Stock Rationing in an M/Ek/1 Make-to-Stock Queue

This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. When demand is Poisson and processing time has an Erlang distribution, we show that a single-state variable called work storage level can be employed to comp...

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Bibliographic Details
Published inManagement science Vol. 46; no. 1; pp. 77 - 87
Main Author Ha, Albert Y
Format Journal Article
LanguageEnglish
Published Hanover, MD., etc INFORMS 01.01.2000
Institute for Operations Research and the Management Sciences
SeriesManagement Science
Subjects
Applications
Capital costs
Cost efficiency
Dynamic Programming
Dynamic Programming/Optimal Control
Inventories
Inventory
Inventory Rationing
Inventory/Production
Make to stock
Modeling
Optimal Control
Optimal policy
Problem sets
Production
Production systems
Production technology
Rationing
Stocks
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Summary:This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. When demand is Poisson and processing time has an Erlang distribution, we show that a single-state variable called work storage level can be employed to completely capture the information regarding inventory level and the status of current production. The optimal rationing policy can be characterized by a sequence of monotone critical work storage levels. For each demand class, there exists a work storage level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher-priority demands. The optimal production policy can also be characterized by a critical work storage level. Our numerical examples indicate that a critical stock level policy, which ignores information on the status of current production, performs very well.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.46.1.77.15135