Structural properties of the lost sales problem with fractional lead times

Y. Xu; Sang Phil Kim; A. Bisi; Suresh Chand; Maqbool Dada

doi:10.1016/j.orl.2019.07.008

Structural properties of the lost sales problem with fractional lead times

Y. Xu, Sang Phil Kim, A. Bisi, Suresh Chand, Maqbool Dada

Carey Business School

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L, is placed to bring the inventory position to R. Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R, review period T, and lead time L. Then, we develop an algorithm to find the optimal stationary R. Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T.

Original language	English (US)
Pages (from-to)	410-416
Number of pages	7
Journal	Operations Research Letters
Volume	47
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2019.07.008
State	Published - Sep 2019

Keywords

Base-stock policy
Fractional lead time
Lost sales
Stochastic inventory system

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2019.07.008

Cite this

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title = "Structural properties of the lost sales problem with fractional lead times",

abstract = "We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L, is placed to bring the inventory position to R. Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R, review period T, and lead time L. Then, we develop an algorithm to find the optimal stationary R. Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T.",

keywords = "Base-stock policy, Fractional lead time, Lost sales, Stochastic inventory system",

author = "Y. Xu and Kim, {Sang Phil} and A. Bisi and Suresh Chand and Maqbool Dada",

note = "Funding Information: The authors are grateful to a reviewer and Professor Sridhar Seshadri for providing constructive suggestions. The first author was supported by the Natural Science Foundation of China ( 71772063 , 71872064 , and 71431004 ). Publisher Copyright: {\textcopyright} 2019 Elsevier B.V. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2019",

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doi = "10.1016/j.orl.2019.07.008",

language = "English (US)",

volume = "47",

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journal = "Operations Research Letters",

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AU - Xu, Y.

AU - Kim, Sang Phil

AU - Bisi, A.

AU - Chand, Suresh

AU - Dada, Maqbool

N1 - Funding Information: The authors are grateful to a reviewer and Professor Sridhar Seshadri for providing constructive suggestions. The first author was supported by the Natural Science Foundation of China ( 71772063 , 71872064 , and 71431004 ). Publisher Copyright: © 2019 Elsevier B.V. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/9

Y1 - 2019/9

N2 - We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L, is placed to bring the inventory position to R. Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R, review period T, and lead time L. Then, we develop an algorithm to find the optimal stationary R. Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T.

AB - We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L, is placed to bring the inventory position to R. Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R, review period T, and lead time L. Then, we develop an algorithm to find the optimal stationary R. Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T.

KW - Base-stock policy

KW - Fractional lead time

KW - Lost sales

KW - Stochastic inventory system

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SP - 410

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -

Structural properties of the lost sales problem with fractional lead times

Abstract

Keywords

ASJC Scopus subject areas

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