Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/312844 
Year of Publication: 
2022
Citation: 
[Journal:] Annals of Operations Research [ISSN:] 1572-9338 [Volume:] 331 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 899-921
Publisher: 
Springer US, New York, NY
Abstract: 
We consider a single-item production–inventory system under a base stock policy for inventory control. We model the system as a closed Gordon–Newell network. The population size of the network is equal to the base stock level, which is the sum of the finished goods and work-in-process inventory. Each exogenous demand, which follows a Poisson process, releases a production order for a new unit and increases the amount of the work-in-process inventory. When there are no items in the finished goods inventory available, arriving demand is lost. The replenishment network operates with state dependent service rates, which we assume to be increasing and concave. First, we analyze the queue length behavior of a two node system and provide conditions under which the mean queue length at the production server is convex in the number of customers in the system. We prove that this leads to convexity of a standard cost function. Using Norton's theorem, we are able to generalize our results for arbitrarily large production–inventory systems.
Subjects: 
Production–inventory theory
Lost sales
Second order properties
Queueing network theory
Norton’s theorem
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.