Impact of dampening demand variability in a production/inventory system with multiple retailers

We study a supply chain consisting of a single manufacturer and two retailers. The manufacturer produces goods on a make-to-order basis, while both retailers maintain an inventory and use a periodic replenishment rule. As opposed to the traditional (r, S) policy, where a retailer at the end of each...

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Detalles Bibliográficos
Autores Principales: Van Houdt B., Pérez J.F.
Formato: Capítulo de libro (Book Chapter)
Lenguaje:Inglés (English)
Publicado: Springer Science 2013
Materias:
Acceso en línea:https://repository.urosario.edu.co/handle/10336/28527
https://doi.org/10.1007/978-1-4614-4909-6_11
id ir-10336-28527
recordtype dspace
spelling ir-10336-285272020-08-28T15:50:27Z Impact of dampening demand variability in a production/inventory system with multiple retailers Impacto de atenuar la variabilidad de la demanda en un sistema de producción / inventario con múltiples minoristas Van Houdt B. Pérez J.F. Structured markov chains Supply chain Inventory MSC: primary 60J22 Secondary 90B30 90B05 We study a supply chain consisting of a single manufacturer and two retailers. The manufacturer produces goods on a make-to-order basis, while both retailers maintain an inventory and use a periodic replenishment rule. As opposed to the traditional (r, S) policy, where a retailer at the end of each period orders the demand seen during the previous period, we assume that the retailers dampen their demand variability by smoothing the order size. More specifically, the order placed at the end of a period is equal to ? times the demand seen during the last period plus (1 ? ?) times the previous order size, with ? ? (0, 1] the smoothing parameter. We develop a GI/M/1-type Markov chain with only two nonzero blocks A 0 and A d to analyze this supply chain. The dimension of these blocks prohibits us from computing its rate matrix R in order to obtain the steady state probabilities. Instead we rely on fast numerical methods that exploit the structure of the matrices A 0 and A d , i.e., the power method, the Gauss–Seidel iteration, and GMRES, to approximate the steady state probabilities. Finally, we provide various numerical examples that indicate that the smoothing parameters can be set in such a manner that all the involved parties benefit from smoothing. We consider both homogeneous and heterogeneous settings for the smoothing parameters. 2013 2020-08-28T15:49:16Z info:eu-repo/semantics/bookPart info:eu-repo/semantics/publishedVersion ISBN: 978-1-4614-4908-9 EISBN: 978-1-4614-4909-6 https://repository.urosario.edu.co/handle/10336/28527 https://doi.org/10.1007/978-1-4614-4909-6_11 eng info:eu-repo/semantics/restrictedAccess application/pdf Springer Science Business Media Matrix-Analytic Methods in Stochastic Models
institution EdocUR - Universidad del Rosario
collection DSpace
language Inglés (English)
topic Structured markov chains
Supply chain
Inventory
MSC: primary 60J22
Secondary 90B30
90B05
spellingShingle Structured markov chains
Supply chain
Inventory
MSC: primary 60J22
Secondary 90B30
90B05
Van Houdt B.
Pérez J.F.
Impact of dampening demand variability in a production/inventory system with multiple retailers
description We study a supply chain consisting of a single manufacturer and two retailers. The manufacturer produces goods on a make-to-order basis, while both retailers maintain an inventory and use a periodic replenishment rule. As opposed to the traditional (r, S) policy, where a retailer at the end of each period orders the demand seen during the previous period, we assume that the retailers dampen their demand variability by smoothing the order size. More specifically, the order placed at the end of a period is equal to ? times the demand seen during the last period plus (1 ? ?) times the previous order size, with ? ? (0, 1] the smoothing parameter. We develop a GI/M/1-type Markov chain with only two nonzero blocks A 0 and A d to analyze this supply chain. The dimension of these blocks prohibits us from computing its rate matrix R in order to obtain the steady state probabilities. Instead we rely on fast numerical methods that exploit the structure of the matrices A 0 and A d , i.e., the power method, the Gauss–Seidel iteration, and GMRES, to approximate the steady state probabilities. Finally, we provide various numerical examples that indicate that the smoothing parameters can be set in such a manner that all the involved parties benefit from smoothing. We consider both homogeneous and heterogeneous settings for the smoothing parameters.
format Capítulo de libro (Book Chapter)
author Van Houdt B.
Pérez J.F.
author_facet Van Houdt B.
Pérez J.F.
author_sort Van Houdt B.
title Impact of dampening demand variability in a production/inventory system with multiple retailers
title_short Impact of dampening demand variability in a production/inventory system with multiple retailers
title_full Impact of dampening demand variability in a production/inventory system with multiple retailers
title_fullStr Impact of dampening demand variability in a production/inventory system with multiple retailers
title_full_unstemmed Impact of dampening demand variability in a production/inventory system with multiple retailers
title_sort impact of dampening demand variability in a production/inventory system with multiple retailers
publisher Springer Science
publishDate 2013
url https://repository.urosario.edu.co/handle/10336/28527
https://doi.org/10.1007/978-1-4614-4909-6_11
_version_ 1676708397079068672
score 11,383098