A Blood Bank Model with Perishable Blood and Demand Impatience

Abstract

Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditionsThis article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact permissions@informs.org.The Publisher does not warrant or guarantee the article's accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright © 2017, The Author(s) Please scroll down for article-it is on subsequent pagesINFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. Abstract. 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 canceled 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 kept in storage, and of the amount of demand for blood (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.

Shot-noise queueing models

“…Solving the first-order differential equation (12), with initial condition φ(0) = 1, immediately gives (10).…”

“…In [12] the following model for a blood bank with perishable blood and demand impatience was studied: Amounts of blood and demands for blood arrive at a blood bank according to two independent compound Poisson processes with jump rates λ b , λ d and with the offered amounts and demanded amounts generically denoted by B and D. If there is enough blood in inventory for a demand, then that demand is instantaneously satisfied; otherwise it is partially satisfied, and not at all if the inventory is empty. Blood has a finite expiration date.…”

Two queues with time-limited polling and workload-dependent service speeds

“…In the recent literature, shot-noise processes have been widely studied in the context of queueing, mathematical finance, and insurance, see, for example, Bar-Lev et al [1] , Bekker [3] , Bekker et al [4] , Blom et al [6] , Dassios and Jang [11] , and Kella and Stadje [15] . However, as far as we know, in polling systems, we are applying the shot-noise process for the first time.…”

A Stochastic Approach to Blood Supply, Demand and Screening in Central Blood Banks - A Review

“…Their engagement has resulted in several papers, (c.f., (Bar-Lev et al, 2009;2017;2017a;2017b;Bar-Lev and Perry, 1989;Bar-Lev et al, 2005;2007;2013;. Other works can be found in (Abolnikov and Dukhovny, 2003;Kopach et al, 2008;Beliën and Forcé, 2012;Civelek et al, 2015;Ghandforoush and Sen, 2010;Karaesmen et al, 2011;Marshall et al, 2004;Sebastian et al, 2012;Shi and Zhao, 2010;Deniz et al, 2010;Blake and Hardy, 2014;Xie et al, 2012).…”