential distribution. Through cancellation of purchases, inventory gets added until their expiry time; where cancellation time follows exponential distribution. Customers arrive according to a Poisson process and service time is exponentially distributed. On arrival if a customer finds the server busy, then he joins a buffer of varying size. If there is no inventory, the arriving customer first try to queue up in a finite waiting room of capacity K. Finding that at full, he joins a pool of infinite capacity with probability γ (0 < γ < 1); else it is lost to the system forever. We discuss two models based on ‘transfer’ of customers from the pool to the waiting room / buffer. In Model 1 when, at a service completion epoch the waiting room size drops to preassigned number L − 1 (1 < L < K) or below, a customer is transferred from pool to waiting room with probability p (0 < p < 1) and positioned as the last among the waiting customers. If at a departure epoch the waiting room turns out to be empty and there is at least one customer in the pool, then the one ahead of all waiting in the pool gets transferred to the waiting room with probability one. We introduce a totally different transfer mechanism in Model 2: when at a service completion epoch, the server turns idle with at least one item in the inventory, the pooled customer is immediately taken for service. At the time of a cancellation if the server is idle with none, one or more customers in the waiting room, then the head of the pooled customer go to the buffer directly for service. Also we assume that no customer joins the system when there is no item in the inventory. Several system performance measures are obtained. A cost function is discussed for each model and some numerical illustrations are presented. Finally a comparison of the two models are made.

GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time

We attempt to derive the steady-state distribution of the queueing-inventory system with positive service time. First we analyze the case of servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair and the corresponding expected minimum cost are computed. As in the case of retrial queue with , we conjecture that for , queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutive to transitions of the inventory level (i.e., the first return time to ) is computed. We also obtain several system performance measures.

https://downloads.hindawi.com/journals/aor/2015/747328.pdf

Analysis of a Multiserver Queueing-Inventory System

In this paper we consider a single server queueing-inventory system having capacity to store S items which have a common-life time (CLT), exponentially distributed with parameter $$\gamma$$
 . On realization of $${\textit{CLT}}$$
 a replenishment order is placed so as to bring the inventory level back to S, the lead time of which follows exponential distribution with parameter $$\beta$$
 . Items remaining are discarded on realization of $${\textit{CLT}}$$
 . Customers waiting in the system stay back on realization of common life time. Reservation of items and cancellation of sold items before its expiry time is permitted. Cancellation takes place according to an exponentially distributed inter-occurrence time with parameter $$i\theta$$
 when there are $$(S-i)$$
 items in the inventory. In this paper we assume that the time required to cancel the reservation is negligible. Customers arrive according to a Poisson process of rate $$\lambda$$
 and service time follows exponential distribution with parameter $$\mu$$
 . The main assumption that no customer joins the system when inventory level is zero leads to a product form solution of the system state distribution. Several system performance measures are obtained.

Dhanya Shajin

Papers

On a queueing-inventory with reservation, cancellation, common life time and retrial

Inventory with Positive Service Time: a Survey

GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time

Analysis of a Multiserver Queueing-Inventory System

A revisit to queueing-inventory system with reservation, cancellation and common life time