Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment

We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and in...

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Main Authors: ANG, Marcus, SIGMAN, Karl, SONG, Jing-Sheng, ZHANG, Hanqin
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Language:English
Published: Institutional Knowledge at Singapore Management University 2017
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Online Access:https://ink.library.smu.edu.sg/lkcsb_research/5831
https://ink.library.smu.edu.sg/context/lkcsb_research/article/6830/viewcontent/Closed_Form_Approximations_2016_afv.pdf
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spelling sg-smu-ink.lkcsb_research-68302020-04-01T08:56:54Z Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment ANG, Marcus SIGMAN, Karl SONG, Jing-Sheng ZHANG, Hanqin We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times. 2017-06-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/lkcsb_research/5831 info:doi/10.1287/opre.2017.1623 https://ink.library.smu.edu.sg/context/lkcsb_research/article/6830/viewcontent/Closed_Form_Approximations_2016_afv.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection Lee Kong Chian School Of Business eng Institutional Knowledge at Singapore Management University inventory system (r q) policy stochastic leadtime asymptotic analysis heavy traffic limit. Operations and Supply Chain Management
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic inventory system
(r
q) policy
stochastic leadtime
asymptotic analysis
heavy traffic limit.
Operations and Supply Chain Management
spellingShingle inventory system
(r
q) policy
stochastic leadtime
asymptotic analysis
heavy traffic limit.
Operations and Supply Chain Management
ANG, Marcus
SIGMAN, Karl
SONG, Jing-Sheng
ZHANG, Hanqin
Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
description We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times.
format text
author ANG, Marcus
SIGMAN, Karl
SONG, Jing-Sheng
ZHANG, Hanqin
author_facet ANG, Marcus
SIGMAN, Karl
SONG, Jing-Sheng
ZHANG, Hanqin
author_sort ANG, Marcus
title Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
title_short Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
title_full Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
title_fullStr Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
title_full_unstemmed Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment
title_sort closed-form approximations for optimal (r, q) and (s, t) policies in a parallel processing environment
publisher Institutional Knowledge at Singapore Management University
publishDate 2017
url https://ink.library.smu.edu.sg/lkcsb_research/5831
https://ink.library.smu.edu.sg/context/lkcsb_research/article/6830/viewcontent/Closed_Form_Approximations_2016_afv.pdf
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