Two perishable inventory systems with one-way substitution

Motivated by the ABO issue of the blood banks system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems -- PIS A and PIS B, are correlated to each other through a so-called one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. Such a one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Hence, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demands process, we develop a unified approach to efficiently and accurately approximate the performance of PIS A. The effectiveness of the approach is investigated by extensive numerical experiments

Simulation Model of Infinite Perishable Queueing Inventory System with Feedback

Perishable Queuing Inventory system with positive service time and customer feedback is considered. The system applies Variable Size Order policy for the inventory replenishment. Stochastic simulation method is used to calculate the system performance measures and find its stationary distribution. The dependence of performance measures on the reorder level is illustrated and analyzed using the numerical experiments.Цель статьи. Предложена имитационная модель системы обслуживания-запасания с положительным временем обслуживания, бесконечной очередью, бесконечной орбитой и обратной связью. В системе обслуживаются заявки двух типов и используется стратегия пополнения запасов с переменным объемом заказов. Время выполнения заказов — случайная величина с показательной функцией распределения.Мета статті. Запропоновано імітаційну модель системи обслуговування-запасання з позитивним часом обслуговування, нескінченною чергою, нескінченною орбітою і зворотним зв’язком. В системі обслуговуються заявки двох типів і використовується стратегія поповнення запасів із змінним обсягом замовлень. Час виконання замовлень є випадковою величиною з показовою функцією розподілу

A blood bank model with perishable blood and demand impatience

We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of time. Furthermore, demand for blood is impatient, i.e., a demand for blood may be cancelled if it cannot be satisfied soon enough. For a range of perishability functions and demand impatience functions, we derive the steady-state distributions of the amount of blood Xb kept in storage, and of the amount of demand for blood Xd (at any point in time, at most one of these quantities is positive). Under certain conditions we also obtain the fluid and diffusion limits of the blood inventory process, showing in particular that the diffusion limit process is an Ornstein-Uhlenbeck process

Diffusion Models for Double-ended Queues with Renewal Arrival Processes

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits

Grocery omnichannel perishable inventories: performance measures and influencing factors

Purpose- Perishable inventory management for the grocery sector has become more challenging with extended omnichannel activities and emerging consumer expectations. This paper aims to identify and formalize key performance measures of omnichannel perishable inventory management (OCPI) and explore the influence of operational and market-related factors on these measures. Design/methodology/approach- The inductive approach of this research synthesizes three performance measures (product waste, lost sales and freshness) and four influencing factors (channel effect, demand variability, product perishability and shelf life visibility) for OCPI, through industry investigation, expert interviews and a systematic literature review. Treating OCPI as a complex adaptive system and considering its transaction costs, this paper formalizes the OCPI performance measures and their influencing factors in two statements and four propositions, which are then tested through numerical analysis with simulation. Findings- Product waste, lost sales and freshness are identified as distinctive OCPI performance measures, which are influenced by product perishability, shelf life visibility, demand variability and channel effects. The OCPI sensitivity to those influencing factors is diverse, whereas those factors are found to moderate each other's effects. Practical implications- To manage perishables more effectively, with less waste and lost sales for the business and fresher products for the consumer, omnichannel firms need to consider store and online channel requirements and strive to reduce demand variability, extend product shelf life and facilitate item-level shelf life visibility. While flexible logistics capacity and dynamic pricing can mitigate demand variability, the product shelf life extension needs modifications in product design, production, or storage conditions. OCPI executives can also increase the product shelf life visibility through advanced stock monitoring/tracking technologies (e.g. smart tags or more comprehensive barcodes), particularly for the online channel which demands fresher products. Originality/value- This paper provides a novel theoretical view on perishables in omnichannel systems. It specifies the OCPI performance, beyond typical inventory policies for cost minimization, while discussing its sensitivity to operations and market factors

A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations

This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a finite-size waiting area, and a storage area containing S items. The service time is distributed exponentially. If each server finds that there are an insufficient number of customers and items in the system after the busy period, they start a vacation. Once the servers vacation is over and it recognizes there is no chance of getting busy, it goes into an idle state if the number of customers or items is not sufficient, otherwise, it will take another vacation. Furthermore, each server's vacation period occurs independently of the other servers. The system accepts a (s, Q) control policy for inventory replenishment. For the steady state analysis, the Marcel F Neuts and B Madhu Rao matrix geometric approximation approach is used owing to the structure of an infinitesimal generator matrix. The necessary stability condition and R matrix are to be computed and presented. After calculating the sufficient system performance measures, an expected total cost of the system is to be constructed and numerically incorporated with the parameters. Additionally, numerical analyses will be conducted to examine the waiting time of customers in the queue and in orbit, as well as the expected rate of customer loss.Comment: 43 pages, 12 figures, 5 table

Optimal Supply & Demand Balance In Service Environments

We study service environments that can be modeled as stochastic finite-capacity double-ended queues, where supply and demand arrive in independent Poisson processes to be instantly paired-off. In the case where throughput (output rate) is not a significant metric of system performance (as typically studied in the literature), we derive analytical results to gain managerial insights. We find that the operational decision on optimal supply/demand balance and the strategic decision on how to achieve that optimal balance can be decoupled and stratified. With the purpose of providing a managerial guide, we identify conditions for when to manipulate demand rather than supply, and vice versa. For the first time in the literature, we study throughput considerations in this context, and we analytically characterize the optimal strategy. Specifically, we show that it is optimal to manipulate either demand, or supply (and not both), and that the optimal system balance and the strategy on how to achieve it are strongly tied. Our findings can shed light on the managerial decision making process in these environments, and they can be used to revisit any governing strategies dictating management of demand (or supply) as a first course of action