Undershoot and order quantity probability distributions in periodic review, reorder point, order-up-to-level inventory systems with continuous demand

Gutiérrez Fernández, Miguel; Rivera Riquelme, Francisco Antonio

Publication:
Undershoot and order quantity probability distributions in periodic review, reorder point, order-up-to-level inventory systems with continuous demand

dc.affiliation.area	UC3M. Área de Ingeniería de Organización	es
dc.affiliation.dpto	UC3M. Departamento de Ingeniería Mecánica	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Ingeniería de Organización	es
dc.contributor.author	Gutiérrez Fernández, Miguel
dc.contributor.author	Rivera Riquelme, Francisco Antonio
dc.contributor.funder	Ministerio de Ciencia, Innovación y Universidades (España)	es
dc.date.accessioned	2021-10-13T10:02:08Z
dc.date.available	2021-10-13T10:02:08Z
dc.date.issued	2021-03
dc.description.abstract	The undershoot of the reorder point in the periodic review, order-up-to-level (R, s, S) inventory system is known to follow a complex probability distribution which depends on the value of S-s (Δ) and the distribution of the demand during the review interval (R). We focus on the continuous demand case with full backlogging and variable lead-time. For this case, a generic formulation of the undershoot probability density function (p.d.f.) is developed. The order quantity probability distribution in (R, s, S) systems is the same as the undershoot probability distribution with a shift of Δ in the random variable. Therefore, the latter opens the possibility of calculating valuable managerial information such as the expected average order quantity, its standard deviation, and the probability that the order quantity is lower than or exceeds a predetermined value. Based on the proposed formulation, we derive an analytical expression of the undershoot p.d.f. (and hence the order quantity p.d.f.) for the case of gamma distributed demand, as well as a tractable approximation for the normal distributed demand. Both expressions are shown to be dependent upon two nondimensional parameters, Δ/μR and the coefficient of variation, with the mean demand during the review interval (μR) acting as a scale parameter. We thus define a nondimensional undershoot p.d.f. (NUPDF). The relevance of full nondimensionalization stems from the fact that gamma and normal NUPDF analyses can be scaled to any case of gamma and normal distributed demands. Although we focus on the inventory management viewpoint, the results for the gamma distributed case can be directly adapted for use in any renewal process.	en
dc.description.sponsorship	The authors would like to acknowledge the Spanish Agencia Estatal de Investigacion, for the support provided throughout the research project code RTI2018-094614-B-I00 (SMASHING) into the "Programa Estatal de I+D+i Orientada a los Retos de la Sociedad".	en
dc.format.extent	24
dc.identifier.bibliographicCitation	Gutierrez, M. & Rivera, F. A. (2021). Undershoot and order quantity probability distributions in periodic review, reorder point, order-up-to-level inventory systems with continuous demand. Applied Mathematical Modelling, 91, 791–814.	en
dc.identifier.doi	https://doi.org/10.1016/j.apm.2020.09.014
dc.identifier.issn	0307-904X
dc.identifier.publicationfirstpage	791
dc.identifier.publicationlastpage	814
dc.identifier.publicationtitle	Applied Mathematical Modelling	en
dc.identifier.publicationvolume	91
dc.identifier.uri	https://hdl.handle.net/10016/33440
dc.identifier.uxxi	AR/0000028314
dc.language.iso	eng
dc.publisher	Elsevier	en
dc.relation.projectID	Gobierno de España. RTI2018-094614-B-I00	es
dc.rights	© 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license.	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Ingeniería Mecánica	es
dc.subject.other	Inventory	en
dc.subject.other	Order quantity	en
dc.subject.other	Renewal theory	en
dc.subject.other	Reorder point	en
dc.subject.other	Undershoot	en
dc.title	Undershoot and order quantity probability distributions in periodic review, reorder point, order-up-to-level inventory systems with continuous demand	en
dc.type	research article	*
dc.type.hasVersion	VoR	*
dspace.entity.type	Publication