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

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dc.contributor.author Gutiérrez Fernández, Miguel
dc.contributor.author Rivera Riquelme, Francisco Antonio
dc.date.accessioned 2021-10-13T10:02:08Z
dc.date.available 2021-10-13T10:02:08Z
dc.date.issued 2021-03
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.
dc.identifier.issn 0307-904X
dc.identifier.uri http://hdl.handle.net/10016/33440
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.
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".
dc.format.extent 24
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Inventory
dc.subject.other Order quantity
dc.subject.other Renewal theory
dc.subject.other Reorder point
dc.subject.other Undershoot
dc.title Undershoot and order quantity probability distributions in periodic review, reorder point, order-up-to-level inventory systems with continuous demand
dc.type article
dc.subject.eciencia Ingeniería Mecánica
dc.identifier.doi https://doi.org/10.1016/j.apm.2020.09.014
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. RTI2018-094614-B-I00
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 791
dc.identifier.publicationlastpage 814
dc.identifier.publicationtitle Applied Mathematical Modelling
dc.identifier.publicationvolume 91
dc.identifier.uxxi AR/0000028314
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades (España)
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